%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWW265+1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.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 7.15s 5.80s
% Output : CNFRefutation 46.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 2395)
% 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,
~ ! [X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X56,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X56,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bt_O_A_091_124_A0_A_060_At_059_At_A_060_A1_059_At_A_060_Ainverse_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_not__sum__squares__lt__zero,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8)),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_nat__diff__split__asm,axiom,
! [X33,X32,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
& ~ hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X61] :
( X32 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X61)
& ~ hBOOL(hAPP(X52,X61)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_abs__add__one__not__less__self,axiom,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__not__less__self) ).
fof(fact_add__leE,axiom,
! [X5,X27,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X27),X5)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
fof(fact_less__fun__def,axiom,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X10,X22),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).
fof(fact_less_Ohyps,axiom,
! [X51] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X51),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,X51))
=> ? [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X51),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Ohyps) ).
fof(fact_not__square__less__zero,axiom,
! [X11,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).
fof(fact_not__add__less1,axiom,
! [X28,X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(fact_not__add__less2,axiom,
! [X21,X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(fact_not__real__square__gt__zero,axiom,
! [X15] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_add__diff__inverse,axiom,
! [X5,X20] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__le__not__le,axiom,
! [X14,X15,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).
fof(fact_linorder__antisym__conv2,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_xt1_I9_J,axiom,
! [X11,X24,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X11)
=> ~ c_Orderings_Oord__class_Oless(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).
fof(fact_linorder__not__le,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless(X10,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).
fof(fact_leD,axiom,
! [X6,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ~ c_Orderings_Oord__class_Oless(X10,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).
fof(fact_linorder__not__less,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X10,X14,X15)
| X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_order__less__asym,axiom,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).
fof(fact_order__less__asym_H,axiom,
! [X24,X11,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ~ c_Orderings_Oord__class_Oless(X10,X24,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).
fof(fact_order__less__imp__not__less,axiom,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).
fof(fact_order__less__not__sym,axiom,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).
fof(fact_sgn__poly__def,axiom,
! [X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_abs__poly__def,axiom,
! [X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X10),X6) = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__poly__def) ).
fof(fact_tsub__def,axiom,
! [X6,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X6)
=> c_Nat__Transfer_Otsub(X6,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X6,X8) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X6)
=> c_Nat__Transfer_Otsub(X6,X8) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(fact_linorder__antisym__conv1,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_abs__not__less__zero,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(fact_norm__not__less__zero,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_abs__if,axiom,
! [X11,X10] :
( class_Groups_Oabs__if(X10)
=> ( ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,X11) )
& ( ~ c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = X11 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).
fof(fact_sgn__if,axiom,
! [X6,X10] :
( class_Groups_Osgn__if(X10)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Ozero__class_Ozero(X10) )
& ( X6 != c_Groups_Ozero__class_Ozero(X10)
=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Oone__class_Oone(X10) )
& ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_linorder__cases,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ( X6 != X8
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).
fof(fact_linorder__neqE,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).
fof(fact_linorder__antisym__conv3,axiom,
! [X15,X14,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X14,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__neqE__linordered__idom,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).
fof(fact_linorder__le__cases,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_leI,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(fact_not__leE,axiom,
! [X6,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> c_Orderings_Oord__class_Oless(X10,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).
fof(fact_zabs__def,axiom,
! [X21] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X21) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X21) = X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(fact_real__abs__def,axiom,
! [X18] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__abs__def) ).
fof(fact_abs__real__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/sandbox2/benchmark/theBenchmark.p',fact_abs__real__def) ).
fof(fact_not__one__le__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(fact_not__one__less__zero,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(fact_linorder__neqE__nat,axiom,
! [X8,X6] :
( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_order__less__irrefl,axiom,
! [X6,X10] :
( class_Orderings_Opreorder(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(fact_less__nat__zero__code,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
fof(fact_not__less0,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
fof(fact_less__zeroE,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(fact_less__not__refl,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(fact_less__irrefl__nat,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_not__pos__poly__0,axiom,
! [X10] :
( class_Rings_Olinordered__idom(X10)
=> ~ c_Polynomial_Opos__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__pos__poly__0) ).
fof(conj_2,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
fof(fact_lemmaCauchy,axiom,
! [X80,X81,X10,X22] :
( ( class_RealVector_Oreal__normed__vector(X22)
& class_Orderings_Oord(X10) )
=> ( ! [X40] :
( c_Orderings_Oord__class_Oless__eq(X10,X81,X40)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,c_Groups_Ominus__class_Ominus(X22,hAPP(X80,X81),hAPP(X80,X40))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [X40] :
( c_Orderings_Oord__class_Oless__eq(X10,X81,X40)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X22,hAPP(X80,X40)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X22,hAPP(X80,X81)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_mrmq__eq,axiom,
! [X63] :
( 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____)),X63)),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____),X63)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mrmq__eq) ).
fof(fact_decr__lemma,axiom,
! [X26,X6,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X6,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,X6,X26)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X48)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).
fof(fact_incr__lemma,axiom,
! [X6,X26,X48] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X48)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,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,X6,X26)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X48))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).
fof(fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096,axiom,
? [X55,X77] :
( X77 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
& X55 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X57] :
( 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,X57),X55),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____))
& ! [X4] : 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____)),X4) = 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),X4),X55)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,X77,X57)),X4))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Ak_Aa_Aqa_O_Aa_A_126_061_A0_A_G_Ak_A_126_061_A0_A_G_Apsize_Aqa_A_L_Ak_A_L_A1_A_061_Apsize_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A_G_A_IALL_Az_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Az_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_L_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aqa_J_Az_J_096) ).
fof(fact_kas_I4_J,axiom,
! [X4] : 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____)),X4) = 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),X4),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I4_J) ).
fof(fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096,axiom,
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))
=> ? [X37] : 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____)),X37)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096psize_Ap_A_061_Ak_A_L_A1_A_061_061_062_AEX_Aw_O_Acmod_A_Ipoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Aw_J_A_060_A1_096) ).
fof(fact_qr,axiom,
! [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X4) = 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____)),X4)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qr) ).
fof(fact_le__fun__def,axiom,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
<=> ! [X3] : c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X3),hAPP(X1,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(fact_mult_Oprod__diff__prod,axiom,
! [X24,X11,X8,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X6,X11)),c_Groups_Ominus__class_Ominus(X10,X8,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X6,X11)),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ominus__class_Ominus(X10,X8,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oprod__diff__prod) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [X20,X54,X8,X6] : 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,X6,X8),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X54),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X54))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X20))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sum__triangle__ineq) ).
fof(fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096,axiom,
~ ! [X3,X23] : 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____)),X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_I_B_Bx_Ay_O_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ax_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_Ay_J_061_061_062_AFalse_096) ).
fof(fact_synthetic__div__correct_H,axiom,
! [X65,X9,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X9),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Osynthetic__div(X10,X65,X9)),c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X65),X9),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))) = X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_le__add__iff1,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X32,X33)),X50),X34),X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).
fof(fact_less__add__iff1,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X32,X33)),X50),X34),X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49))
<=> c_Orderings_Oord__class_Oless__eq(X10,X34,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X33,X32)),X50),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).
fof(fact_less__add__iff2,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49))
<=> c_Orderings_Oord__class_Oless(X10,X34,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X33,X32)),X50),X49)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).
fof(fact_nat__le__add__iff1,axiom,
! [X19,X36,X62,X60,X59] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X60)
=> ( 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),X60),X62),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19))
<=> 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,X60,X59)),X62),X36),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__less__add__iff1,axiom,
! [X19,X36,X62,X60,X59] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X60)
=> ( 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),X60),X62),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19))
<=> 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,X60,X59)),X62),X36),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).
fof(fact_nat__le__add__iff2,axiom,
! [X19,X36,X62,X59,X60] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59)
=> ( 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),X60),X62),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,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,X59,X60)),X62),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).
fof(fact_nat__less__add__iff2,axiom,
! [X19,X36,X62,X59,X60] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59)
=> ( 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),X60),X62),X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,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,X59,X60)),X62),X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).
fof(fact_th01,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th01) ).
fof(fact_order__1,axiom,
! [X65,X11,X10] :
( class_Rings_Oidom(X10)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))))),c_Polynomial_Oorder(X10,X11,X65)),X65) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__1) ).
fof(fact_abs__diff__triangle__ineq,axiom,
! [X48,X9,X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Oplus__class_Oplus(X10,X9,X48))),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X11,X9)),c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X24,X48)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).
fof(fact_reduce__poly__simple,axiom,
! [X5,X24] :
( X24 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ( X5 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ? [X4] : 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),X24),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),X4),X5)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduce__poly__simple) ).
fof(fact_norm__diff__triangle__ineq,axiom,
! [X48,X9,X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Oplus__class_Oplus(X10,X9,X48))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X11,X9)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X24,X48)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__triangle__ineq) ).
fof(fact_poly__cont,axiom,
! [X65,X26,X41] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X41)
=> ? [X61] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61)
& ! [X37] :
( ( 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,X37,X26)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X37,X26)),X61) )
=> 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,X65),X37),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X65),X26))),X41) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__cont) ).
fof(fact_Deriv_Oinverse__diff__inverse,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),c_Groups_Ominus__class_Ominus(X10,X11,X24))),c_Rings_Oinverse__class_Oinverse(X10,X24))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oinverse__diff__inverse) ).
fof(fact_nat__diff__add__eq1,axiom,
! [X5,X20,X47,X21,X28] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X21)
=> 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),X21),X47),X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X47),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,X21,X28)),X47),X20),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__diff__add__eq2,axiom,
! [X5,X20,X47,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> 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),X21),X47),X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X47),X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,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,X28,X21)),X47),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_poly__replicate__append,axiom,
! [X6,X65,X5,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_Omonom(X10,c_Groups_Oone__class_Oone(X10),X5)),X65)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5)),hAPP(c_Polynomial_Opoly(X10,X65),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__replicate__append) ).
fof(fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096,axiom,
? [X4] : 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))))),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Az_O_Apoly_A_IpCons_A1_A_Imonom_Aa_A_Ik_A_N_A1_J_J_J_Az_A_061_A0_096) ).
fof(fact_inf__period_I3_J,axiom,
! [X86,X87,X49,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( c_Rings_Odvd__class_Odvd(X10,X49,X87)
=> ! [X3,X55] :
( c_Rings_Odvd__class_Odvd(X10,X49,c_Groups_Oplus__class_Oplus(X10,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X10,X49,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X55),X87)),X86)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [X86,X87,X49,X10] :
( ( class_Rings_Ocomm__ring(X10)
& class_Rings_Odvd(X10) )
=> ( c_Rings_Odvd__class_Odvd(X10,X49,X87)
=> ! [X3,X55] :
( c_Rings_Odvd__class_Odvd(X10,X49,c_Groups_Oplus__class_Oplus(X10,X3,X86))
<=> c_Rings_Odvd__class_Odvd(X10,X49,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X55),X87)),X86)) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_rnc) ).
fof(fact_zdiv__mono2__neg__lemma,axiom,
! [X75,X76,X43,X18,X66,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X66),X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X76),X75)
=> ( 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),X43),X76),X75),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X66) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [X75,X76,X43,X18,X66,X24] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X66),X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X76),X75)
=> ( 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),X43),X76),X75))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X43,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,X76) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_mult_Opos__bounded,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X72] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X72)
& ! [X77,X82] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),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(X10,X77)),c_RealVector_Onorm__class_Onorm(X10,X82))),X72)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_inverse__add,axiom,
! [X24,X11,X10] :
( class_Fields_Ofield(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)),c_Rings_Oinverse__class_Oinverse(X10,X11))),c_Rings_Oinverse__class_Oinverse(X10,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__add) ).
fof(fact_unique__quotient__lemma,axiom,
! [X18,X66,X75,X76,X24] :
( 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),X24),X76),X75),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X66),X18))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X75)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X24)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,X66) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [X18,X66,X75,X76,X24] :
( 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),X24),X76),X75),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X66),X18))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X18,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X24,X75)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,X76) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_nat__eq__add__iff1,axiom,
! [X19,X36,X62,X60,X59] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,X60)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X62),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19)
<=> 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,X60,X59)),X62),X36) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__eq__add__iff2,axiom,
! [X19,X36,X62,X59,X60] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X62),X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X59),X62),X19)
<=> X36 = 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,X59,X60)),X62),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_eq__add__iff1,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oring(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49)
<=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X32,X33)),X50),X34) = X49 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [X49,X33,X34,X50,X32,X10] :
( class_Rings_Oring(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X50),X34) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X50),X49)
<=> X34 = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X33,X32)),X50),X49) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).
fof(fact_unimodular__reduce__norm,axiom,
! [X26] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X26) = 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,X26,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,X26,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,X26,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,X26,c_Complex_Oii)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unimodular__reduce__norm) ).
fof(fact_mult__diff__mult,axiom,
! [X24,X11,X8,X6,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),c_Groups_Ominus__class_Ominus(X10,X8,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X6,X11)),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__diff__mult) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> 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,X5)),X6),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,X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_combine__common__factor,axiom,
! [X9,X24,X41,X11,X10] :
( class_Rings_Osemiring(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X41),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X41),X9)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)),X41),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).
fof(fact_division__ring__inverse__diff,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),c_Groups_Ominus__class_Ominus(X10,X24,X11))),c_Rings_Oinverse__class_Oinverse(X10,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__diff) ).
fof(fact_division__ring__inverse__add,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),c_Groups_Oplus__class_Oplus(X10,X11,X24))),c_Rings_Oinverse__class_Oinverse(X10,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_division__ring__inverse__add) ).
fof(fact_convex__bound__le,axiom,
! [X46,X47,X8,X11,X6,X10] :
( class_Rings_Olinordered__semiring__1(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X47)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X46)
=> ( c_Groups_Oplus__class_Oplus(X10,X47,X46) = c_Groups_Oone__class_Oone(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X47),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X46),X8)),X11) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).
fof(fact_convex__bound__lt,axiom,
! [X46,X47,X8,X11,X6,X10] :
( class_Rings_Olinordered__semiring__1__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X11)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X47)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X46)
=> ( c_Groups_Oplus__class_Oplus(X10,X47,X46) = c_Groups_Oone__class_Oone(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X47),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X46),X8)),X11) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_unity__coeff__ex,axiom,
! [X38,X52,X10] :
( ( class_Rings_Odvd(X10)
& class_Rings_Osemiring__0(X10) )
=> ( ? [X3] : hBOOL(hAPP(X52,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X38),X3)))
<=> ? [X3] :
( c_Rings_Odvd__class_Odvd(X10,X38,c_Groups_Oplus__class_Oplus(X10,X3,c_Groups_Ozero__class_Ozero(X10)))
& hBOOL(hAPP(X52,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_left__add__mult__distrib,axiom,
! [X27,X28,X47,X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X47),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X47),X27)) = 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,X21,X28)),X47),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_real__mult__inverse__cancel,axiom,
! [X47,X8,X64,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X64)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X64),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X47))
=> 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,X6)),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X64)),X47)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [X14,X15,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X14)))
<=> ( X15 != c_Groups_Ozero__class_Ozero(X10)
| X14 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
! [X68,X69,X71,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),X68)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [X14,X15,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X14)),c_Groups_Ozero__class_Ozero(X10))
<=> ( X15 = c_Groups_Ozero__class_Ozero(X10)
& X14 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_ath,axiom,
! [X53,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X53)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X53,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),X53)),X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ath) ).
fof(fact_mult__pCons__left,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_OpCons(X10,X11,X65)),X66) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X66),c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__left) ).
fof(fact_offset__poly__pCons,axiom,
! [X85,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,c_Polynomial_OpCons(X10,X11,X65),X85) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X85,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X65,X85)),c_Polynomial_OpCons(X10,X11,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X65,X85))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).
fof(fact_real__mult__inverse__cancel2,axiom,
! [X47,X8,X64,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X64)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X64),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X47))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X8),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X47),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X64))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__cancel2) ).
fof(fact_realpow__minus__mult,axiom,
! [X6,X5,X10] :
( class_Groups_Omonoid__mult(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__minus__mult) ).
fof(fact_crossproduct__noteq,axiom,
! [X49,X34,X33,X32,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( ( X32 != X33
& X34 != X49 )
<=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X49)) != c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_crossproduct__eq,axiom,
! [X16,X15,X14,X63,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X63),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X16)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X63),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X14))
<=> ( X63 = X15
| X14 = X16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).
fof(fact_abs__diff__less__iff,axiom,
! [X58,X32,X15,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X15,X32)),X58)
<=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ominus__class_Ominus(X10,X32,X58),X15)
& c_Orderings_Oord__class_Oless(X10,X15,c_Groups_Oplus__class_Oplus(X10,X32,X58)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_mult__pCons__right,axiom,
! [X66,X11,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),c_Polynomial_OpCons(X10,X11,X66)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pCons__right) ).
fof(fact_power__minus,axiom,
! [X5,X11,X10] :
( class_Rings_Oring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).
fof(fact_q__neg__lemma,axiom,
! [X75,X76,X43] :
( 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),X43),X76),X75),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),X75)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X76,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [X75,X76,X43] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X43),X76),X75))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X75,X43)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X43)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X76) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).
fof(fact_abs__triangle__ineq3,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24))),c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_norm__triangle__ineq3,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> 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(X10,X11),c_RealVector_Onorm__class_Onorm(X10,X24))),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq3) ).
fof(fact_pcompose__pCons,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Opcompose(X10,c_Polynomial_OpCons(X10,X11,X65),X66) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X66),c_Polynomial_Opcompose(X10,X65,X66))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__pCons) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
! [X68,X69,X71,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X69)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X71),X68)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
! [X68,X69,X71,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
fof(fact_complex__mod__triangle__ineq2,axiom,
! [X11,X24] : 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,X24,X11)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X24)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__ineq2) ).
fof(fact_complex__mod__triangle__sub,axiom,
! [X26,X25] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X25),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X25,X26)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X26))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__triangle__sub) ).
fof(fact_mult__poly__add__left,axiom,
! [X18,X66,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,X66)),X18) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X18),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X66),X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_nat__diff__split,axiom,
! [X33,X32,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
=> hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X61] :
( X32 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X61)
=> hBOOL(hAPP(X52,X61)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(fact_abs__mult__less,axiom,
! [X48,X24,X9,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X11),X9)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X24),X48)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oabs__class_Oabs(X10,X11)),c_Groups_Oabs__class_Oabs(X10,X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).
fof(fact_mult__monom,axiom,
! [X5,X24,X20,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_Omonom(X10,X11,X20)),c_Polynomial_Omonom(X10,X24,X5)) = c_Polynomial_Omonom(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__monom) ).
fof(fact_power__Suc__less,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).
fof(fact_odd__less__0,axiom,
! [X16] :
( 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),X16),X16),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__less__0) ).
fof(fact_norm__add__less,axiom,
! [X17,X8,X18,X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X8),X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X6,X8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__add__less) ).
fof(fact_poly__mult,axiom,
! [X6,X66,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Polynomial_Opoly(X10,X65),X6)),hAPP(c_Polynomial_Opoly(X10,X66),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__mult) ).
fof(fact_mult__eq__if,axiom,
! [X5,X20] :
( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(fact_le__diff__iff,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X19)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X39))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).
fof(fact_less__diff__iff,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X19)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X39))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).
fof(fact_mult__mono_H,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).
fof(fact_mult__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).
fof(fact_mult__less__le__imp__less,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__strict__mono_H,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__strict__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X48)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X48)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_norm__mult__less,axiom,
! [X17,X8,X18,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),X18)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X8),X17)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X18),X17)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__less) ).
fof(fact_synthetic__div__correct,axiom,
! [X9,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,c_Polynomial_Osmult(X10,X9,c_Polynomial_Osynthetic__div(X10,X65,X9))) = c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X65),X9),c_Polynomial_Osynthetic__div(X10,X65,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__correct) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
! [X66,X8,X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)),X66) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X66)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
fof(fact_power__mult__distrib,axiom,
! [X5,X24,X11,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X24),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_sum__squares__ge__zero,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__ring(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [X6,X10] :
( class_Rings_Oring__1(X10)
=> c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X6),c_Groups_Oone__class_Oone(X10)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X6,c_Groups_Oone__class_Oone(X10))),c_Groups_Ominus__class_Ominus(X10,X6,c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_poly__pCons,axiom,
! [X6,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_OpCons(X10,X11,X65)),X6) = c_Groups_Oplus__class_Oplus(X10,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),hAPP(c_Polynomial_Opoly(X10,X65),X6))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pCons) ).
fof(fact_power__less__power__Suc,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).
fof(fact_mult__right__le__imp__le,axiom,
! [X24,X9,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [X33,X32,X34,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X34)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).
fof(fact_mult__left__le__imp__le,axiom,
! [X24,X11,X9,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).
fof(fact_mult__right__less__imp__less,axiom,
! [X24,X9,X11,X10] :
( class_Rings_Olinordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [X24,X9,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_power__less__imp__less__base,axiom,
! [X24,X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X24),X5))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [X33,X32,X34,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X34)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33))
<=> c_Orderings_Oord__class_Oless(X10,X32,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__left__less__imp__less,axiom,
! [X24,X11,X9,X10] :
( class_Rings_Olinordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [X24,X11,X9,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__le__cancel__left__neg,axiom,
! [X33,X32,X34,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X34,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33))
<=> c_Orderings_Oord__class_Oless__eq(X10,X33,X32) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__less__cancel__left__neg,axiom,
! [X33,X32,X34,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X34,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33))
<=> c_Orderings_Oord__class_Oless(X10,X33,X32) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_power__increasing__iff,axiom,
! [X14,X15,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X33)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X33),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X33),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_power__le__imp__le__exp,axiom,
! [X5,X20,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X20),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).
fof(fact_power__strict__increasing__iff,axiom,
! [X14,X15,X33,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X33)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X33),X15),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X33),X14))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [X5,X20,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X20),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).
fof(fact_diff__pCons,axiom,
! [X66,X24,X65,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X11,X65),c_Polynomial_OpCons(X10,X24,X66)) = c_Polynomial_OpCons(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X65,X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__pCons) ).
fof(fact_add__pCons,axiom,
! [X66,X24,X65,X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X11,X65),c_Polynomial_OpCons(X10,X24,X66)) = c_Polynomial_OpCons(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pCons) ).
fof(fact_poly__power,axiom,
! [X6,X5,X65,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X10)),X65),X5)),X6) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Polynomial_Opoly(X10,X65),X6)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__power) ).
fof(fact_le__mult__natfloor,axiom,
! [X24,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X11)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X24)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X11)),c_RComplete_Onatfloor(X24)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X11),X24))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_Deriv_Oadd__diff__add,axiom,
! [X48,X24,X9,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24),c_Groups_Ominus__class_Ominus(X10,X9,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Deriv_Oadd__diff__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [X48,X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Oplus__class_Oplus(X10,X9,X48)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_power__decreasing,axiom,
! [X11,X35,X5,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X35),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).
fof(fact_power__strict__decreasing,axiom,
! [X11,X35,X5,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X35)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X35),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).
fof(fact_power__strict__mono,axiom,
! [X5,X24,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X24),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [X33,X32,X34,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X32),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X34),X33))
<=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X34)
& c_Orderings_Oord__class_Oless(X10,X32,X33) )
| ( c_Orderings_Oord__class_Oless(X10,X34,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless(X10,X33,X32) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__right__disj,axiom,
! [X33,X34,X32,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X34))
<=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X34)
& c_Orderings_Oord__class_Oless(X10,X32,X33) )
| ( c_Orderings_Oord__class_Oless(X10,X34,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless(X10,X33,X32) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X72] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X72)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X72)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Opos__bounded) ).
fof(fact_norm__mult__ineq,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X6)),c_RealVector_Onorm__class_Onorm(X10,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult__ineq) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> ? [X72] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X72)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X3)),X72)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Opos__bounded) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [X24,X20,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_mult_Odiff__left,axiom,
! [X24,X44,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X11,X44)),X24) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X44),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__left) ).
fof(fact_mult__left_Odiff,axiom,
! [X45,X8,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ominus__class_Ominus(X10,X6,X8)),X45) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)),X9) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)),X9) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult__left_Oadd,axiom,
! [X45,X8,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X6,X8)),X45) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X45)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Oadd) ).
fof(fact_mult_Oadd__left,axiom,
! [X24,X44,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,X44)),X24) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X44),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [X66,X65,X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X65)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X66)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X65,X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [X5,X20,X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X20)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [X69,X71,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),X69) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X69)),X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
fof(fact_abs__triangle__ineq2,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24)),c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).
fof(fact_abs__triangle__ineq2__sym,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ominus__class_Ominus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24)),c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X24,X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).
fof(fact_abs__triangle__ineq4,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).
fof(fact_abs__triangle__ineq,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24)),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).
fof(fact_add__scale__eq__noteq,axiom,
! [X48,X9,X24,X11,X18,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X18 != c_Groups_Ozero__class_Ozero(X10)
=> ( ( X11 = X24
& X9 != X48 )
=> c_Groups_Oplus__class_Oplus(X10,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X9)) != c_Groups_Oplus__class_Oplus(X10,X24,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X18),X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_mult__le__cancel2,axiom,
! [X19,X39,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X39))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__le__cancel1,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_nat__mult__le__cancel1,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X16))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X16)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
fof(fact_nat__mult__less__cancel1,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_nat__power__less__imp__less,axiom,
! [X5,X20,X21] :
( 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X20),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X21),X5))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_real__mult__less__iff1,axiom,
! [X14,X15,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X16),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X16))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_natceiling__eq,axiom,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__eq) ).
fof(fact_norm__triangle__ineq2,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11),c_RealVector_Onorm__class_Onorm(X10,X24)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq2) ).
fof(fact_norm__diff__ineq,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11),c_RealVector_Onorm__class_Onorm(X10,X24)),c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__diff__ineq) ).
fof(fact_norm__triangle__ineq4,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11),c_RealVector_Onorm__class_Onorm(X10,X24))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq4) ).
fof(fact_norm__triangle__ineq,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oplus__class_Oplus(X10,X6,X8)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),c_RealVector_Onorm__class_Onorm(X10,X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__triangle__ineq) ).
fof(fact_mult__smult__left,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Polynomial_Osmult(X10,X11,X65)),X66) = c_Polynomial_Osmult(X10,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__left) ).
fof(fact_poly__diff,axiom,
! [X6,X66,X65,X10] :
( class_Rings_Ocomm__ring(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X65,X66)),X6) = c_Groups_Ominus__class_Ominus(X10,hAPP(c_Polynomial_Opoly(X10,X65),X6),hAPP(c_Polynomial_Opoly(X10,X66),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__diff) ).
fof(fact_poly__add,axiom,
! [X6,X66,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,X66)),X6) = c_Groups_Oplus__class_Oplus(X10,hAPP(c_Polynomial_Opoly(X10,X65),X6),hAPP(c_Polynomial_Opoly(X10,X66),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__add) ).
fof(fact_le__diff__conv2,axiom,
! [X60,X59,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X59)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X39))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X39),X59) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [X25,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X31,X30)),X25) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_zadd__zmult__distrib,axiom,
! [X25,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X30)),X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_diff__mult__distrib,axiom,
! [X27,X5,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)),X27) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_add__mult__distrib,axiom,
! [X27,X5,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)),X27) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_real__add__mult__distrib,axiom,
! [X25,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X31,X30)),X25) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__mult__distrib) ).
fof(fact_norm__power__ineq,axiom,
! [X5,X6,X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X6)),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power__ineq) ).
fof(fact_add__le__imp__le__right,axiom,
! [X24,X9,X11,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X9))
=> c_Orderings_Oord__class_Oless__eq(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).
fof(fact_add__le__cancel__right,axiom,
! [X33,X34,X32,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X32,X34),c_Groups_Oplus__class_Oplus(X10,X33,X34))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).
fof(fact_add__le__imp__le__left,axiom,
! [X24,X11,X9,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X11),c_Groups_Oplus__class_Oplus(X10,X9,X24))
=> c_Orderings_Oord__class_Oless__eq(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).
fof(fact_add__le__cancel__left,axiom,
! [X33,X32,X34,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X34,X32),c_Groups_Oplus__class_Oplus(X10,X34,X33))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).
fof(fact_add__less__imp__less__right,axiom,
! [X24,X9,X11,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X9))
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).
fof(fact_add__less__cancel__right,axiom,
! [X33,X34,X32,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X32,X34),c_Groups_Oplus__class_Oplus(X10,X33,X34))
<=> c_Orderings_Oord__class_Oless(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).
fof(fact_add__less__imp__less__left,axiom,
! [X24,X11,X9,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X11),c_Groups_Oplus__class_Oplus(X10,X9,X24))
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).
fof(fact_add__less__cancel__left,axiom,
! [X33,X32,X34,X10] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X34,X32),c_Groups_Oplus__class_Oplus(X10,X34,X33))
<=> c_Orderings_Oord__class_Oless(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [X5,X20,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X20)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X5)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X27),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X27)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_power__gt1__lemma,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X37] : 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),X37),v_k____)),v_a____)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bw_O_A1_A_L_Aw_A_094_Ak_A_K_Aa_A_061_A0_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact_zpower__zadd__distrib,axiom,
! [X26,X8,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X8)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_offset__poly__eq__0__lemma,axiom,
! [X11,X65,X9,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X9,X65),c_Polynomial_OpCons(X10,X11,X65)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> X65 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X19))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_self__quotient__aux2,axiom,
! [X66,X18,X11] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> ( X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X66))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X66,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [X66,X18,X11] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11)
=> ( X11 = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X11),X66))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X18,X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X66) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_smult__diff__right,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,X11,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X65,X66)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),c_Polynomial_Osmult(X10,X11,X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__right) ).
fof(fact_smult__add__right,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X11,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,X66)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),c_Polynomial_Osmult(X10,X11,X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__right) ).
fof(fact_power__eq__imp__eq__base,axiom,
! [X24,X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X24),X5)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> X11 = X24 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [X20,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X20),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oone__class_Oone(X10))),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [X11,X20,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X20)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oone__class_Oone(X10))),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_natfloor__eq,axiom,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(X6) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__eq) ).
fof(fact_mult__right__le__one__le,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X6),X6) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_norm__ratiotest__lemma,axiom,
! [X8,X6,X9,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),c_RealVector_Onorm__class_Onorm(X10,X8)))
=> X6 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ratiotest__lemma) ).
fof(fact_mult__right__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).
fof(fact_comm__mult__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Oordered__comm__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).
fof(fact_mult__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Oordered__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).
fof(fact_power__mono,axiom,
! [X5,X24,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X24),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).
fof(fact_mult__strict__right__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).
fof(fact_comm__mult__strict__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Olinordered__comm__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).
fof(fact_mult__strict__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).
fof(fact_mult__right__mono__neg,axiom,
! [X9,X11,X24,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).
fof(fact_mult__left__mono__neg,axiom,
! [X9,X11,X24,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).
fof(fact_mult__strict__right__mono__neg,axiom,
! [X9,X11,X24,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X11)
=> ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).
fof(fact_mult__strict__left__mono__neg,axiom,
! [X9,X11,X24,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X11)
=> ( c_Orderings_Oord__class_Oless(X10,X9,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X9),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).
fof(fact_le__add__diff,axiom,
! [X20,X5,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).
fof(fact_add__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X48)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).
fof(fact_add__less__le__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X9,X48)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).
fof(fact_add__le__less__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X48)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).
fof(fact_add__strict__mono,axiom,
! [X48,X9,X24,X11,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X9,X48)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X48)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).
fof(fact_power__increasing,axiom,
! [X11,X35,X5,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X35)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).
fof(fact_power__strict__increasing,axiom,
! [X11,X35,X5,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X35)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).
fof(fact_abs__eq__mult,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__ring__abs(X10)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
| c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10)) )
& ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
| c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10)) ) )
=> c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oabs__class_Oabs(X10,X11)),c_Groups_Oabs__class_Oabs(X10,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).
fof(fact_diff__monom,axiom,
! [X24,X5,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X11,X5),c_Polynomial_Omonom(X10,X24,X5)) = c_Polynomial_Omonom(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__monom) ).
fof(fact_add__monom,axiom,
! [X24,X5,X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X11,X5),c_Polynomial_Omonom(X10,X24,X5)) = c_Polynomial_Omonom(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__monom) ).
fof(fact_smult__diff__left,axiom,
! [X65,X24,X11,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24),X65) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),c_Polynomial_Osmult(X10,X24,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__diff__left) ).
fof(fact_smult__add__left,axiom,
! [X65,X24,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X65) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),c_Polynomial_Osmult(X10,X24,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__add__left) ).
fof(fact_realpow__num__eq__if,axiom,
! [X20,X5,X10] :
( class_Power_Opower(X10)
=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X20),X5) = c_Groups_Oone__class_Oone(X10) )
& ( X5 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X20),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X20),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X20),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_realpow__num__eq__if) ).
fof(fact_smult__pCons,axiom,
! [X65,X24,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X11,c_Polynomial_OpCons(X10,X24,X65)) = c_Polynomial_OpCons(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Polynomial_Osmult(X10,X11,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__pCons) ).
fof(fact_add__le__mono,axiom,
! [X54,X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X54)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
fof(fact_zadd__zless__mono,axiom,
! [X26,X73,X25,X74] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X74,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X73,X26)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X74,X73),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_diff__less__mono,axiom,
! [X9,X24,X11] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X9,X11)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X11,X9),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X24,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).
fof(fact_diff__less__mono2,axiom,
! [X54,X5,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_add__less__mono,axiom,
! [X54,X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X54)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X54)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
fof(fact_sum__squares__eq__zero__iff,axiom,
! [X14,X15,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X14)) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X10)
& X14 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_rabs__ratiotest__lemma,axiom,
! [X8,X6,X9] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X9,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,X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X9),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X8)))
=> X6 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_mult_Odiff__right,axiom,
! [X43,X24,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ominus__class_Ominus(X10,X24,X43)) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Odiff__right) ).
fof(fact_mult__right_Odiff,axiom,
! [X8,X6,X42,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),c_Groups_Ominus__class_Ominus(X10,X6,X8)) = c_Groups_Ominus__class_Ominus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Odiff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [X26,X8,X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),c_Groups_Oplus__class_Oplus(X10,X8,X26)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_mult__right_Oadd,axiom,
! [X8,X6,X42,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),c_Groups_Oplus__class_Oplus(X10,X6,X8)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_mult_Oadd__right,axiom,
! [X43,X24,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Oplus__class_Oplus(X10,X24,X43)) = c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X43)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Oadd__right) ).
fof(fact_mult__less__cancel1,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [X19,X39,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X39))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_zero__less__mult__pos2,axiom,
! [X11,X24,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X11))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).
fof(fact_zero__less__mult__pos,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).
fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oab__semigroup__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)),X9) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
! [X69,X71,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X71)),X69) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X71),X69)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
fof(fact_power__commutes,axiom,
! [X5,X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)),X11) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
! [X68,X69,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X69)),X68) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
fof(fact_nat__less__real__le,axiom,
! [X36,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X36)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X36)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [X36,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X36)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X36),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_poly__monom,axiom,
! [X6,X5,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Omonom(X10,X11,X5)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__monom) ).
fof(fact_synthetic__div__unique,axiom,
! [X18,X66,X9,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,c_Polynomial_Osmult(X10,X9,X66)) = c_Polynomial_OpCons(X10,X18,X66)
=> ( X18 = hAPP(c_Polynomial_Opoly(X10,X65),X9)
& X66 = c_Polynomial_Osynthetic__div(X10,X65,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique) ).
fof(fact_reals__Archimedean6,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> ? [X40] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X40,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X18)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_RealDef_Oreal(tc_Nat_Onat,X40)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reals__Archimedean6) ).
fof(fact_synthetic__div__pCons,axiom,
! [X9,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osynthetic__div(X10,c_Polynomial_OpCons(X10,X11,X65),X9) = c_Polynomial_OpCons(X10,hAPP(c_Polynomial_Opoly(X10,X65),X9),c_Polynomial_Osynthetic__div(X10,X65,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_power__mult,axiom,
! [X5,X20,X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X20)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [X66,X65,X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X65)),X66) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X65),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_zmult__zless__mono2,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X28)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X27)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_mult__less__mono1,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X27)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X27)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X28)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).
fof(fact_real__mult__less__mono2,axiom,
! [X8,X6,X26] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X26)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,X8)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__less__mono2) ).
fof(fact_power__eq__if,axiom,
! [X65,X20] :
( ( X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X65),X20) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X20 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X65),X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X65),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X65),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(fact_le__diff__conv,axiom,
! [X60,X39,X59] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X39),X60)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X59,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).
fof(fact_less__diff__conv,axiom,
! [X39,X59,X60] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X60,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X39))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X60,X39),X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).
fof(fact_mult__le__mono,axiom,
! [X54,X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X54)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X54)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).
fof(fact_add__diff__assoc2,axiom,
! [X21,X28,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X28)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X27),X21) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).
fof(fact_diff__add__assoc2,axiom,
! [X21,X28,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X28)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21),X27) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X27),X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).
fof(fact_diff__add__assoc,axiom,
! [X21,X28,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X28)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28),X27) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).
fof(fact_diff__diff__right,axiom,
! [X21,X28,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X28)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X27)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X27),X28) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).
fof(fact_add__diff__assoc,axiom,
! [X21,X28,X27] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X28)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X27)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).
fof(fact_mult__smult__right,axiom,
! [X66,X11,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),c_Polynomial_Osmult(X10,X11,X66)) = c_Polynomial_Osmult(X10,X11,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__smult__right) ).
fof(fact_poly__smult,axiom,
! [X6,X65,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Osmult(X10,X11,X65)),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(c_Polynomial_Opoly(X10,X65),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__smult) ).
fof(fact_mult__le__0__iff,axiom,
! [X33,X32,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X33),c_Groups_Ozero__class_Ozero(X10))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32)
& c_Orderings_Oord__class_Oless__eq(X10,X33,c_Groups_Ozero__class_Ozero(X10)) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X33) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(fact_zero__le__mult__iff,axiom,
! [X33,X32,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X33))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32)
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X33) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,X33,c_Groups_Ozero__class_Ozero(X10)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(fact_zero__less__zpower__abs__iff,axiom,
! [X19,X15] :
( 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,X15)),X19))
<=> ( X15 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [X30,X31,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X31,X30)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [X30,X31,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X30)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_diff__mult__distrib2,axiom,
! [X5,X20,X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_add__mult__distrib2,axiom,
! [X5,X20,X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_poly__pcompose,axiom,
! [X6,X66,X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Polynomial_Opcompose(X10,X65,X66)),X6) = hAPP(c_Polynomial_Opoly(X10,X65),hAPP(c_Polynomial_Opoly(X10,X66),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__pcompose) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [X20,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X20,X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))),X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_Bseq__inverse__lemma,axiom,
! [X6,X18,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X18,c_RealVector_Onorm__class_Onorm(X10,X6))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X18)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_Rings_Oinverse__class_Oinverse(X10,X6)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X18)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bseq__inverse__lemma) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [X14,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X15),X15),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X14),X14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& X14 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_cq0,axiom,
! [X37] : 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____),X37))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_cq0) ).
fof(fact_add__nonpos__nonpos,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).
fof(fact_add__neg__nonpos,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_add__neg__neg,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).
fof(fact_add__nonneg__nonneg,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).
fof(fact_add__pos__nonneg,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__pos__pos,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X11,X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).
fof(fact_add__gr__0,axiom,
! [X19,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
fof(fact_zmult__assoc,axiom,
! [X29,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X30)),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).
fof(fact_nat__mult__assoc,axiom,
! [X27,X5,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5)),X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).
fof(fact_real__mult__assoc,axiom,
! [X29,X30,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),X30)),X29) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X30),X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__assoc) ).
fof(fact_zpower__zpower,axiom,
! [X26,X8,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X8)),X26) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X8),X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).
fof(fact_split__mult__neg__le,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
& c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10)) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24) ) )
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).
fof(fact_mult__nonpos__nonneg,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).
fof(fact_mult__nonneg__nonpos,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).
fof(fact_mult__nonneg__nonpos2,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X11),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).
fof(fact_mult__neg__pos,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).
fof(fact_mult__pos__neg,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).
fof(fact_mult__pos__neg2,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X11),c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).
fof(fact_split__mult__pos__le,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__ring(X10)
=> ( ( ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24) )
| ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
& c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10)) ) )
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).
fof(fact_mult__nonneg__nonneg,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__cancel__semiring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).
fof(fact_less__1__mult,axiom,
! [X5,X20,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X20)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X5)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X20),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).
fof(fact_mult__pos__pos,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__semiring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__nonpos__nonpos,axiom,
! [X24,X11,X10] :
( class_Rings_Oordered__ring(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).
fof(fact_mult__neg__neg,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__ring__strict(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).
fof(fact_add__right__mono,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).
fof(fact_add__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X9,X11),c_Groups_Oplus__class_Oplus(X10,X9,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).
fof(fact_add__strict__right__mono,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),c_Groups_Oplus__class_Oplus(X10,X24,X9)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).
fof(fact_add__strict__left__mono,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__cancel__ab__semigroup__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X9,X11),c_Groups_Oplus__class_Oplus(X10,X9,X24)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
=> ~ ! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4),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____),X4)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_A_091_124_A0_A_060_Am_059_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096,axiom,
? [X7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X7)
& ! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4),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____),X4)),X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Am_0620_O_AALL_Az_O_Acmod_Az_A_060_061_Acmod_Aw_A_N_N_062_Acmod_A_Ipoly_As_Az_J_A_060_061_Am_096) ).
fof(fact_m_I2_J,axiom,
! [X4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4),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____),X4)),v_m____) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I2_J) ).
fof(fact_c,axiom,
! [X37] : 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____),X37))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_c) ).
fof(fact_one__less__power,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X11)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).
fof(fact_dvd__power__same,axiom,
! [X5,X8,X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X6,X8)
=> c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X8),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).
fof(fact_decseq__def,axiom,
! [X80,X10] :
( class_Orderings_Oorder(X10)
=> ( c_SEQ_Odecseq(X10,X80)
<=> ! [X7,X40] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X7,X40)
=> c_Orderings_Oord__class_Oless__eq(X10,hAPP(X80,X40),hAPP(X80,X7)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decseq__def) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [X5,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X26),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X26,c_RealDef_Oreal(tc_Nat_Onat,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_add__increasing,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X9)
=> c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Oplus__class_Oplus(X10,X11,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).
fof(fact_add__increasing2,axiom,
! [X11,X24,X9,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X9)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X11)
=> c_Orderings_Oord__class_Oless__eq(X10,X24,c_Groups_Oplus__class_Oplus(X10,X11,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).
fof(fact_add__strict__increasing,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X9)
=> c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Oplus__class_Oplus(X10,X11,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X9)
=> c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Oplus__class_Oplus(X10,X11,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_pos__add__strict,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X9)
=> c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Oplus__class_Oplus(X10,X11,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).
fof(fact_real__minus__mult__self__le,axiom,
! [X6,X47] : 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),X47),X47)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_zadd__left__mono,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X21),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).
fof(fact_diff__le__mono,axiom,
! [X54,X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X54),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X54)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [X54,X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X54,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_add__le__mono1,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
fof(fact_real__add__left__mono,axiom,
! [X26,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X6),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X26,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__left__mono) ).
fof(fact_zadd__strict__right__mono,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,X28)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X21,X27),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).
fof(fact_add__less__mono1,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
fof(fact_abs__power__minus,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),X5)) = c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).
fof(fact_dvd__diff,axiom,
! [X26,X8,X6,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X6,X8)
=> ( c_Rings_Odvd__class_Odvd(X10,X6,X26)
=> c_Rings_Odvd__class_Odvd(X10,X6,c_Groups_Ominus__class_Ominus(X10,X8,X26)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).
fof(fact_dvd__add,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X11,X24)
=> ( c_Rings_Odvd__class_Odvd(X10,X11,X9)
=> c_Rings_Odvd__class_Odvd(X10,X11,c_Groups_Oplus__class_Oplus(X10,X24,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).
fof(fact_of__real_Obounded,axiom,
! [X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> ? [X72] :
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_RealVector_Oof__real(X10,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X72)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Obounded) ).
fof(fact_of__real_Ononneg__bounded,axiom,
! [X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> ? [X72] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X72)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_RealVector_Oof__real(X10,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X72)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ononneg__bounded) ).
fof(fact_of__real_Opos__bounded,axiom,
! [X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> ? [X72] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X72)
& ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,c_RealVector_Oof__real(X10,X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3)),X72)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Opos__bounded) ).
fof(fact_abs__add__abs,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Oplus__class_Oplus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24))) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Oabs__class_Oabs(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> 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,X6,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
fof(fact_eq__diff__iff,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X36)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X19)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X39) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X39)
<=> X36 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__less,axiom,
! [X20,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5),X20) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).
fof(fact_natfloor__subtract,axiom,
! [X6,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),X6)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X11))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__subtract) ).
fof(fact_natceiling__subtract,axiom,
! [X6,X11] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X11),X6)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X11))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_smult__dvd__cancel,axiom,
! [X66,X65,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65),X66)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X65,X66) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__dvd__cancel) ).
fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X32,X32))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).
fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,X32,X32))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oplus__class_Oplus(X10,X32,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X32,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_even__less__0__iff,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,X32,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X9) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Oab__semigroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X9) = c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oplus__class_Oplus(X10,X24,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X9) = c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oplus__class_Oplus(X10,X24,X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [X48,X9,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oplus__class_Oplus(X10,X9,X48)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X9),X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [X48,X9,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oplus__class_Oplus(X10,X9,X48)) = c_Groups_Oplus__class_Oplus(X10,X9,c_Groups_Oplus__class_Oplus(X10,X11,X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_real__0__le__add__iff,axiom,
! [X14,X15] :
( 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,X15,X14))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__0__less__add__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X14))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X14,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_inverse__le__imp__le,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le) ).
fof(fact_inverse__less__imp__less,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24))
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less) ).
fof(fact_inverse__le__imp__le__neg,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24))
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__imp__le__neg) ).
fof(fact_inverse__less__imp__less__neg,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Rings_Oinverse__class_Oinverse(X10,X24))
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__imp__less__neg) ).
fof(fact_le__iff__diff__le__0,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X32,X33)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ominus__class_Ominus(X10,X32,X33),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).
fof(fact_less__iff__diff__less__0,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X32,X33)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ominus__class_Ominus(X10,X32,X33),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).
fof(fact_smult__monom,axiom,
! [X5,X24,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X11,c_Polynomial_Omonom(X10,X24,X5)) = c_Polynomial_Omonom(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__monom) ).
fof(fact_smult__smult,axiom,
! [X65,X24,X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X11,c_Polynomial_Osmult(X10,X24,X65)) = c_Polynomial_Osmult(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),X65) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__smult) ).
fof(fact_abs__minus__add__cancel,axiom,
! [X8,X6] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X8))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X8,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> 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),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
fof(fact_nat__0__less__mult__iff,axiom,
! [X19,X36] :
( 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),X36),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X36)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).
fof(fact_real__mult__order,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( 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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__order) ).
fof(fact_abs__mult__pos,axiom,
! [X8,X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oabs__class_Oabs(X10,X8)),X6) = c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_le__cube,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X20))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).
fof(fact_diff__eq__diff__less__eq,axiom,
! [X49,X34,X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X32,X33) = c_Groups_Ominus__class_Ominus(X10,X34,X49)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X32,X33)
<=> c_Orderings_Oord__class_Oless__eq(X10,X34,X49) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_diff__eq__diff__less,axiom,
! [X49,X34,X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X32,X33) = c_Groups_Ominus__class_Ominus(X10,X34,X49)
=> ( c_Orderings_Oord__class_Oless(X10,X32,X33)
<=> c_Orderings_Oord__class_Oless(X10,X34,X49) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).
fof(fact_mult__le__mono1,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28),X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X21),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
! [X68,X69,X70,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),X68)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X69),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X70),X68)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
fof(fact_diff__cancel,axiom,
! [X5,X20,X27] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X20),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).
fof(fact_diff__cancel2,axiom,
! [X5,X27,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X27),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X27)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).
fof(fact_diff__commute,axiom,
! [X27,X28,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X28),X27) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X27),X28),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).
fof(fact_diff__diff__left,axiom,
! [X27,X28,X21] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,X28),X27) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).
fof(fact_zadd__assoc,axiom,
! [X29,X30,X31] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,X30),X29) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X31,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X30,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_nat__add__assoc,axiom,
! [X27,X5,X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5),X27) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
fof(fact_zadd__left__commute,axiom,
! [X26,X8,X6] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X26)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_nat__add__left__commute,axiom,
! [X26,X8,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X26)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
fof(fact_zless__add1__eq,axiom,
! [X16,X63] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X16)
| X63 = X16 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(fact_add1__zle__eq,axiom,
! [X16,X63] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X63,c_Groups_Oone__class_Oone(tc_Int_Oint)),X16)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_zle__add1__eq__le,axiom,
! [X16,X63] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zle__diff1__eq,axiom,
! [X16,X63] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X63,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X16,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X63,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).
fof(fact_dvd__mult__right,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24),X9)
=> c_Rings_Odvd__class_Odvd(X10,X24,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_real__le__eq__diff,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X15,X14),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_less__bin__lemma,axiom,
! [X38,X39] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X39,X38)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X39,X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_zero__less__diff,axiom,
! [X36,X19] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).
fof(fact_less__add__eq__less,axiom,
! [X5,X20,X54,X27] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X27,X54)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X54) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X27,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
fof(fact_natfloor__add,axiom,
! [X11,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X11))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add) ).
fof(fact_natceiling__add,axiom,
! [X11,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X11))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add) ).
fof(fact_abs__le__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,X32),X33)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X32,X33)
& c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__leI,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,X11),X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__less__iff,axiom,
! [X33,X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X32),X33)
<=> ( c_Orderings_Oord__class_Oless(X10,X32,X33)
& c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).
fof(fact_add__leD1,axiom,
! [X5,X27,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X27),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
fof(fact_add__leD2,axiom,
! [X5,X27,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X27),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
fof(fact_add__lessD1,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28),X27)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
fof(fact_real__of__nat__diff,axiom,
! [X20,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X20)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X20),c_RealDef_Oreal(tc_Nat_Onat,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_add__nonneg__eq__0__iff,axiom,
! [X14,X15,X10] :
( class_Groups_Oordered__comm__monoid__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X15)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X14)
=> ( c_Groups_Oplus__class_Oplus(X10,X15,X14) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X15 = c_Groups_Ozero__class_Ozero(X10)
& X14 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_le__imp__inverse__le,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X24),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le) ).
fof(fact_less__imp__inverse__less,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X24),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less) ).
fof(fact_le__imp__inverse__le__neg,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X24),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__inverse__le__neg) ).
fof(fact_less__imp__inverse__less__neg,axiom,
! [X24,X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ( c_Orderings_Oord__class_Oless(X10,X24,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X24),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__inverse__less__neg) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [X19,X15] :
( 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),X15),X19))
<=> ( X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [X19,X15] :
( 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),X15),X19))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_minus__apply,axiom,
! [X15,X83,X84,X22,X10] :
( class_Groups_Ominus(X10)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22,X10),X84,X83),X15) = c_Groups_Ominus__class_Ominus(X10,hAPP(X84,X15),hAPP(X83,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).
fof(fact_one__le__inverse,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse) ).
fof(fact_one__le__inverse__iff,axiom,
! [X15,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X15))
<=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X15)
& c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__inverse__iff) ).
fof(fact_one__less__inverse,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Oone__class_Oone(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse) ).
fof(fact_one__less__inverse__iff,axiom,
! [X15,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Rings_Oinverse__class_Oinverse(X10,X15))
<=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X15)
& c_Orderings_Oord__class_Oless(X10,X15,c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__inverse__iff) ).
fof(fact_abs__le__interval__iff,axiom,
! [X58,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X15),X58)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X58),X15)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X58) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_less__eq__poly__def,axiom,
! [X14,X15,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X10),X15,X14)
<=> ( X15 = X14
| c_Polynomial_Opos__poly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X14,X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_less__poly__def,axiom,
! [X14,X15,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X15,X14)
<=> c_Polynomial_Opos__poly(X10,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X14,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__poly__def) ).
fof(fact_zero__le__power__abs,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oabs__class_Oabs(X10,X11)),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).
fof(fact_pos__poly__pCons,axiom,
! [X51,X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,c_Polynomial_OpCons(X10,X32,X51))
<=> ( c_Polynomial_Opos__poly(X10,X51)
| ( X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
& c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_dvd__smult,axiom,
! [X11,X66,X65,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X65,X66)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X10),X65,c_Polynomial_Osmult(X10,X11,X66)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__smult) ).
fof(fact_power__inject__exp,axiom,
! [X19,X36,X32,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X32)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X32),X36) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X32),X19)
<=> X36 = X19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).
fof(fact_natceiling__le__eq,axiom,
! [X32,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X15),X32)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_RealDef_Oreal(tc_Nat_Onat,X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_less__natfloor,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X5))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X6),X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__natfloor) ).
fof(fact_le__natfloor__eq,axiom,
! [X32,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X32,c_RComplete_Onatfloor(X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X32),X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_one__le__power,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).
fof(fact_zero__le__power,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).
fof(fact_zero__less__power,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).
fof(fact_inverse__le__1__iff,axiom,
! [X15,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X15),c_Groups_Oone__class_Oone(X10))
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Ozero__class_Ozero(X10))
| c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__le__1__iff) ).
fof(fact_inverse__less__1__iff,axiom,
! [X15,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X15),c_Groups_Oone__class_Oone(X10))
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,c_Groups_Ozero__class_Ozero(X10))
| c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__less__1__iff) ).
fof(fact_natfloor__add__one,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_natceiling__add__one,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__add__one) ).
fof(fact_nonzero__inverse__mult__distrib,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X24)),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__mult__distrib) ).
fof(fact_odd__nonzero,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X26),X26) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X6,X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(fact_power_Opower_Opower__0,axiom,
! [X32,X78,X79,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X79,X78),X32),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X79,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_le__imp__0__less,axiom,
! [X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26)
=> 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),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_sgn__times,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Osgn__class_Osgn(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Osgn__class_Osgn(X10,X11)),c_Groups_Osgn__class_Osgn(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).
fof(fact_sgn__mult,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> c_Groups_Osgn__class_Osgn(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Osgn__class_Osgn(X10,X6)),c_Groups_Osgn__class_Osgn(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__mult) ).
fof(fact_abs__mult,axiom,
! [X24,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oabs__class_Oabs(X10,X11)),c_Groups_Oabs__class_Oabs(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).
fof(fact_inverse__mult__distrib,axiom,
! [X24,X11,X10] :
( class_Fields_Ofield__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),c_Rings_Oinverse__class_Oinverse(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__mult__distrib) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [X65,X11,X22] :
( class_Groups_Oab__group__add(X22)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X22),c_Polynomial_OpCons(X22,X11,X65)) = c_Polynomial_OpCons(X22,c_Groups_Ouminus__class_Ouminus(X22,X11),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X22),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_minus__pCons,axiom,
! [X65,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_OpCons(X10,X11,X65)) = c_Polynomial_OpCons(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__pCons) ).
fof(fact_abs__minus__commute,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)) = c_Groups_Oabs__class_Oabs(X10,c_Groups_Ominus__class_Ominus(X10,X24,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).
fof(fact_norm__minus__commute,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)) = c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ominus__class_Ominus(X10,X24,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__commute) ).
fof(fact_norm__mult,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X6)),c_RealVector_Onorm__class_Onorm(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__mult) ).
fof(fact_zless__imp__add1__zle,axiom,
! [X26,X25] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X25,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_le__add__diff__inverse2,axiom,
! [X20,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X20)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5),X5) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).
fof(fact_diff__diff__cancel,axiom,
! [X5,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X5)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X21)) = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_le__add__diff__inverse,axiom,
! [X20,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X20)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).
fof(fact_of__real__mult,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X8)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_RealVector_Oof__real(X10,X6)),c_RealVector_Oof__real(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__mult) ).
fof(fact_le__funE,axiom,
! [X15,X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X15),hAPP(X1,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).
fof(fact_le__funD,axiom,
! [X15,X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
=> c_Orderings_Oord__class_Oless__eq(X22,hAPP(X2,X15),hAPP(X1,X15)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).
fof(fact_less__imp__diff__less,axiom,
! [X5,X27,X28] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X28,X27)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X28,X5),X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [X26,X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_trans__le__add1,axiom,
! [X20,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [X8,X26,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X26)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_trans__le__add2,axiom,
! [X20,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [X26,X8,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_trans__less__add1,axiom,
! [X20,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [X8,X26,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X26)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X8,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_trans__less__add2,axiom,
! [X20,X28,X21] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,X28)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X21,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X28)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
fof(fact_of__real_Odiff,axiom,
! [X8,X6,X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> c_RealVector_Oof__real(X10,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X8)) = c_Groups_Ominus__class_Ominus(X10,c_RealVector_Oof__real(X10,X6),c_RealVector_Oof__real(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Odiff) ).
fof(fact_of__real_Oadd,axiom,
! [X8,X6,X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> c_RealVector_Oof__real(X10,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X8)) = c_Groups_Oplus__class_Oplus(X10,c_RealVector_Oof__real(X10,X6),c_RealVector_Oof__real(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Oadd) ).
fof(fact_zero__le__zpower__abs,axiom,
! [X5,X6] : 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,X6)),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [X19,X36,X39] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X39)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19)
<=> X36 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X6),X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(fact_dvd__trans,axiom,
! [X9,X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X11,X24)
=> ( c_Rings_Odvd__class_Odvd(X10,X24,X9)
=> c_Rings_Odvd__class_Odvd(X10,X11,X9) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).
fof(fact_order__trans,axiom,
! [X26,X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X26)
=> c_Orderings_Oord__class_Oless__eq(X10,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).
fof(fact_xt1_I6_J,axiom,
! [X26,X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X26,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_order__less__le__trans,axiom,
! [X26,X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X26)
=> c_Orderings_Oord__class_Oless(X10,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).
fof(fact_order__le__less__trans,axiom,
! [X26,X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X26)
=> c_Orderings_Oord__class_Oless(X10,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).
fof(fact_order__less__trans,axiom,
! [X26,X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X26)
=> c_Orderings_Oord__class_Oless(X10,X6,X26) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).
fof(fact_xt1_I7_J,axiom,
! [X26,X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X26,X8)
=> c_Orderings_Oord__class_Oless(X10,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).
fof(fact_xt1_I8_J,axiom,
! [X26,X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless(X10,X26,X8)
=> c_Orderings_Oord__class_Oless(X10,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).
fof(fact_xt1_I10_J,axiom,
! [X26,X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless(X10,X26,X8)
=> c_Orderings_Oord__class_Oless(X10,X26,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).
fof(fact_Limits_Ominus__diff__minus,axiom,
! [X24,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Groups_Ouminus__class_Ouminus(X10,X24)) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Limits_Ominus__diff__minus) ).
fof(fact_minus__add__distrib,axiom,
! [X24,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Groups_Ouminus__class_Ouminus(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_minus__add,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24)) = c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X24),c_Groups_Ouminus__class_Ouminus(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X6,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_nonzero__power__inverse,axiom,
! [X5,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__inverse) ).
fof(fact_of__real__diff,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X8)) = c_Groups_Ominus__class_Ominus(X10,c_RealVector_Oof__real(X10,X6),c_RealVector_Oof__real(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__diff) ).
fof(fact_of__real__add,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X8)) = c_Groups_Oplus__class_Oplus(X10,c_RealVector_Oof__real(X10,X6),c_RealVector_Oof__real(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__add) ).
fof(fact_compl__le__compl__iff,axiom,
! [X14,X15,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),c_Groups_Ouminus__class_Ouminus(X10,X14))
<=> c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [X32,X33,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X33),c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_neg__less__iff__less,axiom,
! [X32,X33,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X33),c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless(X10,X32,X33) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_mult__left_Ominus,axiom,
! [X8,X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X6)),X8) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),X24) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_power__abs,axiom,
! [X5,X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Oabs__class_Oabs(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oabs__class_Oabs(X10,X11)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).
fof(fact_power__inverse,axiom,
! [X5,X11,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inverse) ).
fof(fact_minus__mult__left,axiom,
! [X24,X11,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).
fof(fact_smult__minus__right,axiom,
! [X65,X11,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,X11,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X65)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__right) ).
fof(fact_le__imp__diff__is__add,axiom,
! [X39,X59,X60] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X60,X59)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X59,X60) = X39
<=> X59 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X60) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).
fof(fact_norm__power,axiom,
! [X5,X6,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> c_RealVector_Onorm__class_Onorm(X10,hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X6)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__power) ).
fof(fact_add__minus__cancel,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X24)) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_zle__trans,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X28,X27)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X21,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).
fof(fact_le__trans,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X28,X27)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X21,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
fof(fact_real__le__trans,axiom,
! [X27,X28,X21] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X28)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X28,X27)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X21,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__trans) ).
fof(fact_pos__poly__mult,axiom,
! [X66,X65,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,X65)
=> ( c_Polynomial_Opos__poly(X10,X66)
=> c_Polynomial_Opos__poly(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),X66)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__mult) ).
fof(fact_real__of__nat__mult,axiom,
! [X5,X20] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X20)),c_RealDef_Oreal(tc_Nat_Onat,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_of__real__power,axiom,
! [X5,X6,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_RealVector_Oof__real(X10,X6)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__power) ).
fof(fact_poly__minus,axiom,
! [X6,X65,X10] :
( class_Rings_Ocomm__ring(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X65)),X6) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(c_Polynomial_Opoly(X10,X65),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__minus) ).
fof(fact_abs__le__D2,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,X11),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).
fof(fact_minus__le__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X33)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X33),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).
fof(fact_minus__less__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X33)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X33),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).
fof(fact_le__minus__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ouminus__class_Ouminus(X10,X33))
<=> c_Orderings_Oord__class_Oless__eq(X10,X33,c_Groups_Ouminus__class_Ouminus(X10,X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).
fof(fact_less__minus__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ouminus__class_Ouminus(X10,X33))
<=> c_Orderings_Oord__class_Oless(X10,X33,c_Groups_Ouminus__class_Ouminus(X10,X32)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).
fof(fact_real__of__nat__add,axiom,
! [X5,X20] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X20),c_RealDef_Oreal(tc_Nat_Onat,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_zminus__zadd__distrib,axiom,
! [X25,X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X25)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_minus__monom,axiom,
! [X5,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Omonom(X10,X11,X5)) = c_Polynomial_Omonom(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__monom) ).
fof(fact_smult__minus__left,axiom,
! [X65,X11,X10] :
( class_Rings_Ocomm__ring(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X65) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Polynomial_Osmult(X10,X11,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__minus__left) ).
fof(fact_mult__left__idem,axiom,
! [X24,X11,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).
fof(fact_abs__add__one__gt__zero,axiom,
! [X6] : 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,X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__one__gt__zero) ).
fof(fact_inverse__positive__imp__positive,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X11))
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__imp__positive) ).
fof(fact_inverse__negative__imp__negative,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Groups_Ozero__class_Ozero(X10))
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__imp__negative) ).
fof(fact_real__of__nat__le__iff,axiom,
! [X36,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_RealDef_Oreal(tc_Nat_Onat,X36))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_real__of__nat__less__iff,axiom,
! [X36,X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_RealDef_Oreal(tc_Nat_Onat,X36))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X36) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_neg__less__0__iff__less,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_inverse__nonnegative__iff__nonnegative,axiom,
! [X32,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X32))
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonnegative__iff__nonnegative) ).
fof(fact_inverse__positive__iff__positive,axiom,
! [X32,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X32))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__positive__iff__positive) ).
fof(fact_sgn__greater,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Osgn__class_Osgn(X10,X32))
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).
fof(fact_inverse__nonpositive__iff__nonpositive,axiom,
! [X32,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Rings_Oinverse__class_Oinverse(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonpositive__iff__nonpositive) ).
fof(fact_inverse__negative__iff__negative,axiom,
! [X32,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__negative__iff__negative) ).
fof(fact_sgn__less,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Osgn__class_Osgn(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).
fof(fact_neg__0__le__iff__le,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_neg__0__less__iff__less,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_mult__right_Ominus,axiom,
! [X6,X42,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),c_Groups_Ouminus__class_Ouminus(X10,X6)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X42),X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__right,axiom,
! [X24,X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ouminus__class_Ouminus(X10,X24)) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_minus__mult__right,axiom,
! [X24,X11,X10] :
( class_Rings_Oring(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ouminus__class_Ouminus(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).
fof(fact_compl__mono,axiom,
! [X8,X6,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X8),c_Groups_Ouminus__class_Ouminus(X10,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).
fof(fact_le__imp__neg__le,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X24),c_Groups_Ouminus__class_Ouminus(X10,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_zero__less__two,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oplus__class_Oplus(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(fact_real__natfloor__gt__diff__one,axiom,
! [X6] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__gt__diff__one) ).
fof(fact_minus__add__cancel,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Groups_Oplus__class_Oplus(X10,X11,X24)) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_minus__le__self__iff,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X32)
<=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__less__nonneg,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ouminus__class_Ouminus(X10,X32),X32)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_le__minus__self__iff,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless__eq(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_less__minus__self__iff,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ouminus__class_Ouminus(X10,X32))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_zmult__zminus,axiom,
! [X25,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)),X25) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).
fof(fact_complex__of__real__power,axiom,
! [X5,X6] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X6)),X5) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__power) ).
fof(fact_power__real__of__nat,axiom,
! [X5,X20] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X20)),X5) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__power,axiom,
! [X5,X20] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X20)),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_nat__less__cases,axiom,
! [X52,X19,X36] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19)
=> hBOOL(hAPP(hAPP(X52,X19),X36)) )
=> ( ( X36 = X19
=> hBOOL(hAPP(hAPP(X52,X19),X36)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X36)
=> hBOOL(hAPP(hAPP(X52,X19),X36)) )
=> hBOOL(hAPP(hAPP(X52,X19),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
fof(fact_negative__imp__inverse__negative,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Orderings_Oord__class_Oless(X10,c_Rings_Oinverse__class_Oinverse(X10,X11),c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__imp__inverse__negative) ).
fof(fact_positive__imp__inverse__positive,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_positive__imp__inverse__positive) ).
fof(fact_synthetic__div__unique__lemma,axiom,
! [X11,X65,X9,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Polynomial_Osmult(X10,X9,X65) = c_Polynomial_OpCons(X10,X11,X65)
=> X65 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__unique__lemma) ).
fof(fact_abs__mult__self,axiom,
! [X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oabs__class_Oabs(X10,X11)),c_Groups_Oabs__class_Oabs(X10,X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).
fof(fact_minus__mult__minus,axiom,
! [X24,X11,X10] :
( class_Rings_Oring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),c_Groups_Ouminus__class_Ouminus(X10,X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [X24,X11,X10] :
( class_Rings_Oring(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,X11)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ouminus__class_Ouminus(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__dvd__iff,axiom,
! [X14,X15,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,c_Groups_Ouminus__class_Ouminus(X10,X15),X14)
<=> c_Rings_Odvd__class_Odvd(X10,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_abs__dvd__iff,axiom,
! [X39,X36,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,c_Groups_Oabs__class_Oabs(X10,X36),X39)
<=> c_Rings_Odvd__class_Odvd(X10,X36,X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_abs__le__D1,axiom,
! [X24,X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,X11),X24)
=> c_Orderings_Oord__class_Oless__eq(X10,X11,X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).
fof(fact_dvd__minus__iff,axiom,
! [X14,X15,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X15,c_Groups_Ouminus__class_Ouminus(X10,X14))
<=> c_Rings_Odvd__class_Odvd(X10,X15,X14) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__abs__iff,axiom,
! [X39,X36,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Rings_Odvd__class_Odvd(X10,X36,c_Groups_Oabs__class_Oabs(X10,X39))
<=> c_Rings_Odvd__class_Odvd(X10,X36,X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_square__eq__iff,axiom,
! [X33,X32,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X33),X33)
<=> ( X32 = X33
| X32 = c_Groups_Ouminus__class_Ouminus(X10,X33) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).
fof(fact_pos__poly__add,axiom,
! [X66,X65,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Polynomial_Opos__poly(X10,X65)
=> ( c_Polynomial_Opos__poly(X10,X66)
=> c_Polynomial_Opos__poly(X10,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,X66)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__add) ).
fof(fact_diff__eq__diff__eq,axiom,
! [X49,X34,X33,X32,X10] :
( class_Groups_Oab__group__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X32,X33) = c_Groups_Ominus__class_Ominus(X10,X34,X49)
=> ( X32 = X33
<=> X34 = X49 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).
fof(fact_natfloor__power,axiom,
! [X5,X6] :
( X6 = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),X5)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X6)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__power) ).
fof(fact_minus__diff__eq,axiom,
! [X24,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24)) = c_Groups_Ominus__class_Ominus(X10,X24,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_xt1_I5_J,axiom,
! [X6,X8,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> X6 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__antisym,axiom,
! [X8,X6,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> X6 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).
fof(fact_order__antisym__conv,axiom,
! [X15,X14,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X14,X15)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_order__eq__iff,axiom,
! [X14,X15,X10] :
( class_Orderings_Oorder(X10)
=> ( X15 = X14
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X19))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_less__add__one,axiom,
! [X11,X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Oone__class_Oone(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).
fof(fact_pCons__eq__iff,axiom,
! [X67,X33,X51,X32,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_OpCons(X10,X32,X51) = c_Polynomial_OpCons(X10,X33,X67)
<=> ( X32 = X33
& X51 = X67 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_monom__eq__iff,axiom,
! [X33,X19,X32,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_Omonom(X10,X32,X19) = c_Polynomial_Omonom(X10,X33,X19)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__iff) ).
fof(fact_add__right__cancel,axiom,
! [X34,X32,X33,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X33,X32) = c_Groups_Oplus__class_Oplus(X10,X34,X32)
<=> X33 = X34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__right__imp__eq,axiom,
! [X9,X11,X24,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X24,X11) = c_Groups_Oplus__class_Oplus(X10,X9,X11)
=> X24 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__imp__eq,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Ocancel__ab__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X11,X24) = c_Groups_Oplus__class_Oplus(X10,X11,X9)
=> X24 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).
fof(fact_add__left__cancel,axiom,
! [X34,X33,X32,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X32,X33) = c_Groups_Oplus__class_Oplus(X10,X32,X34)
<=> X33 = X34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).
fof(fact_add__left__imp__eq,axiom,
! [X9,X24,X11,X10] :
( class_Groups_Ocancel__semigroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X11,X24) = c_Groups_Oplus__class_Oplus(X10,X11,X9)
=> X24 = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).
fof(fact_abs__zmult__eq__1,axiom,
! [X5,X20] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X5)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X20) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_natceiling__le,axiom,
! [X11,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,X11))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X6),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le) ).
fof(fact_le__natfloor,axiom,
! [X11,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6),X11)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_RComplete_Onatfloor(X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor) ).
fof(fact_order__root,axiom,
! [X32,X51,X10] :
( class_Rings_Oidom(X10)
=> ( hAPP(c_Polynomial_Opoly(X10,X51),X32) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| c_Polynomial_Oorder(X10,X32,X51) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__root) ).
fof(fact_diffs0__imp__equal,axiom,
! [X5,X20] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> X20 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).
fof(fact_real__natfloor__le,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X6)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X6)),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_zero__le__square,axiom,
! [X11,X10] :
( class_Rings_Olinordered__ring(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).
fof(fact_zle__antisym,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X26)
=> X26 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).
fof(fact_le__antisym,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X20)
=> X20 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
fof(fact_real__le__antisym,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26)
=> X26 = X25 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_add__diff__cancel,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Oplus__class_Oplus(X10,X11,X24),X24) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).
fof(fact_diff__add__cancel,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ominus__class_Ominus(X10,X11,X24),X24) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [X19,X36] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X19) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& X19 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_nat__add__right__cancel,axiom,
! [X19,X39,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X39) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X19,X39)
<=> X36 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [X19,X36,X39] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X36) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X19)
<=> X36 = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [X57] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X57) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
=> ~ ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X57),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bq_O_A_091_124_Apsize_Aq_A_061_Apsize_Ap_059_AALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_A_124_093_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
fof(fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096,axiom,
? [X57] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X57) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& ! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X57),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096EX_Aq_O_Apsize_Aq_A_061_Apsize_Ap_A_G_A_IALL_Ax_O_Apoly_Aq_Ax_A_061_Apoly_Ap_A_Ic_A_L_Ax_J_J_096) ).
fof(fact_q_I2_J,axiom,
! [X3] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I2_J) ).
fof(fact_le__iff__add,axiom,
! [X19,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19)
<=> ? [X55] : X19 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X55) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
fof(fact_le__Suc__ex__iff,axiom,
! [X38,X39] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X39,X38)
<=> ? [X40] : X38 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X39,X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__ex__iff) ).
fof(fact_diff__add__0,axiom,
! [X20,X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__0) ).
fof(fact_diff__add__inverse,axiom,
! [X20,X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20),X5) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(fact_diff__add__inverse2,axiom,
! [X5,X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5),X5) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(fact_diff__le__self,axiom,
! [X5,X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(fact_le__add1,axiom,
! [X20,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(fact_le__add2,axiom,
! [X20,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(fact_le__natfloor__eq__one,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X15))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_natceiling__le__eq__one,axiom,
! [X15] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X15),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_zero__less__abs__iff,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oabs__class_Oabs(X10,X32))
<=> X32 != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).
fof(fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096,axiom,
! [X12] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12)
=> ? [X13] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X13)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X13,X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096_B_Bd2_O_A0_A_060_Ad2_A_061_061_062_AEX_Ae_0620_O_Ae_A_060_A1_A_G_Ae_A_060_Ad2_096) ).
fof(fact_mult__cancel2,axiom,
! [X19,X39,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X39) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X19),X39)
<=> ( X36 = X19
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel2) ).
fof(fact_real__mult__right__cancel,axiom,
! [X33,X32,X34] :
( X34 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X32),X34) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X33),X34)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_mult__cancel1,axiom,
! [X19,X36,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19)
<=> ( X36 = X19
| X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [X19,X36,X39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X39),X19)
<=> ( X39 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X36 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_real__mult__left__cancel,axiom,
! [X33,X32,X34] :
( X34 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X34),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X34),X33)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__left__cancel) ).
fof(fact_tsub__eq,axiom,
! [X6,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X6)
=> c_Nat__Transfer_Otsub(X6,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X6,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).
fof(fact_xt1_I11_J,axiom,
! [X11,X24,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X11)
=> ( X11 != X24
=> c_Orderings_Oord__class_Oless(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).
fof(fact_order__le__neq__trans,axiom,
! [X24,X11,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> ( X11 != X24
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).
fof(fact_order__le__imp__less__or__eq,axiom,
! [X8,X6,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
| X6 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).
fof(fact_order__neq__le__trans,axiom,
! [X24,X11,X10] :
( class_Orderings_Oorder(X10)
=> ( X11 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,X24)
=> c_Orderings_Oord__class_Oless(X10,X11,X24) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).
fof(fact_order__le__less,axiom,
! [X14,X15,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
| X15 = X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).
fof(fact_order__less__le,axiom,
! [X14,X15,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& X15 != X14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).
fof(fact_xt1_I12_J,axiom,
! [X24,X11,X10] :
( class_Orderings_Oorder(X10)
=> ( X11 != X24
=> ( c_Orderings_Oord__class_Oless__eq(X10,X24,X11)
=> c_Orderings_Oord__class_Oless(X10,X24,X11) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [X6,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))),X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_natfloor__mono,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X6),c_RComplete_Onatfloor(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__mono) ).
fof(fact_natceiling__mono,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X6),c_RComplete_Onatceiling(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__mono) ).
fof(fact_abs__le__zero__iff,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oabs__class_Oabs(X10,X32),c_Groups_Ozero__class_Ozero(X10))
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).
fof(fact_order__less__imp__le,axiom,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).
fof(fact_abs__minus__le__zero,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oabs__class_Oabs(X10,X11)),c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_int__one__le__iff__zero__less,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X16)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).
fof(fact_zero__less__norm__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X15))
<=> X15 != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [X6] : 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,X6)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_le__square,axiom,
! [X20] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(fact_diff__minus__eq__add,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X11,c_Groups_Ouminus__class_Ouminus(X10,X24)) = c_Groups_Oplus__class_Oplus(X10,X11,X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [X8,X6,X10] :
( class_Rings_Ocomm__ring__1(X10)
=> c_Groups_Ominus__class_Ominus(X10,X6,X8) = c_Groups_Oplus__class_Oplus(X10,X6,c_Groups_Ouminus__class_Ouminus(X10,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_ab__diff__minus,axiom,
! [X24,X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X11,X24) = c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ouminus__class_Ouminus(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X11,X24) = c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ouminus__class_Ouminus(X10,X24)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).
fof(fact_norm__le__zero__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X15),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X15 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_diff__is__0__eq,axiom,
! [X19,X36] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X36,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).
fof(fact_zless__le,axiom,
! [X63,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X63)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X63)
& X16 != X63 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(fact_nat__less__le,axiom,
! [X19,X36] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19)
& X36 != X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [X19,X36] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X36,X19)
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19)
| X36 = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_le__neq__implies__less,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> ( X20 != X5
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
fof(fact_real__less__def,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
& X15 != X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__less__def) ).
fof(fact_less__eq__real__def,axiom,
! [X14,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X15,X14)
| X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_diff__is__0__eq_H,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq_H) ).
fof(fact_complex__i__mult__minus,axiom,
! [X6] : 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),X6)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__mult__minus) ).
fof(fact_uminus__apply,axiom,
! [X15,X84,X22,X10] :
( class_Groups_Ouminus(X10)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X22,X10),X84),X15) = c_Groups_Ouminus__class_Ouminus(X10,hAPP(X84,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).
fof(fact_mult__sgn__abs,axiom,
! [X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Osgn__class_Osgn(X10,X6)),c_Groups_Oabs__class_Oabs(X10,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_monom__0,axiom,
! [X11,X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_Omonom(X10,X11,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X10,X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__0) ).
fof(fact_sgn__1__neg,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X32) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10))
<=> c_Orderings_Oord__class_Oless(X10,X32,c_Groups_Ozero__class_Ozero(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__neg,axiom,
! [X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_less__imp__le__nat,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
fof(fact_less__or__eq__imp__le,axiom,
! [X5,X20] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
| X20 = X5 )
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
fof(fact_abs__of__nonpos,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__of__neg,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).
fof(fact_mult__poly__0__left,axiom,
! [X66,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X66) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_diff__int__def__symmetric,axiom,
! [X25,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X25)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [X25,X26] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X26,X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).
fof(fact_complex__diff__def,axiom,
! [X8,X6] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X6,X8) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X6,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__diff__def) ).
fof(fact_minus__real__def,axiom,
! [X8,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X8) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__diff__def,axiom,
! [X17,X18] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X18,X17) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X18,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__diff__def) ).
fof(fact_zabs__less__one__iff,axiom,
! [X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X16),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> X16 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X19),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_ext,axiom,
! [X1,X2] :
( ! [X3] : hAPP(X2,X3) = hAPP(X1,X3)
=> X2 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
fof(fact_smult__eq__0__iff,axiom,
! [X51,X32,X10] :
( class_Rings_Oidom(X10)
=> ( c_Polynomial_Osmult(X10,X32,X51) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> ( X32 = c_Groups_Ozero__class_Ozero(X10)
| X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__eq__0__iff) ).
fof(fact_real__add__minus__iff,axiom,
! [X32,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X32)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_power__eq__0__iff,axiom,
! [X19,X32,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Omult__zero(X10)
& class_Rings_Ono__zero__divisors(X10)
& class_Rings_Ozero__neq__one(X10) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X32),X19) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X32 = c_Groups_Ozero__class_Ozero(X10)
& X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [X15,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X15),X15) = c_Groups_Oone__class_Oone(X10)
<=> ( X15 = c_Groups_Oone__class_Oone(X10)
| X15 = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_sgn__1__pos,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X32) = c_Groups_Oone__class_Oone(X10)
<=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_sgn__pos,axiom,
! [X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Groups_Osgn__class_Osgn(X10,X11) = c_Groups_Oone__class_Oone(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).
fof(fact_field__inverse,axiom,
! [X11,X10] :
( class_Fields_Ofield(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),X11) = c_Groups_Oone__class_Oone(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse) ).
fof(fact_left__inverse,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Rings_Oinverse__class_Oinverse(X10,X11)),X11) = c_Groups_Oone__class_Oone(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__inverse) ).
fof(fact_pCons__eq__0__iff,axiom,
! [X51,X32,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_OpCons(X10,X32,X51) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> ( X32 = c_Groups_Ozero__class_Ozero(X10)
& X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_offset__poly__eq__0__iff,axiom,
! [X88,X51,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,X51,X88) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__eq__0__iff) ).
fof(fact_linorder__neq__iff,axiom,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( X15 != X14
<=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
| c_Orderings_Oord__class_Oless(X10,X14,X15) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_linorder__less__linear,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
| X6 = X8
| c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).
fof(fact_constant__def,axiom,
! [X2,X22,X10] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X10,X22,X2)
<=> ! [X3,X23] : hAPP(X2,X3) = hAPP(X2,X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_constant__def) ).
fof(fact_abs__of__nonneg,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Groups_Oabs__class_Oabs(X10,X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).
fof(fact_abs__of__pos,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X11)
=> c_Groups_Oabs__class_Oabs(X10,X11) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(fact_linorder__linear,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
| c_Orderings_Oord__class_Oless__eq(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).
fof(fact_linorder__le__less__linear,axiom,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
| c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X9,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,X9) = c_Groups_Oplus__class_Oplus(X10,X9,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_minus__unique,axiom,
! [X24,X11,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X11,X24) = c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,X11) = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [X33,X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X32 = c_Groups_Ouminus__class_Ouminus(X10,X33)
<=> c_Groups_Oplus__class_Oplus(X10,X32,X33) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_add__eq__0__iff,axiom,
! [X14,X15,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X15,X14) = c_Groups_Ozero__class_Ozero(X10)
<=> X14 = c_Groups_Ouminus__class_Ouminus(X10,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_monom__eq__0__iff,axiom,
! [X19,X32,X10] :
( class_Groups_Ozero(X10)
=> ( c_Polynomial_Omonom(X10,X32,X19) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0__iff) ).
fof(fact_abs__ge__minus__self,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),c_Groups_Oabs__class_Oabs(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096constant_A_Ipoly_Aq_J_A_061_061_062_AFalse_096) ).
fof(fact_qnc,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_qnc) ).
fof(fact_less_Oprems,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less_Oprems) ).
fof(fact_assms,axiom,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(fact_mult__poly__0__right,axiom,
! [X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X10)),X65),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [X24,X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X24),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
fof(fact_inverse__unique,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) = c_Groups_Oone__class_Oone(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,X11) = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__unique) ).
fof(fact_zless__linear,axiom,
! [X8,X6] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X8)
| X6 = X8
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X8,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).
fof(fact_nat__neq__iff,axiom,
! [X19,X36] :
( X36 != X19
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X36,X19)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X19,X36) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
fof(fact_zle__linear,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(fact_nat__le__linear,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(fact_real__le__linear,axiom,
! [X25,X26] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X26,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__linear) ).
fof(fact_mult__eq__0__iff,axiom,
! [X33,X32,X10] :
( class_Rings_Oring__no__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X32),X33) = c_Groups_Ozero__class_Ozero(X10)
<=> ( X32 = c_Groups_Ozero__class_Ozero(X10)
| X33 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(fact_divisors__zero,axiom,
! [X24,X11,X10] :
( class_Rings_Ono__zero__divisors(X10)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) = c_Groups_Ozero__class_Ozero(X10)
=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
| X24 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).
fof(fact_no__zero__divisors,axiom,
! [X24,X11,X10] :
( class_Rings_Ono__zero__divisors(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X24) != c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).
fof(fact_dvd__if__abs__eq,axiom,
! [X27,X54,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Oabs__class_Oabs(X10,X54) = c_Groups_Oabs__class_Oabs(X10,X27)
=> c_Rings_Odvd__class_Odvd(X10,X54,X27) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [X66,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X66) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X66) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_zadd__commute,axiom,
! [X25,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_nat__add__commute,axiom,
! [X5,X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(fact_double__eq__0__iff,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Oplus__class_Oplus(X10,X32,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).
fof(fact_double__zero__sym,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Oplus__class_Oplus(X10,X32,X32)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(fact_eq__iff__diff__eq__0,axiom,
! [X33,X32,X10] :
( class_Groups_Oab__group__add(X10)
=> ( X32 = X33
<=> c_Groups_Ominus__class_Ominus(X10,X32,X33) = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(fact_right__minus__eq,axiom,
! [X33,X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ominus__class_Ominus(X10,X32,X33) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).
fof(fact_field__power__not__zero,axiom,
! [X5,X11,X10] :
( class_Rings_Oring__1__no__zero__divisors(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X5) != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).
fof(fact_real__add__eq__0__iff,axiom,
! [X14,X15] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X15,X14) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X14 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_add__0__iff,axiom,
! [X32,X33,X10] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
=> ( X33 = c_Groups_Oplus__class_Oplus(X10,X33,X32)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_abs__sgn,axiom,
! [X27,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Oabs__class_Oabs(X10,X27) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X27),c_Groups_Osgn__class_Osgn(X10,X27)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).
fof(fact_poly__zero,axiom,
! [X51,X10] :
( ( class_Int_Oring__char__0(X10)
& class_Rings_Oidom(X10) )
=> ( c_Polynomial_Opoly(X10,X51) = c_Polynomial_Opoly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
<=> X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__zero) ).
fof(fact_real__mult__inverse__left,axiom,
! [X6] :
( X6 != 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,X6)),X6) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__inverse__left) ).
fof(fact_order__less__imp__not__eq2,axiom,
! [X8,X6,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> X8 != X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(fact_order__less__imp__not__eq,axiom,
! [X8,X6,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> X6 != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).
fof(fact_less__imp__neq,axiom,
! [X8,X6,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> X6 != X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(fact_pCons__0__0,axiom,
! [X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_OpCons(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pCons__0__0) ).
fof(fact_one__poly__def,axiom,
! [X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10)) = c_Polynomial_OpCons(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__poly__def) ).
fof(fact_natfloor__neg,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__neg) ).
fof(fact_natceiling__neg,axiom,
! [X6] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(X6) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__neg) ).
fof(fact_right__inverse,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Groups_Oone__class_Oone(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse) ).
fof(fact_neq0__conv,axiom,
! [X19] :
( X19 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(fact_abs__ge__zero,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oabs__class_Oabs(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_norm__inverse,axiom,
! [X11,X10] :
( ( class_RealVector_Oreal__normed__div__algebra(X10)
& class_Rings_Odivision__ring__inverse__zero(X10) )
=> c_RealVector_Onorm__class_Onorm(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__inverse) ).
fof(fact_nonzero__abs__inverse,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oabs__class_Oabs(X10,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__inverse) ).
fof(fact_nonzero__inverse__minus__eq,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__minus__eq) ).
fof(fact_le__0__eq,axiom,
! [X19] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X19,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(fact_zmult__commute,axiom,
! [X25,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(fact_nat__mult__commute,axiom,
! [X5,X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_real__mult__commute,axiom,
! [X25,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X26),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_ab__left__minus,axiom,
! [X11,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X11) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(fact_left__minus,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11),X11) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(fact_right__minus,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(fact_of__real__inverse,axiom,
! [X6,X10] :
( ( class_RealVector_Oreal__div__algebra(X10)
& class_Rings_Odivision__ring__inverse__zero(X10) )
=> c_RealVector_Oof__real(X10,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X6)) = c_Rings_Oinverse__class_Oinverse(X10,c_RealVector_Oof__real(X10,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__inverse) ).
fof(fact_of__real_Ominus,axiom,
! [X6,X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> c_RealVector_Oof__real(X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X6)) = c_Groups_Ouminus__class_Ouminus(X10,c_RealVector_Oof__real(X10,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ominus) ).
fof(fact_add__is__0,axiom,
! [X19,X36] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X36,X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(fact_nonzero__norm__inverse,axiom,
! [X11,X10] :
( class_RealVector_Oreal__normed__div__algebra(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__norm__inverse) ).
fof(fact_offset__poly__0,axiom,
! [X85,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X85) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_offset__poly__0) ).
fof(fact_pcompose__0,axiom,
! [X66,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Opcompose(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X66) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pcompose__0) ).
fof(fact_synthetic__div__0,axiom,
! [X9,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osynthetic__div(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X9) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_smult__0__right,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,X11,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__right) ).
fof(fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096,axiom,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
=> ? [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_Ap_Ac_A_061_A0_A_061_061_062_AEX_Az_O_Apoly_Ap_Az_A_061_A0_096) ).
fof(fact_gr__implies__not0,axiom,
! [X5,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
=> X5 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
fof(fact_norm__ge__zero,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X10,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__ge__zero) ).
fof(fact_power__0__left,axiom,
! [X5,X10] :
( ( class_Power_Opower(X10)
& class_Rings_Osemiring__0(X10) )
=> ( ( X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X5) = c_Groups_Oone__class_Oone(X10) )
& ( X5 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Ozero__class_Ozero(X10)),X5) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).
fof(fact_add__eq__self__zero,axiom,
! [X5,X20] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X5) = X20
=> X5 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(fact_real__natceiling__ge,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X6))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_nonzero__of__real__inverse,axiom,
! [X6,X10] :
( class_RealVector_Oreal__div__algebra(X10)
=> ( X6 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_RealVector_Oof__real(X10,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X6)) = c_Rings_Oinverse__class_Oinverse(X10,c_RealVector_Oof__real(X10,X6)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__of__real__inverse) ).
fof(fact_poly__1,axiom,
! [X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10))),X6) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__1) ).
fof(fact_poly__0,axiom,
! [X6,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> hAPP(c_Polynomial_Opoly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X6) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__0) ).
fof(fact_abs__ge__self,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,X11,c_Groups_Oabs__class_Oabs(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(fact_less__not__refl2,axiom,
! [X20,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X20)
=> X20 != X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__not__refl3,axiom,
! [X53,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X53)
=> X17 != X53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
fof(fact_sgn__minus,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_Groups_Ouminus__class_Ouminus(X10,X6)) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Osgn__class_Osgn(X10,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__minus) ).
fof(fact_abs__inverse,axiom,
! [X11,X10] :
( class_Fields_Olinordered__field__inverse__zero(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oabs__class_Oabs(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__inverse) ).
fof(fact_inverse__minus__eq,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Ouminus__class_Ouminus(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__minus__eq) ).
fof(fact_add__poly__code_I1_J,axiom,
! [X66,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X66) = X66 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_diff__poly__code_I2_J,axiom,
! [X65,X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X10),X65,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [X65,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X10),X65,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_pos__poly__total,axiom,
! [X65,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X65 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
| c_Polynomial_Opos__poly(X10,X65)
| c_Polynomial_Opos__poly(X10,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X65)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__poly__total) ).
fof(fact_mult__is__0,axiom,
! [X19,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( X36 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__is__0) ).
fof(fact_of__real__minus,axiom,
! [X6,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X6)) = c_Groups_Ouminus__class_Ouminus(X10,c_RealVector_Oof__real(X10,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__minus) ).
fof(fact_sgn__of__real,axiom,
! [X18,X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_RealVector_Oof__real(X10,X18)) = c_RealVector_Oof__real(X10,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X18)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__of__real) ).
fof(fact_mult__eq__self__implies__10,axiom,
! [X5,X20] :
( X20 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X5)
=> ( X5 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X20 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__self__implies__10) ).
fof(fact_diff__0,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,c_Groups_Ozero__class_Ozero(X10),X11) = c_Groups_Ouminus__class_Ouminus(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [X19,X36] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [X19,X36] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X19)
<=> ( X36 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& X19 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26),X26) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_monom__eq__0,axiom,
! [X5,X10] :
( class_Groups_Ozero(X10)
=> c_Polynomial_Omonom(X10,c_Groups_Ozero__class_Ozero(X10),X5) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_monom__eq__0) ).
fof(fact_smult__0__left,axiom,
! [X65,X10] :
( class_Rings_Ocomm__semiring__0(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Ozero__class_Ozero(X10),X65) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__0__left) ).
fof(fact_power__power__power,axiom,
! [X10] :
( class_Power_Opower(X10)
=> c_Power_Opower__class_Opower(X10) = c_Power_Opower_Opower(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Otimes__class_Otimes(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X11) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(fact_mult__zero__left,axiom,
! [X11,X10] :
( class_Rings_Omult__zero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X11) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(fact_mult_Ozero__left,axiom,
! [X24,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X24) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__left) ).
fof(fact_mult__left_Ozero,axiom,
! [X8,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Ozero__class_Ozero(X10)),X8) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left_Ozero) ).
fof(fact_power__one,axiom,
! [X5,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),c_Groups_Oone__class_Oone(X10)),X5) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_zero__le__one,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(fact_zero__less__one,axiom,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),c_Groups_Oone__class_Oone(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(fact_mult__1,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(fact_mult__1__left,axiom,
! [X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),c_Groups_Oone__class_Oone(X10)),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(fact_mult__zero__right,axiom,
! [X11,X10] :
( class_Rings_Omult__zero(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(fact_mult_Ozero__right,axiom,
! [X11,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ozero__right) ).
fof(fact_mult__right_Ozero,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__algebra(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right_Ozero) ).
fof(fact_smult__1__left,axiom,
! [X65,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Polynomial_Osmult(X10,c_Groups_Oone__class_Oone(X10),X65) = X65 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smult__1__left) ).
fof(fact_add__0__left,axiom,
! [X11,X10] :
( class_Groups_Omonoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_add__0,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,c_Groups_Ozero__class_Ozero(X10),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(fact_diff__0__right,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X11,c_Groups_Ozero__class_Ozero(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(fact_add__0__right,axiom,
! [X11,X10] :
( class_Groups_Omonoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ozero__class_Ozero(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ozero__class_Ozero(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_add_Ocomm__neutral,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__add(X10)
=> c_Groups_Oplus__class_Oplus(X10,X11,c_Groups_Ozero__class_Ozero(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(fact_one__dvd,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,c_Groups_Oone__class_Oone(X10),X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__0__right,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X11,c_Groups_Ozero__class_Ozero(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(fact_power__0,axiom,
! [X11,X10] :
( class_Power_Opower(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Oone__class_Oone(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(fact_mult_Ocomm__neutral,axiom,
! [X11,X10] :
( class_Groups_Ocomm__monoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Oone__class_Oone(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(fact_mult__1__right,axiom,
! [X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),c_Groups_Oone__class_Oone(X10)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(fact_diff__self,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ominus__class_Ominus(X10,X11,X11) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(fact_order__eq__refl,axiom,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( X6 = X8
=> c_Orderings_Oord__class_Oless__eq(X10,X6,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).
fof(fact_nonzero__inverse__eq__imp__eq,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X11) = c_Rings_Oinverse__class_Oinverse(X10,X24)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> ( X24 != c_Groups_Ozero__class_Ozero(X10)
=> X11 = X24 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__eq__imp__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [X6,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X6),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(fact_power__one__right,axiom,
! [X11,X10] :
( class_Groups_Omonoid__mult(X10)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(fact_zero__le__natfloor,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_zero__le__natceiling,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_dvd__refl,axiom,
! [X11,X10] :
( class_Rings_Ocomm__semiring__1(X10)
=> c_Rings_Odvd__class_Odvd(X10,X11,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(fact_order__refl,axiom,
! [X6,X10] :
( class_Orderings_Opreorder(X10)
=> c_Orderings_Oord__class_Oless__eq(X10,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(fact_sgn__sgn,axiom,
! [X11,X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_Groups_Osgn__class_Osgn(X10,X11)) = c_Groups_Osgn__class_Osgn(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(fact_abs__idempotent,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Oabs__class_Oabs(X10,X11)) = c_Groups_Oabs__class_Oabs(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(fact_abs__minus__cancel,axiom,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = c_Groups_Oabs__class_Oabs(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_norm__minus__cancel,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ouminus__class_Ouminus(X10,X6)) = c_RealVector_Onorm__class_Onorm(X10,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_poly__eq__iff,axiom,
! [X67,X51,X10] :
( ( class_Int_Oring__char__0(X10)
& class_Rings_Oidom(X10) )
=> ( c_Polynomial_Opoly(X10,X51) = c_Polynomial_Opoly(X10,X67)
<=> X51 = X67 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_times_Oidem,axiom,
! [X11,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).
fof(fact_mult__idem,axiom,
! [X6,X10] :
( class_Lattices_Oab__semigroup__idem__mult(X10)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).
fof(fact_gr0I,axiom,
! [X5] :
( X5 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(fact_abs__norm__cancel,axiom,
! [X11,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X11)) = c_RealVector_Onorm__class_Onorm(X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_norm__of__real,axiom,
! [X18,X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_RealVector_Oof__real(X10,X18)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(fact_diff__0__eq__0,axiom,
! [X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(fact_norm__sgn,axiom,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Osgn__class_Osgn(X10,X6)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X6 != c_Groups_Ozero__class_Ozero(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Osgn__class_Osgn(X10,X6)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__sgn) ).
fof(fact_zadd__0,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X5] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_minus__nat_Odiff__0,axiom,
! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(fact_zadd__0__right,axiom,
! [X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).
fof(fact_Nat_Oadd__0__right,axiom,
! [X20] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(fact_eq__imp__le,axiom,
! [X5,X20] :
( X20 = X5
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_le0,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [X10] :
( class_Groups_Oab__group__add(X10)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_diff__self__eq__0,axiom,
! [X20] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(fact_mult__0,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X5) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(fact_inverse__eq__iff__eq,axiom,
! [X33,X32,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X32) = c_Rings_Oinverse__class_Oinverse(X10,X33)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__iff__eq) ).
fof(fact_inverse__eq__imp__eq,axiom,
! [X24,X11,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X11) = c_Rings_Oinverse__class_Oinverse(X10,X24)
=> X11 = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__imp__eq) ).
fof(fact_compl__eq__compl__iff,axiom,
! [X14,X15,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X15) = c_Groups_Ouminus__class_Ouminus(X10,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [X33,X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X32) = c_Groups_Ouminus__class_Ouminus(X10,X33)
<=> X32 = X33 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_of__real__eq__iff,axiom,
! [X14,X15,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> ( c_RealVector_Oof__real(X10,X15) = c_RealVector_Oof__real(X10,X14)
<=> X15 = X14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__iff) ).
fof(fact_nonzero__inverse__inverse__eq,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = X11 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__inverse__inverse__eq) ).
fof(fact_zmult__1,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(fact_nat__mult__1,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(fact_real__mult__1,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X26) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_zle__refl,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(fact_le__refl,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(fact_real__le__refl,axiom,
! [X25] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(fact_mult__0__right,axiom,
! [X20] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(fact_zmult__1__right,axiom,
! [X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(fact_nat__mult__1__right,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_inverse__inverse__eq,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Rings_Oinverse__class_Oinverse(X10,X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__inverse__eq) ).
fof(fact_double__compl,axiom,
! [X6,X10] :
( class_Lattices_Oboolean__algebra(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X6)) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(fact_minus__minus,axiom,
! [X11,X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ouminus__class_Ouminus(X10,X11)) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [X6] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X6)) = c_RealDef_Oreal(tc_Nat_Onat,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_minus__equation__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X32) = X33
<=> c_Groups_Ouminus__class_Ouminus(X10,X33) = X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_equation__minus__iff,axiom,
! [X33,X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( X32 = c_Groups_Ouminus__class_Ouminus(X10,X33)
<=> X33 = c_Groups_Ouminus__class_Ouminus(X10,X32) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_psize__eq__0__iff,axiom,
! [X51,X10] :
( class_Groups_Ozero(X10)
=> ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X10,X51) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> X51 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psize__eq__0__iff) ).
fof(fact_real__of__nat__inject,axiom,
! [X36,X19] :
( c_RealDef_Oreal(tc_Nat_Onat,X19) = c_RealDef_Oreal(tc_Nat_Onat,X36)
<=> X19 = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ozero__class_Ozero(X10) = c_Groups_Ouminus__class_Ouminus(X10,X32)
<=> c_Groups_Ozero__class_Ozero(X10) = X32 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_inverse__eq__1__iff,axiom,
! [X15,X10] :
( class_Fields_Ofield__inverse__zero(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X15) = c_Groups_Oone__class_Oone(X10)
<=> X15 = c_Groups_Oone__class_Oone(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__eq__1__iff) ).
fof(fact_sgn__0__0,axiom,
! [X32,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(fact_sgn__zero__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_Groups_Osgn__class_Osgn(X10,X15) = c_Groups_Ozero__class_Ozero(X10)
<=> X15 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_abs__eq__0,axiom,
! [X32,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ( c_Groups_Oabs__class_Oabs(X10,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(fact_nonzero__imp__inverse__nonzero,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,X11) != c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__imp__inverse__nonzero) ).
fof(fact_inverse__zero__imp__zero,axiom,
! [X11,X10] :
( class_Rings_Odivision__ring(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X11) = c_Groups_Ozero__class_Ozero(X10)
=> X11 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero__imp__zero) ).
fof(fact_inverse__nonzero__iff__nonzero,axiom,
! [X32,X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> ( c_Rings_Oinverse__class_Oinverse(X10,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__nonzero__iff__nonzero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [X32,X10] :
( class_Groups_Ogroup__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X32) = c_Groups_Ozero__class_Ozero(X10)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_of__real__eq__0__iff,axiom,
! [X15,X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> ( c_RealVector_Oof__real(X10,X15) = c_Groups_Ozero__class_Ozero(X10)
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__eq__0__iff) ).
fof(fact_norm__eq__zero,axiom,
! [X15,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ( c_RealVector_Onorm__class_Onorm(X10,X15) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X15 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__eq__zero) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [X90,X89] :
( class_Groups_Ouminus(X89)
=> class_Groups_Ouminus(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [X90,X89] :
( class_Groups_Ominus(X89)
=> class_Groups_Ominus(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [X90,X89] :
( class_Lattices_Oboolean__algebra(X89)
=> class_Lattices_Oboolean__algebra(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [X90,X89] :
( class_Orderings_Oorder(X89)
=> class_Orderings_Oorder(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [X90,X89] :
( class_Orderings_Oord(X89)
=> class_Orderings_Oord(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [X90,X89] :
( class_Orderings_Opreorder(X89)
=> class_Orderings_Opreorder(tc_fun(X90,X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(fact_zminus__zminus,axiom,
! [X26] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X26)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(fact_neg__equal__zero,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( c_Groups_Ouminus__class_Ouminus(X10,X32) = X32
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_equal__neg__zero,axiom,
! [X32,X10] :
( class_Groups_Olinordered__ab__group__add(X10)
=> ( X32 = c_Groups_Ouminus__class_Ouminus(X10,X32)
<=> X32 = c_Groups_Ozero__class_Ozero(X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_of__real_Ozero,axiom,
! [X10] :
( ( class_RealVector_Oreal__algebra__1(X10)
& class_RealVector_Oreal__normed__vector(X10) )
=> c_RealVector_Oof__real(X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real_Ozero) ).
fof(fact_sgn__one,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__one) ).
fof(fact_sgn0,axiom,
! [X10] :
( class_Groups_Osgn__if(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).
fof(fact_sgn__zero,axiom,
! [X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_Groups_Osgn__class_Osgn(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__zero) ).
fof(fact_abs__one,axiom,
! [X10] :
( class_Rings_Olinordered__idom(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
fof(fact_abs__zero,axiom,
! [X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> c_Groups_Oabs__class_Oabs(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(fact_inverse__1,axiom,
! [X10] :
( class_Rings_Odivision__ring(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__1) ).
fof(fact_field__inverse__zero,axiom,
! [X10] :
( class_Fields_Ofield__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__inverse__zero) ).
fof(fact_inverse__zero,axiom,
! [X10] :
( class_Rings_Odivision__ring__inverse__zero(X10)
=> c_Rings_Oinverse__class_Oinverse(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__zero) ).
fof(fact_minus__zero,axiom,
! [X10] :
( class_Groups_Ogroup__add(X10)
=> c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(fact_norm__one,axiom,
! [X10] :
( class_RealVector_Oreal__normed__algebra__1(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Oone__class_Oone(X10)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__one) ).
fof(fact_norm__zero,axiom,
! [X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> c_RealVector_Onorm__class_Onorm(X10,c_Groups_Ozero__class_Ozero(X10)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__zero) ).
fof(fact_of__real__1,axiom,
! [X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__1) ).
fof(fact_of__real__0,axiom,
! [X10] :
( class_RealVector_Oreal__algebra__1(X10)
=> c_RealVector_Oof__real(X10,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__real__0) ).
fof(fact_natfloor__real__of__nat,axiom,
! [X5] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X5)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_natceiling__real__of__nat,axiom,
! [X5] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X5)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [X19] :
( c_RealDef_Oreal(tc_Nat_Onat,X19) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X19 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_real__norm__def,axiom,
! [X18] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X18) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_zero__neq__one,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Ozero__class_Ozero(X10) != c_Groups_Oone__class_Oone(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).
fof(fact_one__neq__zero,axiom,
! [X10] :
( class_Rings_Ozero__neq__one(X10)
=> c_Groups_Oone__class_Oone(X10) != c_Groups_Ozero__class_Ozero(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Odvd(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ominus(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Oone(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [X89] :
( class_Groups_Ocancel__comm__monoid__add(X89)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [X89] :
( class_Rings_Ocomm__ring__1(X89)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [X89] :
( class_Groups_Ocomm__monoid__add(X89)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [X89] :
( class_Groups_Ozero(X89)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [X89] :
( class_Rings_Ocomm__ring(X89)
=> class_Rings_Oring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [X89] :
( class_Groups_Oab__group__add(X89)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [X89] :
( class_Rings_Oidom(X89)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__0(X89)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_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/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Power_Opower(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [X89] :
( class_Rings_Ocomm__semiring__1(X89)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [X89] :
( class_Rings_Olinordered__idom(X89)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X89)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_060_061_Acmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_J_A_L_Acmod_A_I_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096) ).
fof(fact_th11,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th11) ).
fof(fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_I1_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_A_061cmod_A_Icomplex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_A_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_096) ).
fof(fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_0611_A_L_Acomplex__of__real_At_A_094_Ak_A_K_A_Iw_A_094_Ak_A_K_Aa_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a____,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_Ia_A_L_Acomplex__of__real_At_A_K_Aw_A_K_Apoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_A_061complex__of__real_A_I1_A_N_At_A_094_Ak_J_A_L_Icomplex__of__real_At_A_K_Aw_J_A_094_Ak_A_K_A_Icomplex__of__real_At_A_K_Aw_J_A_Kpoly_As_A_Icomplex__of__real_At_A_K_Aw_J_096) ).
fof(conj_0,hypothesis,
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____)))) = 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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact__096cmod_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_A_061t_A_094_Ak_A_K_A_It_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Acmod_A_Ipoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_J_096,axiom,
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____)))) = 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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_s____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096cmod_A_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_A_061t_A_094_Ak_A_K_A_It_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Acmod_A_Ipoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_J_096) ).
fof(fact_th30,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th30) ).
fof(fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096poly_Aq_A0_A_061_Apoly_A_Ismult_A_Iinverse_A_Ipoly_Aq_A0_J_J_Aq_J_A0_A_K_Apoly_Aq_A0_096) ).
fof(fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096t_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Am_J_A_060_A1_096) ).
fof(fact_inv0,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv0) ).
fof(fact_t_I3_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),v_m____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I3_J) ).
fof(fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096,axiom,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)) = c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0961_A_L_Aw_A_094_Ak_A_K_Aa_A_N_A1_A_061_A0_A_N_A1_096) ).
fof(fact_r01,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r01) ).
fof(conj_1,hypothesis,
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____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(fact_th02,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),c_Polynomial_Omonom(tc_Complex_Ocomplex,v_a____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_th02) ).
fof(fact_kas_I3_J,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_s____),v_k____),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I3_J) ).
fof(fact_w,axiom,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w) ).
fof(fact_lgqr,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,c_Polynomial_Osmult(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))),v_q____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lgqr) ).
fof(fact_tw,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tw) ).
fof(fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_t____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096t_A_K_Acmod_Aw_A_060_061_A1_A_K_Acmod_Aw_096) ).
fof(fact_wm1,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),v_w____),v_k____)),v_a____) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wm1) ).
fof(fact_k1n,axiom,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_k1n) ).
fof(fact__0960_A_060_At_A_094_Ak_096,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_t____),v_k____)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__0960_A_060_At_A_094_Ak_096) ).
fof(fact_kn,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_k____,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kn) ).
fof(fact_pqc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pqc0) ).
fof(fact_a00,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_a00) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
fof(fact_int__0__less__1,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(fact_i__mult__eq2,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_i__mult__eq2) ).
fof(fact_complex__of__real__minus__one,axiom,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__minus__one) ).
fof(fact_pc0,axiom,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),v_c____) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pc0) ).
fof(fact_m_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_m_I1_J) ).
fof(fact_t_I1_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I1_J) ).
fof(fact_t_I2_J,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_t_I2_J) ).
fof(fact_inverse__i,axiom,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Complex_Oii),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inverse__i) ).
fof(fact_q_I1_J,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_q____) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q_I1_J) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_INVERSE__ZERO,axiom,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INVERSE__ZERO) ).
fof(fact_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(fact_natfloor__one,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__one) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natfloor__zero) ).
fof(fact_natceiling__one,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__one) ).
fof(fact_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_natceiling__zero) ).
fof(fact_int__0__neq__1,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__i__not__zero) ).
fof(fact_kas_I2_J,axiom,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I2_J) ).
fof(fact_kas_I1_J,axiom,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_kas_I1_J) ).
fof(fact_w0,axiom,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_w0) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
fof(arity_Int__Oint__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Olinordered__ab__group__add,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__semigroup__add,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_RealDef__Oreal__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Fields_Ofield,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field) ).
fof(arity_Complex__Ocomplex__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Fields_Ofield__inverse__zero) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Complex__Ocomplex__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero) ).
fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__div__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__div__algebra) ).
fof(arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__comm__semiring,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__semiring,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(arity_RealDef__Oreal__Rings_Oordered__cancel__semiring,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring__strict,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__ring,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__no__zero__divisors,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semiring__strict,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__idom,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Complex__Ocomplex__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(arity_RealDef__Oreal__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(i_0_1280,plain,
~ ! [X56] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X56)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X56,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X56,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_1281,plain,
! [X8,X6,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oplus__class_Oplus(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X8),X8)),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(i_0_1282,plain,
! [X33,X32,X52] :
( hBOOL(hAPP(X52,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X32,X33)))
<=> ~ ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X32,X33)
& ~ hBOOL(hAPP(X52,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
| ? [X61] :
( X32 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X33,X61)
& ~ hBOOL(hAPP(X52,X61)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(i_0_1283,plain,
! [X6] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X6),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X6),
inference(fof_simplification,[status(thm)],[fact_abs__add__one__not__less__self]) ).
fof(i_0_1284,plain,
! [X5,X27,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X27),X5)
=> ~ ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X5)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X27,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_add__leE]) ).
fof(i_0_1285,plain,
! [X1,X2,X10,X22] :
( class_Orderings_Oord(X22)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X10,X22),X2,X1)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X2,X1)
& ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X22),X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).
fof(i_0_1286,plain,
! [X51] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X51),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,X51))
=> ? [X4] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X51),X4) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_simplification,[status(thm)],[fact_less_Ohyps]) ).
fof(i_0_1287,plain,
! [X11,X10] :
( class_Rings_Olinordered__ring(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).
fof(i_0_1288,plain,
! [X28,X21] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X21,X28),X21),
inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).
fof(i_0_1289,plain,
! [X21,X28] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X28,X21),X21),
inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).
fof(i_0_1290,plain,
! [X15] :
( ~ 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),X15),X15))
<=> X15 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_simplification,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(i_0_1291,plain,
! [X5,X20] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X20,X5)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X20,X5)) = X20 ),
inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).
fof(i_0_1292,plain,
! [X14,X15,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
& ~ c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ) ),
inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).
fof(i_0_1293,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(i_0_1294,plain,
! [X11,X24,X10] :
( class_Orderings_Oorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X24,X11)
=> ~ c_Orderings_Oord__class_Oless(X10,X11,X24) ) ),
inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).
fof(i_0_1295,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless(X10,X14,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).
fof(i_0_1296,plain,
! [X6,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> ~ c_Orderings_Oord__class_Oless(X10,X6,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_leD]) ).
fof(i_0_1297,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> c_Orderings_Oord__class_Oless__eq(X10,X14,X15) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).
fof(i_0_1298,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> ( c_Orderings_Oord__class_Oless(X10,X14,X15)
| X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(i_0_1299,plain,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).
fof(i_0_1300,plain,
! [X24,X11,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X11,X24)
=> ~ c_Orderings_Oord__class_Oless(X10,X24,X11) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).
fof(i_0_1301,plain,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).
fof(i_0_1302,plain,
! [X8,X6,X10] :
( class_Orderings_Opreorder(X10)
=> ( c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ~ c_Orderings_Oord__class_Oless(X10,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).
fof(i_0_1303,plain,
! [X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)) )
& ( X6 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X6)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X10))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__poly__def]) ).
fof(i_0_1304,plain,
! [X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X10),X6) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X10),X6) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X10),X6,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X10),X6) = X6 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__poly__def]) ).
fof(i_0_1305,plain,
! [X6,X8] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X6)
=> c_Nat__Transfer_Otsub(X6,X8) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X6,X8) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X8,X6)
=> c_Nat__Transfer_Otsub(X6,X8) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).
fof(i_0_1306,plain,
! [X14,X15,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
=> ( c_Orderings_Oord__class_Oless__eq(X10,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(i_0_1307,plain,
! [X11,X10] :
( class_Groups_Oordered__ab__group__add__abs(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oabs__class_Oabs(X10,X11),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).
fof(i_0_1308,plain,
! [X6,X10] :
( class_RealVector_Oreal__normed__vector(X10)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X10,X6),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_simplification,[status(thm)],[fact_norm__not__less__zero]) ).
fof(i_0_1309,plain,
! [X11,X10] :
( class_Groups_Oabs__if(X10)
=> ( ( c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = c_Groups_Ouminus__class_Ouminus(X10,X11) )
& ( ~ c_Orderings_Oord__class_Oless(X10,X11,c_Groups_Ozero__class_Ozero(X10))
=> c_Groups_Oabs__class_Oabs(X10,X11) = X11 ) ) ),
inference(fof_simplification,[status(thm)],[fact_abs__if]) ).
fof(i_0_1310,plain,
! [X6,X10] :
( class_Groups_Osgn__if(X10)
=> ( ( X6 = c_Groups_Ozero__class_Ozero(X10)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Ozero__class_Ozero(X10) )
& ( X6 != c_Groups_Ozero__class_Ozero(X10)
=> ( ( c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Oone__class_Oone(X10) )
& ( ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Ozero__class_Ozero(X10),X6)
=> c_Groups_Osgn__class_Osgn(X10,X6) = c_Groups_Ouminus__class_Ouminus(X10,c_Groups_Oone__class_Oone(X10)) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).
fof(i_0_1311,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_simplification,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(i_0_1312,plain,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> ( X6 != X8
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).
fof(i_0_1313,plain,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).
fof(i_0_1314,plain,
! [X15,X14,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X14,X15)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X15,X14)
<=> X15 = X14 ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(i_0_1315,plain,
! [X8,X6,X10] :
( class_Rings_Olinordered__idom(X10)
=> ( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless(X10,X8,X6) ) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).
fof(i_0_1316,plain,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).
fof(i_0_1317,plain,
! [X8,X6,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless(X10,X6,X8)
=> c_Orderings_Oord__class_Oless__eq(X10,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
fof(i_0_1318,plain,
! [X6,X8,X10] :
( class_Orderings_Olinorder(X10)
=> ( ~ c_Orderings_Oord__class_Oless__eq(X10,X8,X6)
=> c_Orderings_Oord__class_Oless(X10,X6,X8) ) ),
inference(fof_simplification,[status(thm)],[fact_not__leE]) ).
fof(i_0_1319,plain,
! [X21] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X21) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X21) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X21,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,X21) = X21 ) ),
inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).
fof(i_0_1320,plain,
! [X18] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X18) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X18,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X18) = X18 ) ),
inference(fof_simplification,[status(thm)],[fact_real__abs__def]) ).
fof(i_0_1321,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_abs__real__def]) ).
fof(i_0_1322,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless__eq(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).
fof(i_0_1323,plain,
! [X10] :
( class_Rings_Olinordered__semidom(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Ozero__class_Ozero(X10)) ),
inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).
fof(i_0_1324,plain,
! [X8,X6] :
( X6 != X8
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X8)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X8,X6) ) ),
inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).
fof(i_0_1325,plain,
! [X6,X10] :
( class_Orderings_Opreorder(X10)
=> ~ c_Orderings_Oord__class_Oless(X10,X6,X6) ),
inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).
fof(i_0_1326,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).
fof(i_0_1327,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_not__less0]) ).
fof(i_0_1328,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).
fof(i_0_1329,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X5),
inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).
fof(i_0_1330,plain,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X5),
inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).
fof(i_0_1331,plain,
! [X10] :
( class_Rings_Olinordered__idom(X10)
=> ~ c_Polynomial_Opos__poly(X10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))) ),
inference(fof_simplification,[status(thm)],[fact_not__pos__poly__0]) ).
fof(i_0_1332,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_2])]) ).
fof(i_0_1333,plain,
! [X5129,X5130,X5131,X5132,X5134] :
( ( c_Orderings_Oord__class_Oless__eq(X5131,X5130,esk27_4(X5129,X5130,X5131,X5132))
| ~ c_Orderings_Oord__class_Oless__eq(X5131,X5130,X5134)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5132,hAPP(X5129,X5134)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5132,hAPP(X5129,X5130))))
| ~ class_RealVector_Oreal__normed__vector(X5132)
| ~ class_Orderings_Oord(X5131) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5132,c_Groups_Ominus__class_Ominus(X5132,hAPP(X5129,X5130),hAPP(X5129,esk27_4(X5129,X5130,X5131,X5132)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(X5131,X5130,X5134)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5132,hAPP(X5129,X5134)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5132,hAPP(X5129,X5130))))
| ~ class_RealVector_Oreal__normed__vector(X5132)
| ~ class_Orderings_Oord(X5131) ) ),
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_1334,plain,
! [X3926] :
( ( ~ 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____)),X3926)),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____),X3926)),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____),X3926)),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____)),X3926)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mrmq__eq])]) ).
fof(i_0_1335,plain,
! [X4838,X4839,X4840] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4840)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4839,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,X4839,X4838)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4840)),X4838) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).
fof(i_0_1336,plain,
! [X4835,X4836,X4837] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4837)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4836,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4835,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,X4835,X4836)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X4837))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).
fof(i_0_1337,plain,
! [X5110] :
( 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____)),X5110) = 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),X5110),esk23_0)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,esk24_0,esk25_0)),X5110))) ),
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_1338,plain,
! [X3927] : 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____)),X3927) = 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),X3927),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),X3927))),
inference(variable_rename,[status(thm)],[fact_kas_I4_J]) ).
fof(i_0_1339,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____)),esk15_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_1340,plain,
! [X3925] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3925) = 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____)),X3925)),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_1341,plain,
! [X4911,X4912,X4913,X4914,X4915] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4913,X4914),X4912,X4911)
| c_Orderings_Oord__class_Oless__eq(X4914,hAPP(X4912,X4915),hAPP(X4911,X4915))
| ~ class_Orderings_Oord(X4914) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4914,hAPP(X4912,esk22_4(X4911,X4912,X4913,X4914)),hAPP(X4911,esk22_4(X4911,X4912,X4913,X4914)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4913,X4914),X4912,X4911)
| ~ class_Orderings_Oord(X4914) ) ),
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_1342,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_0)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk9_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk9_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_1280])])]) ).
fof(i_0_1343,plain,
! [X3422,X3423,X3424,X3425,X3426] :
( ~ class_RealVector_Oreal__normed__algebra(X3426)
| c_Groups_Ominus__class_Ominus(X3426,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3426),X3425),X3424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3426),X3423),X3422)) = c_Groups_Oplus__class_Oplus(X3426,c_Groups_Oplus__class_Oplus(X3426,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3426),c_Groups_Ominus__class_Ominus(X3426,X3425,X3423)),c_Groups_Ominus__class_Ominus(X3426,X3424,X3422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3426),c_Groups_Ominus__class_Ominus(X3426,X3425,X3423)),X3422)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3426),X3423),c_Groups_Ominus__class_Ominus(X3426,X3424,X3422))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oprod__diff__prod])]) ).
fof(i_0_1344,plain,
! [X3848,X3849,X3850,X3851] : 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,X3851,X3850),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3849),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3848)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3851,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3849))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3850,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3848))))),
inference(variable_rename,[status(thm)],[fact_abs__sum__triangle__ineq]) ).
fof(i_0_1345,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____)),esk16_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____)),esk17_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_1346,plain,
! [X4590,X4591,X4592] :
( ~ class_Rings_Ocomm__ring__1(X4592)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4592),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4592)),c_Polynomial_OpCons(X4592,c_Groups_Ouminus__class_Ouminus(X4592,X4591),c_Polynomial_OpCons(X4592,c_Groups_Oone__class_Oone(X4592),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4592))))),c_Polynomial_Osynthetic__div(X4592,X4590,X4591)),c_Polynomial_OpCons(X4592,hAPP(c_Polynomial_Opoly(X4592,X4590),X4591),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4592)))) = X4590 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H])]) ).
fof(i_0_1347,plain,
! [X3454,X3455,X3456,X3457,X3458,X3459] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3459,c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),X3458),X3457),X3456),c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),X3455),X3457),X3454))
| c_Orderings_Oord__class_Oless__eq(X3459,c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),c_Groups_Ominus__class_Ominus(X3459,X3458,X3455)),X3457),X3456),X3454)
| ~ class_Rings_Oordered__ring(X3459) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3459,c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),c_Groups_Ominus__class_Ominus(X3459,X3458,X3455)),X3457),X3456),X3454)
| c_Orderings_Oord__class_Oless__eq(X3459,c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),X3458),X3457),X3456),c_Groups_Oplus__class_Oplus(X3459,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3459),X3455),X3457),X3454))
| ~ class_Rings_Oordered__ring(X3459) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).
fof(i_0_1348,plain,
! [X3466,X3467,X3468,X3469,X3470,X3471] :
( ( ~ c_Orderings_Oord__class_Oless(X3471,c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),X3470),X3469),X3468),c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),X3467),X3469),X3466))
| c_Orderings_Oord__class_Oless(X3471,c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),c_Groups_Ominus__class_Ominus(X3471,X3470,X3467)),X3469),X3468),X3466)
| ~ class_Rings_Oordered__ring(X3471) )
& ( ~ c_Orderings_Oord__class_Oless(X3471,c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),c_Groups_Ominus__class_Ominus(X3471,X3470,X3467)),X3469),X3468),X3466)
| c_Orderings_Oord__class_Oless(X3471,c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),X3470),X3469),X3468),c_Groups_Oplus__class_Oplus(X3471,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3471),X3467),X3469),X3466))
| ~ class_Rings_Oordered__ring(X3471) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).
fof(i_0_1349,plain,
! [X3460,X3461,X3462,X3463,X3464,X3465] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3465,c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),X3464),X3463),X3462),c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),X3461),X3463),X3460))
| c_Orderings_Oord__class_Oless__eq(X3465,X3462,c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),c_Groups_Ominus__class_Ominus(X3465,X3461,X3464)),X3463),X3460))
| ~ class_Rings_Oordered__ring(X3465) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3465,X3462,c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),c_Groups_Ominus__class_Ominus(X3465,X3461,X3464)),X3463),X3460))
| c_Orderings_Oord__class_Oless__eq(X3465,c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),X3464),X3463),X3462),c_Groups_Oplus__class_Oplus(X3465,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3465),X3461),X3463),X3460))
| ~ class_Rings_Oordered__ring(X3465) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).
fof(i_0_1350,plain,
! [X3472,X3473,X3474,X3475,X3476,X3477] :
( ( ~ c_Orderings_Oord__class_Oless(X3477,c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),X3476),X3475),X3474),c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),X3473),X3475),X3472))
| c_Orderings_Oord__class_Oless(X3477,X3474,c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),c_Groups_Ominus__class_Ominus(X3477,X3473,X3476)),X3475),X3472))
| ~ class_Rings_Oordered__ring(X3477) )
& ( ~ c_Orderings_Oord__class_Oless(X3477,X3474,c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),c_Groups_Ominus__class_Ominus(X3477,X3473,X3476)),X3475),X3472))
| c_Orderings_Oord__class_Oless(X3477,c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),X3476),X3475),X3474),c_Groups_Oplus__class_Oplus(X3477,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3477),X3473),X3475),X3472))
| ~ class_Rings_Oordered__ring(X3477) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).
fof(i_0_1351,plain,
! [X3893,X3894,X3895,X3896,X3897] :
( ( ~ 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),X3896),X3895),X3894),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3897),X3895),X3893))
| 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,X3896,X3897)),X3895),X3894),X3893)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3897,X3896) )
& ( ~ 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,X3896,X3897)),X3895),X3894),X3893)
| 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),X3896),X3895),X3894),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3897),X3895),X3893))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3897,X3896) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).
fof(i_0_1352,plain,
! [X3907,X3908,X3909,X3910,X3911] :
( ( ~ 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),X3910),X3909),X3908),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3911),X3909),X3907))
| 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,X3910,X3911)),X3909),X3908),X3907)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3911,X3910) )
& ( ~ 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,X3910,X3911)),X3909),X3908),X3907)
| 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),X3910),X3909),X3908),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3911),X3909),X3907))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3911,X3910) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).
fof(i_0_1353,plain,
! [X3878,X3879,X3880,X3881,X3882] :
( ( ~ 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),X3882),X3880),X3879),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3881),X3880),X3878))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3879,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,X3881,X3882)),X3880),X3878))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3882,X3881) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3879,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,X3881,X3882)),X3880),X3878))
| 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),X3882),X3880),X3879),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3881),X3880),X3878))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3882,X3881) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).
fof(i_0_1354,plain,
! [X3902,X3903,X3904,X3905,X3906] :
( ( ~ 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),X3906),X3904),X3903),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3905),X3904),X3902))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3903,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,X3905,X3906)),X3904),X3902))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3906,X3905) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3903,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,X3905,X3906)),X3904),X3902))
| 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),X3906),X3904),X3903),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3905),X3904),X3902))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3906,X3905) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).
fof(i_0_1355,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_1356,plain,
! [X5342,X5343,X5344] :
( ~ class_Rings_Oidom(X5344)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5344),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X5344)),c_Polynomial_OpCons(X5344,c_Groups_Ouminus__class_Ouminus(X5344,X5343),c_Polynomial_OpCons(X5344,c_Groups_Oone__class_Oone(X5344),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5344))))),c_Polynomial_Oorder(X5344,X5343,X5342)),X5342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__1])]) ).
fof(i_0_1357,plain,
! [X4225,X4226,X4227,X4228,X4229] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4229)
| c_Orderings_Oord__class_Oless__eq(X4229,c_Groups_Oabs__class_Oabs(X4229,c_Groups_Ominus__class_Ominus(X4229,c_Groups_Oplus__class_Oplus(X4229,X4228,X4227),c_Groups_Oplus__class_Oplus(X4229,X4226,X4225))),c_Groups_Oplus__class_Oplus(X4229,c_Groups_Oabs__class_Oabs(X4229,c_Groups_Ominus__class_Ominus(X4229,X4228,X4226)),c_Groups_Oabs__class_Oabs(X4229,c_Groups_Ominus__class_Ominus(X4229,X4227,X4225)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).
fof(i_0_1358,plain,
! [X4593,X4594] :
( X4594 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| X4593 = 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),X4594),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),esk19_2(X4593,X4594)),X4593)))),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_1359,plain,
! [X3480,X3481,X3482,X3483,X3484] :
( ~ class_RealVector_Oreal__normed__vector(X3484)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3484,c_Groups_Ominus__class_Ominus(X3484,c_Groups_Oplus__class_Oplus(X3484,X3483,X3482),c_Groups_Oplus__class_Oplus(X3484,X3481,X3480))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3484,c_Groups_Ominus__class_Ominus(X3484,X3483,X3481)),c_RealVector_Onorm__class_Onorm(X3484,c_Groups_Ominus__class_Ominus(X3484,X3482,X3480)))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__triangle__ineq])]) ).
fof(i_0_1360,plain,
! [X5266,X5267,X5268,X5270] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_3(X5266,X5267,X5268))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5268) )
& ( ~ 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,X5270,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,X5270,X5267)),esk35_3(X5266,X5267,X5268))
| 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,X5266),X5270),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X5266),X5267))),X5268)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5268) ) ),
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_1361,plain,
! [X3918,X3919,X3920] :
( ~ class_Rings_Odivision__ring(X3920)
| X3919 = c_Groups_Ozero__class_Ozero(X3920)
| X3918 = c_Groups_Ozero__class_Ozero(X3920)
| c_Groups_Ominus__class_Ominus(X3920,c_Rings_Oinverse__class_Oinverse(X3920,X3919),c_Rings_Oinverse__class_Oinverse(X3920,X3918)) = c_Groups_Ouminus__class_Ouminus(X3920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3920),c_Rings_Oinverse__class_Oinverse(X3920,X3919)),c_Groups_Ominus__class_Ominus(X3920,X3919,X3918))),c_Rings_Oinverse__class_Oinverse(X3920,X3918))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oinverse__diff__inverse])]) ).
fof(i_0_1362,plain,
! [X3888,X3889,X3890,X3891,X3892] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3892,X3891)
| 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),X3891),X3890),X3889),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3892),X3890),X3888)) = 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,X3891,X3892)),X3890),X3889),X3888) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).
fof(i_0_1363,plain,
! [X3873,X3874,X3875,X3876,X3877] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3877,X3876)
| 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),X3877),X3875),X3874),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3876),X3875),X3873)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3874,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,X3876,X3877)),X3875),X3873)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).
fof(i_0_1364,plain,
! [X4127,X4128,X4129,X4130] :
( ~ class_Rings_Ocomm__ring__1(X4130)
| hAPP(c_Polynomial_Opoly(X4130,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4130)),c_Polynomial_Omonom(X4130,c_Groups_Oone__class_Oone(X4130),X4129)),X4128)),X4127) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4130),hAPP(hAPP(c_Power_Opower__class_Opower(X4130),X4127),X4129)),hAPP(c_Polynomial_Opoly(X4130,X4128),X4127)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__replicate__append])]) ).
fof(i_0_1365,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))))),esk18_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_1366,plain,
! [X5367,X5368,X5369,X5370,X5371,X5372] :
( ( ~ c_Rings_Odvd__class_Odvd(X5370,X5369,c_Groups_Oplus__class_Oplus(X5370,X5371,X5367))
| c_Rings_Odvd__class_Odvd(X5370,X5369,c_Groups_Oplus__class_Oplus(X5370,c_Groups_Ominus__class_Ominus(X5370,X5371,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5370),X5372),X5368)),X5367))
| ~ c_Rings_Odvd__class_Odvd(X5370,X5369,X5368)
| ~ class_Rings_Ocomm__ring(X5370)
| ~ class_Rings_Odvd(X5370) )
& ( ~ c_Rings_Odvd__class_Odvd(X5370,X5369,c_Groups_Oplus__class_Oplus(X5370,c_Groups_Ominus__class_Ominus(X5370,X5371,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5370),X5372),X5368)),X5367))
| c_Rings_Odvd__class_Odvd(X5370,X5369,c_Groups_Oplus__class_Oplus(X5370,X5371,X5367))
| ~ c_Rings_Odvd__class_Odvd(X5370,X5369,X5368)
| ~ class_Rings_Ocomm__ring(X5370)
| ~ class_Rings_Odvd(X5370) ) ),
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_1367,plain,
! [X5361,X5362,X5363,X5364,X5365,X5366] :
( ( ~ c_Rings_Odvd__class_Odvd(X5364,X5363,c_Groups_Oplus__class_Oplus(X5364,X5365,X5361))
| c_Rings_Odvd__class_Odvd(X5364,X5363,c_Groups_Oplus__class_Oplus(X5364,c_Groups_Ominus__class_Ominus(X5364,X5365,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5364),X5366),X5362)),X5361))
| ~ c_Rings_Odvd__class_Odvd(X5364,X5363,X5362)
| ~ class_Rings_Ocomm__ring(X5364)
| ~ class_Rings_Odvd(X5364) )
& ( ~ c_Rings_Odvd__class_Odvd(X5364,X5363,c_Groups_Oplus__class_Oplus(X5364,c_Groups_Ominus__class_Ominus(X5364,X5365,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5364),X5366),X5362)),X5361))
| c_Rings_Odvd__class_Odvd(X5364,X5363,c_Groups_Oplus__class_Oplus(X5364,X5365,X5361))
| ~ c_Rings_Odvd__class_Odvd(X5364,X5363,X5362)
| ~ class_Rings_Ocomm__ring(X5364)
| ~ class_Rings_Odvd(X5364) ) ),
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_1368,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_1369,plain,
! [X4873,X4874,X4875,X4876,X4877,X4878] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4878),X4877),X4876) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4875),X4874),X4873)
| ~ 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),X4875),X4874),X4873),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4876,X4878)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4873)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4875)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4875,X4878)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4874,X4877) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).
fof(i_0_1370,plain,
! [X4884,X4885,X4886,X4887,X4888,X4889] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4889),X4888),X4887) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4886),X4885),X4884)
| ~ 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),X4886),X4885),X4884))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4884,X4886)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4887)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4886)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4886,X4889)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4888,X4885) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).
fof(i_0_1371,plain,
! [X5135,X5137,X5138] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_1(X5135))
| ~ class_RealVector_Oreal__normed__algebra(X5135) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5135,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5135),X5137),X5138)),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(X5135,X5137)),c_RealVector_Onorm__class_Onorm(X5135,X5138))),esk28_1(X5135)))
| ~ class_RealVector_Oreal__normed__algebra(X5135) ) ),
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_1372,plain,
! [X3991,X3992,X3993] :
( ~ class_Fields_Ofield(X3993)
| X3992 = c_Groups_Ozero__class_Ozero(X3993)
| X3991 = c_Groups_Ozero__class_Ozero(X3993)
| c_Groups_Oplus__class_Oplus(X3993,c_Rings_Oinverse__class_Oinverse(X3993,X3992),c_Rings_Oinverse__class_Oinverse(X3993,X3991)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3993),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3993),c_Groups_Oplus__class_Oplus(X3993,X3992,X3991)),c_Rings_Oinverse__class_Oinverse(X3993,X3992))),c_Rings_Oinverse__class_Oinverse(X3993,X3991)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__add])]) ).
fof(i_0_1373,plain,
! [X4890,X4891,X4892,X4893,X4894] :
( ~ 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),X4894),X4893),X4892),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4894),X4891),X4890))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4892)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4892,X4894)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4890,X4894)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4893,X4891) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).
fof(i_0_1374,plain,
! [X4879,X4880,X4881,X4882,X4883] :
( ~ 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),X4883),X4882),X4881),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4883),X4880),X4879))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4879,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4883,X4879)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4883,X4881)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4880,X4882) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).
fof(i_0_1375,plain,
! [X3883,X3884,X3885,X3886,X3887] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3886),X3885),X3884) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3887),X3885),X3883)
| 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,X3886,X3887)),X3885),X3884) = X3883
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3887,X3886) )
& ( 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,X3886,X3887)),X3885),X3884) != X3883
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3886),X3885),X3884) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3887),X3885),X3883)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3887,X3886) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).
fof(i_0_1376,plain,
! [X3868,X3869,X3870,X3871,X3872] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3870),X3869) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3871),X3870),X3868)
| X3869 = 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,X3871,X3872)),X3870),X3868)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3872,X3871) )
& ( X3869 != 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,X3871,X3872)),X3870),X3868)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3872),X3870),X3869) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3871),X3870),X3868)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3872,X3871) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).
fof(i_0_1377,plain,
! [X3427,X3428,X3429,X3430,X3431,X3432] :
( ( c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3431),X3430),X3429) != c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3428),X3430),X3427)
| c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),c_Groups_Ominus__class_Ominus(X3432,X3431,X3428)),X3430),X3429) = X3427
| ~ class_Rings_Oring(X3432) )
& ( c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),c_Groups_Ominus__class_Ominus(X3432,X3431,X3428)),X3430),X3429) != X3427
| c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3431),X3430),X3429) = c_Groups_Oplus__class_Oplus(X3432,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3432),X3428),X3430),X3427)
| ~ class_Rings_Oring(X3432) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).
fof(i_0_1378,plain,
! [X3433,X3434,X3435,X3436,X3437,X3438] :
( ( c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),X3437),X3436),X3435) != c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),X3434),X3436),X3433)
| X3435 = c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),c_Groups_Ominus__class_Ominus(X3438,X3434,X3437)),X3436),X3433)
| ~ class_Rings_Oring(X3438) )
& ( X3435 != c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),c_Groups_Ominus__class_Ominus(X3438,X3434,X3437)),X3436),X3433)
| c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),X3437),X3436),X3435) = c_Groups_Oplus__class_Oplus(X3438,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3438),X3434),X3436),X3433)
| ~ class_Rings_Oring(X3438) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).
fof(i_0_1379,plain,
! [X4768] :
( c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4768) != 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,X4768,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,X4768,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,X4768,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,X4768,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_1380,plain,
! [X3417,X3418,X3419,X3420,X3421] :
( ~ class_Rings_Oring(X3421)
| c_Groups_Ominus__class_Ominus(X3421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3421),X3420),X3419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3421),X3418),X3417)) = c_Groups_Oplus__class_Oplus(X3421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3421),X3420),c_Groups_Ominus__class_Ominus(X3421,X3419,X3417)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3421),c_Groups_Ominus__class_Ominus(X3421,X3420,X3418)),X3417)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__diff__mult])]) ).
fof(i_0_1381,plain,
! [X5253,X5254] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5254)
| 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,X5253)),X5254),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,X5254,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X5253)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_LIMSEQ__inverse__realpow__zero__lemma])]) ).
fof(i_0_1382,plain,
! [X3058,X3059,X3060,X3061,X3062] :
( ~ class_Rings_Osemiring(X3062)
| c_Groups_Oplus__class_Oplus(X3062,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3062),X3061),X3060),c_Groups_Oplus__class_Oplus(X3062,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3062),X3059),X3060),X3058)) = c_Groups_Oplus__class_Oplus(X3062,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3062),c_Groups_Oplus__class_Oplus(X3062,X3061,X3059)),X3060),X3058) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).
fof(i_0_1383,plain,
! [X3342,X3343,X3344] :
( ~ class_Rings_Odivision__ring(X3344)
| X3343 = c_Groups_Ozero__class_Ozero(X3344)
| X3342 = c_Groups_Ozero__class_Ozero(X3344)
| c_Groups_Ominus__class_Ominus(X3344,c_Rings_Oinverse__class_Oinverse(X3344,X3343),c_Rings_Oinverse__class_Oinverse(X3344,X3342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3344),c_Rings_Oinverse__class_Oinverse(X3344,X3343)),c_Groups_Ominus__class_Ominus(X3344,X3342,X3343))),c_Rings_Oinverse__class_Oinverse(X3344,X3342)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__diff])]) ).
fof(i_0_1384,plain,
! [X3447,X3448,X3449] :
( ~ class_Rings_Odivision__ring(X3449)
| X3448 = c_Groups_Ozero__class_Ozero(X3449)
| X3447 = c_Groups_Ozero__class_Ozero(X3449)
| c_Groups_Oplus__class_Oplus(X3449,c_Rings_Oinverse__class_Oinverse(X3449,X3448),c_Rings_Oinverse__class_Oinverse(X3449,X3447)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3449),c_Rings_Oinverse__class_Oinverse(X3449,X3448)),c_Groups_Oplus__class_Oplus(X3449,X3448,X3447))),c_Rings_Oinverse__class_Oinverse(X3449,X3447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_division__ring__inverse__add])]) ).
fof(i_0_1385,plain,
! [X3116,X3117,X3118,X3119,X3120,X3121] :
( ~ class_Rings_Olinordered__semiring__1(X3121)
| ~ c_Orderings_Oord__class_Oless__eq(X3121,X3120,X3119)
| ~ c_Orderings_Oord__class_Oless__eq(X3121,X3118,X3119)
| ~ c_Orderings_Oord__class_Oless__eq(X3121,c_Groups_Ozero__class_Ozero(X3121),X3117)
| ~ c_Orderings_Oord__class_Oless__eq(X3121,c_Groups_Ozero__class_Ozero(X3121),X3116)
| c_Groups_Oplus__class_Oplus(X3121,X3117,X3116) != c_Groups_Oone__class_Oone(X3121)
| c_Orderings_Oord__class_Oless__eq(X3121,c_Groups_Oplus__class_Oplus(X3121,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3121),X3117),X3120),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3121),X3116),X3118)),X3119) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).
fof(i_0_1386,plain,
! [X3128,X3129,X3130,X3131,X3132,X3133] :
( ~ class_Rings_Olinordered__semiring__1__strict(X3133)
| ~ c_Orderings_Oord__class_Oless(X3133,X3132,X3131)
| ~ c_Orderings_Oord__class_Oless(X3133,X3130,X3131)
| ~ c_Orderings_Oord__class_Oless__eq(X3133,c_Groups_Ozero__class_Ozero(X3133),X3129)
| ~ c_Orderings_Oord__class_Oless__eq(X3133,c_Groups_Ozero__class_Ozero(X3133),X3128)
| c_Groups_Oplus__class_Oplus(X3133,X3129,X3128) != c_Groups_Oone__class_Oone(X3133)
| c_Orderings_Oord__class_Oless(X3133,c_Groups_Oplus__class_Oplus(X3133,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3133),X3129),X3132),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3133),X3128),X3130)),X3131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).
fof(i_0_1387,plain,
! [X5373,X5374,X5375,X5376,X5378] :
( ( c_Rings_Odvd__class_Odvd(X5375,X5373,c_Groups_Oplus__class_Oplus(X5375,esk37_3(X5373,X5374,X5375),c_Groups_Ozero__class_Ozero(X5375)))
| ~ hBOOL(hAPP(X5374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5375),X5373),X5376)))
| ~ class_Rings_Odvd(X5375)
| ~ class_Rings_Osemiring__0(X5375) )
& ( hBOOL(hAPP(X5374,esk37_3(X5373,X5374,X5375)))
| ~ hBOOL(hAPP(X5374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5375),X5373),X5376)))
| ~ class_Rings_Odvd(X5375)
| ~ class_Rings_Osemiring__0(X5375) )
& ( ~ c_Rings_Odvd__class_Odvd(X5375,X5373,c_Groups_Oplus__class_Oplus(X5375,X5378,c_Groups_Ozero__class_Ozero(X5375)))
| ~ hBOOL(hAPP(X5374,X5378))
| hBOOL(hAPP(X5374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5375),X5373),esk38_3(X5373,X5374,X5375))))
| ~ class_Rings_Odvd(X5375)
| ~ class_Rings_Osemiring__0(X5375) ) ),
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_1388,plain,
! [X3632,X3633,X3634,X3635] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3635),X3634),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3633),X3634),X3632)) = 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,X3635,X3633)),X3634),X3632),
inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(i_0_1389,plain,
! [X4000,X4001,X4002,X4003] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4003)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4002)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4002),X4001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4003),X4000))
| 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,X4003)),X4001),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4002)),X4000)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel])]) ).
fof(i_0_1390,plain,
! [X4035,X4036,X4037] :
( ( ~ c_Orderings_Oord__class_Oless(X4037,c_Groups_Ozero__class_Ozero(X4037),c_Groups_Oplus__class_Oplus(X4037,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4036),X4036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4035),X4035)))
| X4036 != c_Groups_Ozero__class_Ozero(X4037)
| X4035 != c_Groups_Ozero__class_Ozero(X4037)
| ~ class_Rings_Olinordered__ring__strict(X4037) )
& ( X4036 = c_Groups_Ozero__class_Ozero(X4037)
| c_Orderings_Oord__class_Oless(X4037,c_Groups_Ozero__class_Ozero(X4037),c_Groups_Oplus__class_Oplus(X4037,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4036),X4036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4035),X4035)))
| ~ class_Rings_Olinordered__ring__strict(X4037) )
& ( X4035 = c_Groups_Ozero__class_Ozero(X4037)
| c_Orderings_Oord__class_Oless(X4037,c_Groups_Ozero__class_Ozero(X4037),c_Groups_Oplus__class_Oplus(X4037,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4036),X4036),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4037),X4035),X4035)))
| ~ class_Rings_Olinordered__ring__strict(X4037) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).
fof(i_0_1391,plain,
! [X4643,X4644,X4645,X4646,X4647] :
( ~ class_Rings_Ocomm__semiring__1(X4647)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4646),X4645)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4644),X4643)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4644),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4647),X4646),X4645)),X4643)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).
fof(i_0_1392,plain,
! [X4029,X4030,X4031] :
( ( X4030 = c_Groups_Ozero__class_Ozero(X4031)
| ~ c_Orderings_Oord__class_Oless__eq(X4031,c_Groups_Oplus__class_Oplus(X4031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4030),X4030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4029),X4029)),c_Groups_Ozero__class_Ozero(X4031))
| ~ class_Rings_Olinordered__ring__strict(X4031) )
& ( X4029 = c_Groups_Ozero__class_Ozero(X4031)
| ~ c_Orderings_Oord__class_Oless__eq(X4031,c_Groups_Oplus__class_Oplus(X4031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4030),X4030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4029),X4029)),c_Groups_Ozero__class_Ozero(X4031))
| ~ class_Rings_Olinordered__ring__strict(X4031) )
& ( X4030 != c_Groups_Ozero__class_Ozero(X4031)
| X4029 != c_Groups_Ozero__class_Ozero(X4031)
| c_Orderings_Oord__class_Oless__eq(X4031,c_Groups_Oplus__class_Oplus(X4031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4030),X4030),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4031),X4029),X4029)),c_Groups_Ozero__class_Ozero(X4031))
| ~ class_Rings_Olinordered__ring__strict(X4031) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).
fof(i_0_1393,plain,
! [X4032,X4033,X4034] :
( ~ class_Rings_Olinordered__ring(X4034)
| ~ c_Orderings_Oord__class_Oless(X4034,c_Groups_Oplus__class_Oplus(X4034,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4034),X4033),X4033),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4034),X4032),X4032)),c_Groups_Ozero__class_Ozero(X4034)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1281])]) ).
fof(i_0_1394,plain,
! [X3700,X3701] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3701)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3701,X3700)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3700,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),X3700)),X3701),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ath])]) ).
fof(i_0_1395,plain,
! [X4205,X4206,X4207,X4208] :
( ~ class_Rings_Ocomm__semiring__0(X4208)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4208)),c_Polynomial_OpCons(X4208,X4207,X4206)),X4205) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4208),c_Polynomial_Osmult(X4208,X4207,X4205),c_Polynomial_OpCons(X4208,c_Groups_Ozero__class_Ozero(X4208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4208)),X4206),X4205))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__left])]) ).
fof(i_0_1396,plain,
! [X5345,X5346,X5347,X5348] :
( ~ class_Rings_Ocomm__semiring__0(X5348)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5348,c_Polynomial_OpCons(X5348,X5347,X5346),X5345) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5348),c_Polynomial_Osmult(X5348,X5345,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5348,X5346,X5345)),c_Polynomial_OpCons(X5348,X5347,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5348,X5346,X5345))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__pCons])]) ).
fof(i_0_1397,plain,
! [X4004,X4005,X4006,X4007] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4007)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4006)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4006),X4005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4007),X4004))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4005),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4007)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X4004),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X4006))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__inverse__cancel2])]) ).
fof(i_0_1398,plain,
! [X3912,X3913,X3914] :
( ~ class_Groups_Omonoid__mult(X3914)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3913)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3914),hAPP(hAPP(c_Power_Opower__class_Opower(X3914),X3912),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3913,c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X3912) = hAPP(hAPP(c_Power_Opower__class_Opower(X3914),X3912),X3913) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__minus__mult])]) ).
fof(i_0_1399,plain,
! [X4692,X4693,X4694,X4695,X4696] :
( ( X4695 = X4694
| X4693 = X4692
| c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4692)) != c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4693))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4696) )
& ( X4695 != X4694
| c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4692)) = c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4693))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4696) )
& ( X4693 != X4692
| c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4692)) = c_Groups_Oplus__class_Oplus(X4696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4695),X4692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4696),X4694),X4693))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4696) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).
fof(i_0_1400,plain,
! [X4705,X4706,X4707,X4708,X4709] :
( ( c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4705)) != c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4707))
| X4708 = X4706
| X4707 = X4705
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4709) )
& ( X4708 != X4706
| c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4705)) = c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4707))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4709) )
& ( X4707 != X4705
| c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4707),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4705)) = c_Groups_Oplus__class_Oplus(X4709,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4708),X4705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4709),X4706),X4707))
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4709) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).
fof(i_0_1401,plain,
! [X4042,X4043,X4044,X4045] :
( ( c_Orderings_Oord__class_Oless(X4045,c_Groups_Ominus__class_Ominus(X4045,X4043,X4042),X4044)
| ~ c_Orderings_Oord__class_Oless(X4045,c_Groups_Oabs__class_Oabs(X4045,c_Groups_Ominus__class_Ominus(X4045,X4044,X4043)),X4042)
| ~ class_Rings_Olinordered__idom(X4045) )
& ( c_Orderings_Oord__class_Oless(X4045,X4044,c_Groups_Oplus__class_Oplus(X4045,X4043,X4042))
| ~ c_Orderings_Oord__class_Oless(X4045,c_Groups_Oabs__class_Oabs(X4045,c_Groups_Ominus__class_Ominus(X4045,X4044,X4043)),X4042)
| ~ class_Rings_Olinordered__idom(X4045) )
& ( ~ c_Orderings_Oord__class_Oless(X4045,c_Groups_Ominus__class_Ominus(X4045,X4043,X4042),X4044)
| ~ c_Orderings_Oord__class_Oless(X4045,X4044,c_Groups_Oplus__class_Oplus(X4045,X4043,X4042))
| c_Orderings_Oord__class_Oless(X4045,c_Groups_Oabs__class_Oabs(X4045,c_Groups_Ominus__class_Ominus(X4045,X4044,X4043)),X4042)
| ~ class_Rings_Olinordered__idom(X4045) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff])])]) ).
fof(i_0_1402,plain,
! [X4209,X4210,X4211,X4212] :
( ~ class_Rings_Ocomm__semiring__0(X4212)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4212)),X4211),c_Polynomial_OpCons(X4212,X4210,X4209)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4212),c_Polynomial_Osmult(X4212,X4210,X4211),c_Polynomial_OpCons(X4212,c_Groups_Ozero__class_Ozero(X4212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4212)),X4211),X4209))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pCons__right])]) ).
fof(i_0_1403,plain,
! [X3122,X3123,X3124] :
( ~ class_Rings_Oring__1(X3124)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3124),c_Groups_Ouminus__class_Ouminus(X3124,X3123)),X3122) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3124),hAPP(hAPP(c_Power_Opower__class_Opower(X3124),c_Groups_Ouminus__class_Ouminus(X3124,c_Groups_Oone__class_Oone(X3124))),X3122)),hAPP(hAPP(c_Power_Opower__class_Opower(X3124),X3123),X3122)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).
fof(i_0_1404,plain,
! [X4895,X4896,X4897] :
( ~ 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),X4897),X4896),X4895),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),X4895)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4897)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4896,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_1405,plain,
! [X4898,X4899,X4900] :
( ~ 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),X4900),X4899),X4898))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4898,X4900)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4900)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4899) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).
fof(i_0_1406,plain,
! [X4544,X4545,X4546] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4546)
| c_Orderings_Oord__class_Oless__eq(X4546,c_Groups_Oabs__class_Oabs(X4546,c_Groups_Ominus__class_Ominus(X4546,c_Groups_Oabs__class_Oabs(X4546,X4545),c_Groups_Oabs__class_Oabs(X4546,X4544))),c_Groups_Oabs__class_Oabs(X4546,c_Groups_Ominus__class_Ominus(X4546,X4545,X4544))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).
fof(i_0_1407,plain,
! [X3898,X3899,X3900] :
( ~ class_RealVector_Oreal__normed__vector(X3900)
| 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(X3900,X3899),c_RealVector_Onorm__class_Onorm(X3900,X3898))),c_RealVector_Onorm__class_Onorm(X3900,c_Groups_Ominus__class_Ominus(X3900,X3899,X3898))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq3])]) ).
fof(i_0_1408,plain,
! [X4743,X4744,X4745,X4746] :
( ~ class_Rings_Ocomm__semiring__0(X4746)
| c_Polynomial_Opcompose(X4746,c_Polynomial_OpCons(X4746,X4745,X4744),X4743) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4746),c_Polynomial_OpCons(X4746,X4745,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4746))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4746)),X4743),c_Polynomial_Opcompose(X4746,X4744,X4743))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__pCons])]) ).
fof(i_0_1409,plain,
! [X4648,X4649,X4650,X4651,X4652] :
( ~ class_Rings_Ocomm__semiring__1(X4652)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),X4651),X4650)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),X4649),X4648)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),X4651),X4649)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4652),X4650),X4648)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).
fof(i_0_1410,plain,
! [X4638,X4639,X4640,X4641,X4642] :
( ~ class_Rings_Ocomm__semiring__1(X4642)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),X4641),X4640)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),X4639),X4638)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),X4641),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),X4640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4642),X4639),X4638))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).
fof(i_0_1411,plain,
! [X4008,X4009] : 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,X4009,X4008)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4009)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4008)),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__ineq2]) ).
fof(i_0_1412,plain,
! [X3489,X3490] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3490),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3490,X3489)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3489))),
inference(variable_rename,[status(thm)],[fact_complex__mod__triangle__sub]) ).
fof(i_0_1413,plain,
! [X4057,X4058,X4059,X4060] :
( ~ class_Rings_Ocomm__semiring__0(X4060)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4060)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4060),X4059,X4058)),X4057) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4060)),X4059),X4057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4060)),X4058),X4057)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left])]) ).
fof(i_0_1414,plain,
! [X3860,X3861,X3862,X3863,X3864,X3865,X3866] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3861,X3860)
| hBOOL(hAPP(X3862,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3862,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3861,X3860))) )
& ( X3861 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3860,X3863)
| hBOOL(hAPP(X3862,X3863))
| ~ hBOOL(hAPP(X3862,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3861,X3860))) )
& ( X3865 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3864,esk14_3(X3864,X3865,X3866))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3865,X3864)
| hBOOL(hAPP(X3866,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3864))) )
& ( ~ hBOOL(hAPP(X3866,esk14_3(X3864,X3865,X3866)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3865,X3864)
| hBOOL(hAPP(X3866,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3864))) )
& ( X3865 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3864,esk14_3(X3864,X3865,X3866))
| ~ hBOOL(hAPP(X3866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3866,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3864))) )
& ( ~ hBOOL(hAPP(X3866,esk14_3(X3864,X3865,X3866)))
| ~ hBOOL(hAPP(X3866,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3866,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3865,X3864))) ) ),
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_1415,plain,
! [X3852,X3853,X3854,X3855,X3856,X3857,X3858] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3853,X3852)
| hBOOL(hAPP(X3854,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X3854,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3853,X3852))) )
& ( X3853 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3852,X3855)
| hBOOL(hAPP(X3854,X3855))
| ~ hBOOL(hAPP(X3854,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3853,X3852))) )
& ( X3857 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3856,esk13_3(X3856,X3857,X3858))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3857,X3856)
| hBOOL(hAPP(X3858,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3857,X3856))) )
& ( ~ hBOOL(hAPP(X3858,esk13_3(X3856,X3857,X3858)))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3857,X3856)
| hBOOL(hAPP(X3858,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3857,X3856))) )
& ( X3857 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3856,esk13_3(X3856,X3857,X3858))
| ~ hBOOL(hAPP(X3858,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3858,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3857,X3856))) )
& ( ~ hBOOL(hAPP(X3858,esk13_3(X3856,X3857,X3858)))
| ~ hBOOL(hAPP(X3858,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| hBOOL(hAPP(X3858,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3857,X3856))) ) ),
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_1282])])])])])]) ).
fof(i_0_1416,plain,
! [X3764,X3765,X3766,X3767,X3768] :
( ~ class_Rings_Olinordered__idom(X3768)
| ~ c_Orderings_Oord__class_Oless(X3768,c_Groups_Oabs__class_Oabs(X3768,X3767),X3766)
| ~ c_Orderings_Oord__class_Oless(X3768,c_Groups_Oabs__class_Oabs(X3768,X3765),X3764)
| c_Orderings_Oord__class_Oless(X3768,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3768),c_Groups_Oabs__class_Oabs(X3768,X3767)),c_Groups_Oabs__class_Oabs(X3768,X3765)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3768),X3766),X3764)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).
fof(i_0_1417,plain,
! [X4065,X4066,X4067,X4068,X4069] :
( ~ class_Rings_Ocomm__semiring__0(X4069)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4069)),c_Polynomial_Omonom(X4069,X4068,X4067)),c_Polynomial_Omonom(X4069,X4066,X4065)) = c_Polynomial_Omonom(X4069,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4069),X4068),X4066),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4067,X4065)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__monom])]) ).
fof(i_0_1418,plain,
! [X2793,X2794,X2795] :
( ~ class_Rings_Olinordered__semidom(X2795)
| ~ c_Orderings_Oord__class_Oless(X2795,c_Groups_Ozero__class_Ozero(X2795),X2794)
| ~ c_Orderings_Oord__class_Oless(X2795,X2794,c_Groups_Oone__class_Oone(X2795))
| c_Orderings_Oord__class_Oless(X2795,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2795),X2794),hAPP(hAPP(c_Power_Opower__class_Opower(X2795),X2794),X2793)),hAPP(hAPP(c_Power_Opower__class_Opower(X2795),X2794),X2793)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).
fof(i_0_1419,plain,
! [X4774] :
( ( ~ 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),X4774),X4774),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4774,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4774,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),X4774),X4774),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_1420,plain,
! [X3066,X3067,X3068,X3069,X3070] :
( ~ class_RealVector_Oreal__normed__vector(X3070)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3070,X3069),X3068)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3070,X3067),X3066)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3070,c_Groups_Oplus__class_Oplus(X3070,X3069,X3067)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3068,X3066)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__add__less])]) ).
fof(i_0_1421,plain,
! [X4131,X4132,X4133,X4134] :
( ~ class_Rings_Ocomm__semiring__0(X4134)
| hAPP(c_Polynomial_Opoly(X4134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4134)),X4133),X4132)),X4131) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4134),hAPP(c_Polynomial_Opoly(X4134,X4133),X4131)),hAPP(c_Polynomial_Opoly(X4134,X4132),X4131)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__mult])]) ).
fof(i_0_1422,plain,
! [X4017,X4018] :
( ( X4018 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4018),X4017) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4018),X4017) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4017,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4018,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X4017)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).
fof(i_0_1423,plain,
! [X3739,X3740,X3741] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3740,X3741),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3739,X3741))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3740,X3739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3741,X3739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3741,X3740) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3740,X3739)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3740,X3741),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3739,X3741))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3741,X3739)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3741,X3740) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).
fof(i_0_1424,plain,
! [X3799,X3800,X3801] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3800,X3801),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3799,X3801))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3800,X3799)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3801,X3799)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3801,X3800) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3800,X3799)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3800,X3801),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3799,X3801))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3801,X3799)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3801,X3800) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).
fof(i_0_1425,plain,
! [X3192,X3193,X3194,X3195,X3196] :
( ~ class_Rings_Oordered__semiring(X3196)
| ~ c_Orderings_Oord__class_Oless__eq(X3196,X3195,X3194)
| ~ c_Orderings_Oord__class_Oless__eq(X3196,X3193,X3192)
| ~ c_Orderings_Oord__class_Oless__eq(X3196,c_Groups_Ozero__class_Ozero(X3196),X3195)
| ~ c_Orderings_Oord__class_Oless__eq(X3196,c_Groups_Ozero__class_Ozero(X3196),X3193)
| c_Orderings_Oord__class_Oless__eq(X3196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3195),X3193),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3196),X3194),X3192)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).
fof(i_0_1426,plain,
! [X3197,X3198,X3199,X3200,X3201] :
( ~ class_Rings_Oordered__semiring(X3201)
| ~ c_Orderings_Oord__class_Oless__eq(X3201,X3200,X3199)
| ~ c_Orderings_Oord__class_Oless__eq(X3201,X3198,X3197)
| ~ c_Orderings_Oord__class_Oless__eq(X3201,c_Groups_Ozero__class_Ozero(X3201),X3199)
| ~ c_Orderings_Oord__class_Oless__eq(X3201,c_Groups_Ozero__class_Ozero(X3201),X3198)
| c_Orderings_Oord__class_Oless__eq(X3201,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3200),X3198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3201),X3199),X3197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).
fof(i_0_1427,plain,
! [X3292,X3293,X3294,X3295,X3296] :
( ~ class_Rings_Olinordered__semiring__strict(X3296)
| ~ c_Orderings_Oord__class_Oless(X3296,X3295,X3294)
| ~ c_Orderings_Oord__class_Oless__eq(X3296,X3293,X3292)
| ~ c_Orderings_Oord__class_Oless__eq(X3296,c_Groups_Ozero__class_Ozero(X3296),X3295)
| ~ c_Orderings_Oord__class_Oless(X3296,c_Groups_Ozero__class_Ozero(X3296),X3293)
| c_Orderings_Oord__class_Oless(X3296,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3296),X3295),X3293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3296),X3294),X3292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).
fof(i_0_1428,plain,
! [X3297,X3298,X3299,X3300,X3301] :
( ~ class_Rings_Olinordered__semiring__strict(X3301)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,X3300,X3299)
| ~ c_Orderings_Oord__class_Oless(X3301,X3298,X3297)
| ~ c_Orderings_Oord__class_Oless(X3301,c_Groups_Ozero__class_Ozero(X3301),X3300)
| ~ c_Orderings_Oord__class_Oless__eq(X3301,c_Groups_Ozero__class_Ozero(X3301),X3298)
| c_Orderings_Oord__class_Oless(X3301,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3300),X3298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3301),X3299),X3297)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).
fof(i_0_1429,plain,
! [X3287,X3288,X3289,X3290,X3291] :
( ~ class_Rings_Olinordered__semiring__strict(X3291)
| ~ c_Orderings_Oord__class_Oless(X3291,X3290,X3289)
| ~ c_Orderings_Oord__class_Oless(X3291,X3288,X3287)
| ~ c_Orderings_Oord__class_Oless__eq(X3291,c_Groups_Ozero__class_Ozero(X3291),X3290)
| ~ c_Orderings_Oord__class_Oless__eq(X3291,c_Groups_Ozero__class_Ozero(X3291),X3288)
| c_Orderings_Oord__class_Oless(X3291,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3291),X3290),X3288),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3291),X3289),X3287)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).
fof(i_0_1430,plain,
! [X3282,X3283,X3284,X3285,X3286] :
( ~ class_Rings_Olinordered__semiring__strict(X3286)
| ~ c_Orderings_Oord__class_Oless(X3286,X3285,X3284)
| ~ c_Orderings_Oord__class_Oless(X3286,X3283,X3282)
| ~ c_Orderings_Oord__class_Oless(X3286,c_Groups_Ozero__class_Ozero(X3286),X3284)
| ~ c_Orderings_Oord__class_Oless__eq(X3286,c_Groups_Ozero__class_Ozero(X3286),X3283)
| c_Orderings_Oord__class_Oless(X3286,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3285),X3283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3286),X3284),X3282)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).
fof(i_0_1431,plain,
! [X2807,X2808,X2809,X2810,X2811] :
( ~ class_RealVector_Oreal__normed__algebra(X2811)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2811,X2810),X2809)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2811,X2808),X2807)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2811,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2811),X2810),X2808)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2809),X2807)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__less])]) ).
fof(i_0_1432,plain,
! [X4609,X4610,X4611] :
( ~ class_Rings_Ocomm__semiring__0(X4611)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4611),X4610,c_Polynomial_Osmult(X4611,X4609,c_Polynomial_Osynthetic__div(X4611,X4610,X4609))) = c_Polynomial_OpCons(X4611,hAPP(c_Polynomial_Opoly(X4611,X4610),X4609),c_Polynomial_Osynthetic__div(X4611,X4610,X4609)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct])]) ).
fof(i_0_1433,plain,
! [X4714,X4715,X4716,X4717] :
( ~ class_Rings_Ocomm__semiring__1(X4717)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4717),X4716),X4715)),X4714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4717),hAPP(hAPP(c_Power_Opower__class_Opower(X4717),X4716),X4714)),hAPP(hAPP(c_Power_Opower__class_Opower(X4717),X4715),X4714)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).
fof(i_0_1434,plain,
! [X2882,X2883,X2884,X2885] :
( ~ class_Groups_Ocomm__monoid__mult(X2885)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2885),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2885),X2884),X2883)),X2882) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2885),hAPP(hAPP(c_Power_Opower__class_Opower(X2885),X2884),X2882)),hAPP(hAPP(c_Power_Opower__class_Opower(X2885),X2883),X2882)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).
fof(i_0_1435,plain,
! [X4026,X4027,X4028] :
( ~ class_Rings_Olinordered__ring(X4028)
| c_Orderings_Oord__class_Oless__eq(X4028,c_Groups_Ozero__class_Ozero(X4028),c_Groups_Oplus__class_Oplus(X4028,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4028),X4027),X4027),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4028),X4026),X4026))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).
fof(i_0_1436,plain,
! [X3478,X3479] :
( ~ class_Rings_Oring__1(X3479)
| c_Groups_Ominus__class_Ominus(X3479,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3479),X3478),X3478),c_Groups_Oone__class_Oone(X3479)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3479),c_Groups_Oplus__class_Oplus(X3479,X3478,c_Groups_Oone__class_Oone(X3479))),c_Groups_Ominus__class_Ominus(X3479,X3478,c_Groups_Oone__class_Oone(X3479))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored])]) ).
fof(i_0_1437,plain,
! [X4038,X4039,X4040,X4041] :
( ~ class_Rings_Ocomm__semiring__0(X4041)
| hAPP(c_Polynomial_Opoly(X4041,c_Polynomial_OpCons(X4041,X4040,X4039)),X4038) = c_Groups_Oplus__class_Oplus(X4041,X4040,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4041),X4038),hAPP(c_Polynomial_Opoly(X4041,X4039),X4038))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pCons])]) ).
fof(i_0_1438,plain,
! [X2994,X2995,X2996] :
( ~ class_Rings_Olinordered__semidom(X2996)
| ~ c_Orderings_Oord__class_Oless(X2996,c_Groups_Oone__class_Oone(X2996),X2995)
| c_Orderings_Oord__class_Oless(X2996,hAPP(hAPP(c_Power_Opower__class_Opower(X2996),X2995),X2994),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2996),X2995),hAPP(hAPP(c_Power_Opower__class_Opower(X2996),X2995),X2994))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).
fof(i_0_1439,plain,
! [X3007,X3008,X3009,X3010] :
( ~ class_Rings_Olinordered__semiring__strict(X3010)
| ~ c_Orderings_Oord__class_Oless__eq(X3010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3010),X3009),X3008),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3010),X3007),X3008))
| ~ c_Orderings_Oord__class_Oless(X3010,c_Groups_Ozero__class_Ozero(X3010),X3008)
| c_Orderings_Oord__class_Oless__eq(X3010,X3009,X3007) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).
fof(i_0_1440,plain,
! [X3274,X3275,X3276,X3277] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3276),X3275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3276),X3274))
| c_Orderings_Oord__class_Oless__eq(X3277,X3275,X3274)
| ~ c_Orderings_Oord__class_Oless(X3277,c_Groups_Ozero__class_Ozero(X3277),X3276)
| ~ class_Rings_Olinordered__ring__strict(X3277) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3277,X3275,X3274)
| c_Orderings_Oord__class_Oless__eq(X3277,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3276),X3275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3277),X3276),X3274))
| ~ c_Orderings_Oord__class_Oless(X3277,c_Groups_Ozero__class_Ozero(X3277),X3276)
| ~ class_Rings_Olinordered__ring__strict(X3277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).
fof(i_0_1441,plain,
! [X3003,X3004,X3005,X3006] :
( ~ class_Rings_Olinordered__semiring__strict(X3006)
| ~ c_Orderings_Oord__class_Oless__eq(X3006,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3006),X3005),X3004),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3006),X3005),X3003))
| ~ c_Orderings_Oord__class_Oless(X3006,c_Groups_Ozero__class_Ozero(X3006),X3005)
| c_Orderings_Oord__class_Oless__eq(X3006,X3004,X3003) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).
fof(i_0_1442,plain,
! [X3302,X3303,X3304,X3305] :
( ~ class_Rings_Olinordered__semiring(X3305)
| ~ c_Orderings_Oord__class_Oless(X3305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3305),X3304),X3303),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3305),X3302),X3303))
| ~ c_Orderings_Oord__class_Oless__eq(X3305,c_Groups_Ozero__class_Ozero(X3305),X3303)
| c_Orderings_Oord__class_Oless(X3305,X3304,X3302) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).
fof(i_0_1443,plain,
! [X3306,X3307,X3308,X3309] :
( ~ class_Rings_Olinordered__semiring__strict(X3309)
| ~ c_Orderings_Oord__class_Oless(X3309,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3309),X3308),X3307),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3309),X3306),X3307))
| ~ c_Orderings_Oord__class_Oless__eq(X3309,c_Groups_Ozero__class_Ozero(X3309),X3307)
| c_Orderings_Oord__class_Oless(X3309,X3308,X3306) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).
fof(i_0_1444,plain,
! [X2970,X2971,X2972,X2973] :
( ~ class_Rings_Olinordered__semidom(X2973)
| ~ c_Orderings_Oord__class_Oless(X2973,hAPP(hAPP(c_Power_Opower__class_Opower(X2973),X2972),X2971),hAPP(hAPP(c_Power_Opower__class_Opower(X2973),X2970),X2971))
| ~ c_Orderings_Oord__class_Oless__eq(X2973,c_Groups_Ozero__class_Ozero(X2973),X2970)
| c_Orderings_Oord__class_Oless(X2973,X2972,X2970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).
fof(i_0_1445,plain,
! [X3218,X3219,X3220,X3221] :
( ( ~ c_Orderings_Oord__class_Oless(X3221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3221),X3220),X3219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3221),X3220),X3218))
| c_Orderings_Oord__class_Oless(X3221,X3219,X3218)
| ~ c_Orderings_Oord__class_Oless(X3221,c_Groups_Ozero__class_Ozero(X3221),X3220)
| ~ class_Rings_Olinordered__ring__strict(X3221) )
& ( ~ c_Orderings_Oord__class_Oless(X3221,X3219,X3218)
| c_Orderings_Oord__class_Oless(X3221,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3221),X3220),X3219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3221),X3220),X3218))
| ~ c_Orderings_Oord__class_Oless(X3221,c_Groups_Ozero__class_Ozero(X3221),X3220)
| ~ class_Rings_Olinordered__ring__strict(X3221) ) ),
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] :
( ~ class_Rings_Olinordered__semiring(X3018)
| ~ c_Orderings_Oord__class_Oless(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,c_Groups_Ozero__class_Ozero(X3018),X3017)
| c_Orderings_Oord__class_Oless(X3018,X3016,X3015) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).
fof(i_0_1447,plain,
! [X3011,X3012,X3013,X3014] :
( ~ class_Rings_Olinordered__semiring__strict(X3014)
| ~ c_Orderings_Oord__class_Oless(X3014,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3014),X3013),X3012),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3014),X3013),X3011))
| ~ c_Orderings_Oord__class_Oless__eq(X3014,c_Groups_Ozero__class_Ozero(X3014),X3013)
| c_Orderings_Oord__class_Oless(X3014,X3012,X3011) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).
fof(i_0_1448,plain,
! [X3278,X3279,X3280,X3281] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3281,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3280),X3279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3280),X3278))
| c_Orderings_Oord__class_Oless__eq(X3281,X3278,X3279)
| ~ c_Orderings_Oord__class_Oless(X3281,X3280,c_Groups_Ozero__class_Ozero(X3281))
| ~ class_Rings_Olinordered__ring__strict(X3281) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3281,X3278,X3279)
| c_Orderings_Oord__class_Oless__eq(X3281,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3280),X3279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3281),X3280),X3278))
| ~ c_Orderings_Oord__class_Oless(X3281,X3280,c_Groups_Ozero__class_Ozero(X3281))
| ~ class_Rings_Olinordered__ring__strict(X3281) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).
fof(i_0_1449,plain,
! [X3237,X3238,X3239,X3240] :
( ( ~ c_Orderings_Oord__class_Oless(X3240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3240),X3239),X3238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3240),X3239),X3237))
| c_Orderings_Oord__class_Oless(X3240,X3237,X3238)
| ~ c_Orderings_Oord__class_Oless(X3240,X3239,c_Groups_Ozero__class_Ozero(X3240))
| ~ class_Rings_Olinordered__ring__strict(X3240) )
& ( ~ c_Orderings_Oord__class_Oless(X3240,X3237,X3238)
| c_Orderings_Oord__class_Oless(X3240,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3240),X3239),X3238),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3240),X3239),X3237))
| ~ c_Orderings_Oord__class_Oless(X3240,X3239,c_Groups_Ozero__class_Ozero(X3240))
| ~ class_Rings_Olinordered__ring__strict(X3240) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).
fof(i_0_1450,plain,
! [X2990,X2991,X2992,X2993] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X2993,hAPP(hAPP(c_Power_Opower__class_Opower(X2993),X2992),X2991),hAPP(hAPP(c_Power_Opower__class_Opower(X2993),X2992),X2990))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2991,X2990)
| ~ c_Orderings_Oord__class_Oless(X2993,c_Groups_Oone__class_Oone(X2993),X2992)
| ~ class_Rings_Olinordered__semidom(X2993) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2991,X2990)
| c_Orderings_Oord__class_Oless__eq(X2993,hAPP(hAPP(c_Power_Opower__class_Opower(X2993),X2992),X2991),hAPP(hAPP(c_Power_Opower__class_Opower(X2993),X2992),X2990))
| ~ c_Orderings_Oord__class_Oless(X2993,c_Groups_Oone__class_Oone(X2993),X2992)
| ~ class_Rings_Olinordered__semidom(X2993) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).
fof(i_0_1451,plain,
! [X2986,X2987,X2988,X2989] :
( ~ class_Rings_Olinordered__semidom(X2989)
| ~ c_Orderings_Oord__class_Oless(X2989,c_Groups_Oone__class_Oone(X2989),X2988)
| ~ c_Orderings_Oord__class_Oless__eq(X2989,hAPP(hAPP(c_Power_Opower__class_Opower(X2989),X2988),X2987),hAPP(hAPP(c_Power_Opower__class_Opower(X2989),X2988),X2986))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2987,X2986) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).
fof(i_0_1452,plain,
! [X2929,X2930,X2931,X2932] :
( ( ~ c_Orderings_Oord__class_Oless(X2932,hAPP(hAPP(c_Power_Opower__class_Opower(X2932),X2931),X2930),hAPP(hAPP(c_Power_Opower__class_Opower(X2932),X2931),X2929))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2930,X2929)
| ~ c_Orderings_Oord__class_Oless(X2932,c_Groups_Oone__class_Oone(X2932),X2931)
| ~ class_Rings_Olinordered__semidom(X2932) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2930,X2929)
| c_Orderings_Oord__class_Oless(X2932,hAPP(hAPP(c_Power_Opower__class_Opower(X2932),X2931),X2930),hAPP(hAPP(c_Power_Opower__class_Opower(X2932),X2931),X2929))
| ~ c_Orderings_Oord__class_Oless(X2932,c_Groups_Oone__class_Oone(X2932),X2931)
| ~ class_Rings_Olinordered__semidom(X2932) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).
fof(i_0_1453,plain,
! [X2925,X2926,X2927,X2928] :
( ~ class_Rings_Olinordered__semidom(X2928)
| ~ c_Orderings_Oord__class_Oless(X2928,c_Groups_Oone__class_Oone(X2928),X2927)
| ~ c_Orderings_Oord__class_Oless(X2928,hAPP(hAPP(c_Power_Opower__class_Opower(X2928),X2927),X2926),hAPP(hAPP(c_Power_Opower__class_Opower(X2928),X2927),X2925))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2926,X2925) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).
fof(i_0_1454,plain,
! [X4157,X4158,X4159,X4160,X4161] :
( ~ class_Groups_Oab__group__add(X4161)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4161),c_Polynomial_OpCons(X4161,X4160,X4159),c_Polynomial_OpCons(X4161,X4158,X4157)) = c_Polynomial_OpCons(X4161,c_Groups_Ominus__class_Ominus(X4161,X4160,X4158),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4161),X4159,X4157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__pCons])]) ).
fof(i_0_1455,plain,
! [X4145,X4146,X4147,X4148,X4149] :
( ~ class_Groups_Ocomm__monoid__add(X4149)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4149),c_Polynomial_OpCons(X4149,X4148,X4147),c_Polynomial_OpCons(X4149,X4146,X4145)) = c_Polynomial_OpCons(X4149,c_Groups_Oplus__class_Oplus(X4149,X4148,X4146),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4149),X4147,X4145)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pCons])]) ).
fof(i_0_1456,plain,
! [X4153,X4154,X4155,X4156] :
( ~ class_Rings_Ocomm__semiring__1(X4156)
| hAPP(c_Polynomial_Opoly(X4156,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(X4156)),X4155),X4154)),X4153) = hAPP(hAPP(c_Power_Opower__class_Opower(X4156),hAPP(c_Polynomial_Opoly(X4156,X4155),X4153)),X4154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__power])]) ).
fof(i_0_1457,plain,
! [X5155,X5156] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5155)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(X5156)),c_RComplete_Onatfloor(X5155)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5156),X5155))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor])]) ).
fof(i_0_1458,plain,
! [X3931,X3932,X3933,X3934,X3935] :
( ~ class_Groups_Oab__group__add(X3935)
| c_Groups_Ominus__class_Ominus(X3935,c_Groups_Oplus__class_Oplus(X3935,X3934,X3933),c_Groups_Oplus__class_Oplus(X3935,X3932,X3931)) = c_Groups_Oplus__class_Oplus(X3935,c_Groups_Ominus__class_Ominus(X3935,X3934,X3932),c_Groups_Ominus__class_Ominus(X3935,X3933,X3931)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Deriv_Oadd__diff__add])]) ).
fof(i_0_1459,plain,
! [X4653,X4654,X4655,X4656,X4657] :
( ~ class_Rings_Ocomm__semiring__1(X4657)
| c_Groups_Oplus__class_Oplus(X4657,c_Groups_Oplus__class_Oplus(X4657,X4656,X4655),c_Groups_Oplus__class_Oplus(X4657,X4654,X4653)) = c_Groups_Oplus__class_Oplus(X4657,c_Groups_Oplus__class_Oplus(X4657,X4656,X4654),c_Groups_Oplus__class_Oplus(X4657,X4655,X4653)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).
fof(i_0_1460,plain,
! [X2978,X2979,X2980,X2981] :
( ~ class_Rings_Olinordered__semidom(X2981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2980,X2979)
| ~ c_Orderings_Oord__class_Oless__eq(X2981,c_Groups_Ozero__class_Ozero(X2981),X2978)
| ~ c_Orderings_Oord__class_Oless__eq(X2981,X2978,c_Groups_Oone__class_Oone(X2981))
| c_Orderings_Oord__class_Oless__eq(X2981,hAPP(hAPP(c_Power_Opower__class_Opower(X2981),X2978),X2979),hAPP(hAPP(c_Power_Opower__class_Opower(X2981),X2978),X2980)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).
fof(i_0_1461,plain,
! [X2982,X2983,X2984,X2985] :
( ~ class_Rings_Olinordered__semidom(X2985)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2984,X2983)
| ~ c_Orderings_Oord__class_Oless(X2985,c_Groups_Ozero__class_Ozero(X2985),X2982)
| ~ c_Orderings_Oord__class_Oless(X2985,X2982,c_Groups_Oone__class_Oone(X2985))
| c_Orderings_Oord__class_Oless(X2985,hAPP(hAPP(c_Power_Opower__class_Opower(X2985),X2982),X2983),hAPP(hAPP(c_Power_Opower__class_Opower(X2985),X2982),X2984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).
fof(i_0_1462,plain,
! [X2974,X2975,X2976,X2977] :
( ~ class_Rings_Olinordered__semidom(X2977)
| ~ c_Orderings_Oord__class_Oless(X2977,X2976,X2975)
| ~ c_Orderings_Oord__class_Oless__eq(X2977,c_Groups_Ozero__class_Ozero(X2977),X2976)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2974)
| c_Orderings_Oord__class_Oless(X2977,hAPP(hAPP(c_Power_Opower__class_Opower(X2977),X2976),X2974),hAPP(hAPP(c_Power_Opower__class_Opower(X2977),X2975),X2974)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).
fof(i_0_1463,plain,
! [X3214,X3215,X3216,X3217] :
( ( c_Orderings_Oord__class_Oless(X3217,X3216,c_Groups_Ozero__class_Ozero(X3217))
| c_Orderings_Oord__class_Oless(X3217,c_Groups_Ozero__class_Ozero(X3217),X3216)
| ~ c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( c_Orderings_Oord__class_Oless(X3217,X3214,X3215)
| c_Orderings_Oord__class_Oless(X3217,c_Groups_Ozero__class_Ozero(X3217),X3216)
| ~ c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( c_Orderings_Oord__class_Oless(X3217,X3216,c_Groups_Ozero__class_Ozero(X3217))
| c_Orderings_Oord__class_Oless(X3217,X3215,X3214)
| ~ c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( c_Orderings_Oord__class_Oless(X3217,X3214,X3215)
| c_Orderings_Oord__class_Oless(X3217,X3215,X3214)
| ~ c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( ~ c_Orderings_Oord__class_Oless(X3217,c_Groups_Ozero__class_Ozero(X3217),X3216)
| ~ c_Orderings_Oord__class_Oless(X3217,X3215,X3214)
| c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) )
& ( ~ c_Orderings_Oord__class_Oless(X3217,X3216,c_Groups_Ozero__class_Ozero(X3217))
| ~ c_Orderings_Oord__class_Oless(X3217,X3214,X3215)
| c_Orderings_Oord__class_Oless(X3217,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3217),X3216),X3214))
| ~ class_Rings_Olinordered__ring__strict(X3217) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).
fof(i_0_1464,plain,
! [X3210,X3211,X3212,X3213] :
( ( c_Orderings_Oord__class_Oless(X3213,X3211,c_Groups_Ozero__class_Ozero(X3213))
| c_Orderings_Oord__class_Oless(X3213,c_Groups_Ozero__class_Ozero(X3213),X3211)
| ~ c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) )
& ( c_Orderings_Oord__class_Oless(X3213,X3210,X3212)
| c_Orderings_Oord__class_Oless(X3213,c_Groups_Ozero__class_Ozero(X3213),X3211)
| ~ c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) )
& ( c_Orderings_Oord__class_Oless(X3213,X3211,c_Groups_Ozero__class_Ozero(X3213))
| c_Orderings_Oord__class_Oless(X3213,X3212,X3210)
| ~ c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) )
& ( c_Orderings_Oord__class_Oless(X3213,X3210,X3212)
| c_Orderings_Oord__class_Oless(X3213,X3212,X3210)
| ~ c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) )
& ( ~ c_Orderings_Oord__class_Oless(X3213,c_Groups_Ozero__class_Ozero(X3213),X3211)
| ~ c_Orderings_Oord__class_Oless(X3213,X3212,X3210)
| c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) )
& ( ~ c_Orderings_Oord__class_Oless(X3213,X3211,c_Groups_Ozero__class_Ozero(X3213))
| ~ c_Orderings_Oord__class_Oless(X3213,X3210,X3212)
| c_Orderings_Oord__class_Oless(X3213,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3212),X3211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3213),X3210),X3211))
| ~ class_Rings_Olinordered__ring__strict(X3213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).
fof(i_0_1465,plain,
! [X5139,X5140,X5142] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X5139,X5140))
| ~ class_RealVector_Oreal__normed__algebra(X5140) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5140,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5140),X5142),X5139)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5140,X5142)),esk29_2(X5139,X5140)))
| ~ class_RealVector_Oreal__normed__algebra(X5140) ) ),
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_1466,plain,
! [X2812,X2813,X2814] :
( ~ class_RealVector_Oreal__normed__algebra(X2814)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2814),X2813),X2812)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2814,X2813)),c_RealVector_Onorm__class_Onorm(X2814,X2812))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult__ineq])]) ).
fof(i_0_1467,plain,
! [X5143,X5144,X5146] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk30_2(X5143,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),X5143),X5146)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X5144,X5146)),esk30_2(X5143,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__right_Opos__bounded])])])])]) ).
fof(i_0_1468,plain,
! [X4701,X4702,X4703,X4704] :
( ~ class_Rings_Ocomm__semiring__1(X4704)
| c_Groups_Oplus__class_Oplus(X4704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4704),X4703),X4702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4704),X4701),X4702)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4704),c_Groups_Oplus__class_Oplus(X4704,X4703,X4701)),X4702) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).
fof(i_0_1469,plain,
! [X3385,X3386,X3387,X3388] :
( ~ class_RealVector_Oreal__normed__algebra(X3388)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3388),c_Groups_Ominus__class_Ominus(X3388,X3387,X3386)),X3385) = c_Groups_Ominus__class_Ominus(X3388,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3388),X3387),X3385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3388),X3386),X3385)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__left])]) ).
fof(i_0_1470,plain,
! [X3381,X3382,X3383,X3384] :
( ~ class_RealVector_Oreal__normed__algebra(X3384)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3384),c_Groups_Ominus__class_Ominus(X3384,X3383,X3382)),X3381) = c_Groups_Ominus__class_Ominus(X3384,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3384),X3383),X3381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3384),X3382),X3381)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Odiff])]) ).
fof(i_0_1471,plain,
! [X4697,X4698,X4699,X4700] :
( ~ class_Rings_Ocomm__semiring__1(X4700)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4700),c_Groups_Oplus__class_Oplus(X4700,X4699,X4698)),X4697) = c_Groups_Oplus__class_Oplus(X4700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4700),X4699),X4697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4700),X4698),X4697)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).
fof(i_0_1472,plain,
! [X3054,X3055,X3056,X3057] :
( ~ class_Rings_Ocomm__semiring(X3057)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3057),c_Groups_Oplus__class_Oplus(X3057,X3056,X3055)),X3054) = c_Groups_Oplus__class_Oplus(X3057,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3057),X3056),X3054),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3057),X3055),X3054)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).
fof(i_0_1473,plain,
! [X3095,X3096,X3097,X3098] :
( ~ class_RealVector_Oreal__normed__algebra(X3098)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),c_Groups_Oplus__class_Oplus(X3098,X3097,X3096)),X3095) = c_Groups_Oplus__class_Oplus(X3098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3097),X3095),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3098),X3096),X3095)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Oadd])]) ).
fof(i_0_1474,plain,
! [X3091,X3092,X3093,X3094] :
( ~ class_RealVector_Oreal__normed__algebra(X3094)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3094),c_Groups_Oplus__class_Oplus(X3094,X3093,X3092)),X3091) = c_Groups_Oplus__class_Oplus(X3094,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3094),X3093),X3091),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3094),X3092),X3091)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__left])]) ).
fof(i_0_1475,plain,
! [X4613,X4614,X4615,X4616] :
( ~ class_Rings_Ocomm__semiring__1(X4616)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4616),hAPP(hAPP(c_Power_Opower__class_Opower(X4616),X4615),X4614)),hAPP(hAPP(c_Power_Opower__class_Opower(X4616),X4615),X4613)) = hAPP(hAPP(c_Power_Opower__class_Opower(X4616),X4615),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4614,X4613)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).
fof(i_0_1476,plain,
! [X3112,X3113,X3114,X3115] :
( ~ class_Groups_Omonoid__mult(X3115)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3115),X3114),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3113,X3112)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3115),hAPP(hAPP(c_Power_Opower__class_Opower(X3115),X3114),X3113)),hAPP(hAPP(c_Power_Opower__class_Opower(X3115),X3114),X3112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).
fof(i_0_1477,plain,
! [X4634,X4635,X4636,X4637] :
( ~ class_Rings_Ocomm__semiring__1(X4637)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4636),X4635)),X4634) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4637),X4636),X4634)),X4635) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).
fof(i_0_1478,plain,
! [X4547,X4548,X4549] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4549)
| c_Orderings_Oord__class_Oless__eq(X4549,c_Groups_Ominus__class_Ominus(X4549,c_Groups_Oabs__class_Oabs(X4549,X4548),c_Groups_Oabs__class_Oabs(X4549,X4547)),c_Groups_Oabs__class_Oabs(X4549,c_Groups_Ominus__class_Ominus(X4549,X4548,X4547))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).
fof(i_0_1479,plain,
! [X4550,X4551,X4552] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4552)
| c_Orderings_Oord__class_Oless__eq(X4552,c_Groups_Ominus__class_Ominus(X4552,c_Groups_Oabs__class_Oabs(X4552,X4551),c_Groups_Oabs__class_Oabs(X4552,X4550)),c_Groups_Oabs__class_Oabs(X4552,c_Groups_Ominus__class_Ominus(X4552,X4550,X4551))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).
fof(i_0_1480,plain,
! [X4222,X4223,X4224] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4224)
| c_Orderings_Oord__class_Oless__eq(X4224,c_Groups_Oabs__class_Oabs(X4224,c_Groups_Ominus__class_Ominus(X4224,X4223,X4222)),c_Groups_Oplus__class_Oplus(X4224,c_Groups_Oabs__class_Oabs(X4224,X4223),c_Groups_Oabs__class_Oabs(X4224,X4222))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).
fof(i_0_1481,plain,
! [X4541,X4542,X4543] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4543)
| c_Orderings_Oord__class_Oless__eq(X4543,c_Groups_Oabs__class_Oabs(X4543,c_Groups_Oplus__class_Oplus(X4543,X4542,X4541)),c_Groups_Oplus__class_Oplus(X4543,c_Groups_Oabs__class_Oabs(X4543,X4542),c_Groups_Oabs__class_Oabs(X4543,X4541))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).
fof(i_0_1482,plain,
! [X4724,X4725,X4726,X4727,X4728,X4729] :
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4729)
| X4728 = c_Groups_Ozero__class_Ozero(X4729)
| X4727 != X4726
| X4725 = X4724
| c_Groups_Oplus__class_Oplus(X4729,X4727,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4729),X4728),X4725)) != c_Groups_Oplus__class_Oplus(X4729,X4726,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4729),X4728),X4724)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).
fof(i_0_1483,plain,
! [X3687,X3688,X3689] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3689),X3688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3687),X3688))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3688)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3689,X3687) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3688)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3689),X3688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3687),X3688)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3689,X3687)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3689),X3688),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3687),X3688)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).
fof(i_0_1484,plain,
! [X3684,X3685,X3686] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3684))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3686)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3685,X3684) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3686)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3684)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3685,X3684)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3686),X3684)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).
fof(i_0_1485,plain,
! [X3313,X3314,X3315] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3315),X3314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3315),X3313))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3314,X3313)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3315) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3314,X3313)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3315),X3314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3315),X3313))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3315) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).
fof(i_0_1486,plain,
! [X2801,X2802,X2803] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2802),X2803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2801),X2803))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2802,X2801)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2803) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2802,X2801)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2802),X2803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2801),X2803))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2803) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1])])]) ).
fof(i_0_1487,plain,
! [X2804,X2805,X2806] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2806),X2805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2806),X2804))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2805,X2804)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2806) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2805,X2804)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2806),X2805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2806),X2804))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2806) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2])])]) ).
fof(i_0_1488,plain,
! [X3673,X3674,X3675] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3675),X3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3675),X3673))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3674,X3673)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3675) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3674,X3673)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3675),X3674),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3675),X3673))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3675) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).
fof(i_0_1489,plain,
! [X2824,X2825,X2826] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2826)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2826),X2825),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2826),X2824))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2825,X2824) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).
fof(i_0_1490,plain,
! [X2952,X2953,X2954] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2953),X2954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2952),X2954))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2953,X2952)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2954) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2953,X2952)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2953),X2954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2952),X2954))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2954) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1])])]) ).
fof(i_0_1491,plain,
! [X5177,X5178] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5178),X5177)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5177,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5178),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatceiling(X5177) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5178,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__eq])]) ).
fof(i_0_1492,plain,
! [X3349,X3350,X3351] :
( ~ class_RealVector_Oreal__normed__vector(X3351)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3351,X3350),c_RealVector_Onorm__class_Onorm(X3351,X3349)),c_RealVector_Onorm__class_Onorm(X3351,c_Groups_Ominus__class_Ominus(X3351,X3350,X3349))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq2])]) ).
fof(i_0_1493,plain,
! [X3486,X3487,X3488] :
( ~ class_RealVector_Oreal__normed__vector(X3488)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3488,X3487),c_RealVector_Onorm__class_Onorm(X3488,X3486)),c_RealVector_Onorm__class_Onorm(X3488,c_Groups_Oplus__class_Oplus(X3488,X3487,X3486))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__diff__ineq])]) ).
fof(i_0_1494,plain,
! [X3356,X3357,X3358] :
( ~ class_RealVector_Oreal__normed__vector(X3358)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3358,c_Groups_Ominus__class_Ominus(X3358,X3357,X3356)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3358,X3357),c_RealVector_Onorm__class_Onorm(X3358,X3356))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq4])]) ).
fof(i_0_1495,plain,
! [X3063,X3064,X3065] :
( ~ class_RealVector_Oreal__normed__vector(X3065)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3065,c_Groups_Oplus__class_Oplus(X3065,X3064,X3063)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3065,X3064),c_RealVector_Onorm__class_Onorm(X3065,X3063))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__triangle__ineq])]) ).
fof(i_0_1496,plain,
! [X4116,X4117,X4118,X4119] :
( ~ class_Rings_Ocomm__semiring__0(X4119)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4119)),c_Polynomial_Osmult(X4119,X4118,X4117)),X4116) = c_Polynomial_Osmult(X4119,X4118,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4119)),X4117),X4116)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__left])]) ).
fof(i_0_1497,plain,
! [X4141,X4142,X4143,X4144] :
( ~ class_Rings_Ocomm__ring(X4144)
| hAPP(c_Polynomial_Opoly(X4144,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4144),X4143,X4142)),X4141) = c_Groups_Ominus__class_Ominus(X4144,hAPP(c_Polynomial_Opoly(X4144,X4143),X4141),hAPP(c_Polynomial_Opoly(X4144,X4142),X4141)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__diff])]) ).
fof(i_0_1498,plain,
! [X4135,X4136,X4137,X4138] :
( ~ class_Rings_Ocomm__semiring__0(X4138)
| hAPP(c_Polynomial_Opoly(X4138,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4138),X4137,X4136)),X4135) = c_Groups_Oplus__class_Oplus(X4138,hAPP(c_Polynomial_Opoly(X4138,X4137),X4135),hAPP(c_Polynomial_Opoly(X4138,X4136),X4135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__add])]) ).
fof(i_0_1499,plain,
! [X3816,X3817,X3818] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3816,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3817,X3818))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3816,X3818),X3817)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3818,X3817) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3816,X3818),X3817)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3816,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3817,X3818))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3818,X3817) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).
fof(i_0_1500,plain,
! [X4805,X4806,X4807] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4807,X4806)),X4805) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4807),X4805),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4806),X4805)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(i_0_1501,plain,
! [X4785,X4786,X4787] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4787,X4786)),X4785) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4787),X4785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4786),X4785)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(i_0_1502,plain,
! [X3761,X3762,X3763] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3763,X3762)),X3761) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3763),X3761),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3762),X3761)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).
fof(i_0_1503,plain,
! [X3636,X3637,X3638] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3638,X3637)),X3636) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3638),X3636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3637),X3636)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).
fof(i_0_1504,plain,
! [X3403,X3404,X3405] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3405,X3404)),X3403) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3405),X3403),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3404),X3403)),
inference(variable_rename,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(i_0_1505,plain,
! [X2798,X2799,X2800] :
( ~ class_RealVector_Oreal__normed__algebra__1(X2800)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2800,hAPP(hAPP(c_Power_Opower__class_Opower(X2800),X2799),X2798)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2800,X2799)),X2798)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power__ineq])]) ).
fof(i_0_1506,plain,
! [X4313,X4314,X4315,X4316] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4316)
| ~ c_Orderings_Oord__class_Oless__eq(X4316,c_Groups_Oplus__class_Oplus(X4316,X4315,X4314),c_Groups_Oplus__class_Oplus(X4316,X4313,X4314))
| c_Orderings_Oord__class_Oless__eq(X4316,X4315,X4313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).
fof(i_0_1507,plain,
! [X4292,X4293,X4294,X4295] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4295,c_Groups_Oplus__class_Oplus(X4295,X4294,X4293),c_Groups_Oplus__class_Oplus(X4295,X4292,X4293))
| c_Orderings_Oord__class_Oless__eq(X4295,X4294,X4292)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4295) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4295,X4294,X4292)
| c_Orderings_Oord__class_Oless__eq(X4295,c_Groups_Oplus__class_Oplus(X4295,X4294,X4293),c_Groups_Oplus__class_Oplus(X4295,X4292,X4293))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4295) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).
fof(i_0_1508,plain,
! [X4317,X4318,X4319,X4320] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4320)
| ~ c_Orderings_Oord__class_Oless__eq(X4320,c_Groups_Oplus__class_Oplus(X4320,X4319,X4318),c_Groups_Oplus__class_Oplus(X4320,X4319,X4317))
| c_Orderings_Oord__class_Oless__eq(X4320,X4318,X4317) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).
fof(i_0_1509,plain,
! [X4296,X4297,X4298,X4299] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4299,c_Groups_Oplus__class_Oplus(X4299,X4298,X4297),c_Groups_Oplus__class_Oplus(X4299,X4298,X4296))
| c_Orderings_Oord__class_Oless__eq(X4299,X4297,X4296)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4299) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4299,X4297,X4296)
| c_Orderings_Oord__class_Oless__eq(X4299,c_Groups_Oplus__class_Oplus(X4299,X4298,X4297),c_Groups_Oplus__class_Oplus(X4299,X4298,X4296))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4299) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).
fof(i_0_1510,plain,
! [X4342,X4343,X4344,X4345] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4345)
| ~ c_Orderings_Oord__class_Oless(X4345,c_Groups_Oplus__class_Oplus(X4345,X4344,X4343),c_Groups_Oplus__class_Oplus(X4345,X4342,X4343))
| c_Orderings_Oord__class_Oless(X4345,X4344,X4342) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).
fof(i_0_1511,plain,
! [X4321,X4322,X4323,X4324] :
( ( ~ c_Orderings_Oord__class_Oless(X4324,c_Groups_Oplus__class_Oplus(X4324,X4323,X4322),c_Groups_Oplus__class_Oplus(X4324,X4321,X4322))
| c_Orderings_Oord__class_Oless(X4324,X4323,X4321)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4324) )
& ( ~ c_Orderings_Oord__class_Oless(X4324,X4323,X4321)
| c_Orderings_Oord__class_Oless(X4324,c_Groups_Oplus__class_Oplus(X4324,X4323,X4322),c_Groups_Oplus__class_Oplus(X4324,X4321,X4322))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4324) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).
fof(i_0_1512,plain,
! [X4346,X4347,X4348,X4349] :
( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4349)
| ~ c_Orderings_Oord__class_Oless(X4349,c_Groups_Oplus__class_Oplus(X4349,X4348,X4347),c_Groups_Oplus__class_Oplus(X4349,X4348,X4346))
| c_Orderings_Oord__class_Oless(X4349,X4347,X4346) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).
fof(i_0_1513,plain,
! [X4325,X4326,X4327,X4328] :
( ( ~ c_Orderings_Oord__class_Oless(X4328,c_Groups_Oplus__class_Oplus(X4328,X4327,X4326),c_Groups_Oplus__class_Oplus(X4328,X4327,X4325))
| c_Orderings_Oord__class_Oless(X4328,X4326,X4325)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4328) )
& ( ~ c_Orderings_Oord__class_Oless(X4328,X4326,X4325)
| c_Orderings_Oord__class_Oless(X4328,c_Groups_Oplus__class_Oplus(X4328,X4327,X4326),c_Groups_Oplus__class_Oplus(X4328,X4327,X4325))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X4328) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).
fof(i_0_1514,plain,
! [X3742,X3743,X3744] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3744,X3743)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3744,X3742)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3743,X3744),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3742,X3744)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3743,X3742) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).
fof(i_0_1515,plain,
! [X2819,X2820,X2821] :
( ~ class_Rings_Olinordered__semidom(X2821)
| ~ c_Orderings_Oord__class_Oless(X2821,c_Groups_Oone__class_Oone(X2821),X2820)
| c_Orderings_Oord__class_Oless(X2821,c_Groups_Oone__class_Oone(X2821),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2821),X2820),hAPP(hAPP(c_Power_Opower__class_Opower(X2821),X2820),X2819))) ),
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),esk7_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,
! [X4760,X4761,X4762] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4762),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4761,X4760)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4762),X4761)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4762),X4760)),
inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(i_0_1518,plain,
! [X4019,X4020,X4021,X4022] :
( ~ class_Rings_Ocomm__semiring__0(X4022)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4022),c_Polynomial_Osmult(X4022,X4021,X4020),c_Polynomial_OpCons(X4022,X4019,X4020)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4022))
| X4020 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4022)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__lemma])]) ).
fof(i_0_1519,plain,
! [X3607,X3608,X3609] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3609,X3608),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3609,X3607))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3608,X3607)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3609,X3608),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3609,X3607)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).
fof(i_0_1520,plain,
! [X3580,X3581,X3582] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,X3581),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,X3580))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3581,X3580) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3581,X3580)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,X3581),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3582,X3580)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).
fof(i_0_1521,plain,
! [X4867,X4868,X4869] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4869)
| X4869 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4868,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4869),X4867))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4868)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4867,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,
! [X4870,X4871,X4872] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4872)
| X4872 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4872),X4870))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4871,X4872)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4870) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).
fof(i_0_1523,plain,
! [X4108,X4109,X4110,X4111] :
( ~ class_Rings_Ocomm__ring(X4111)
| c_Polynomial_Osmult(X4111,X4110,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4111),X4109,X4108)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4111),c_Polynomial_Osmult(X4111,X4110,X4109),c_Polynomial_Osmult(X4111,X4110,X4108)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__right])]) ).
fof(i_0_1524,plain,
! [X4123,X4124,X4125,X4126] :
( ~ class_Rings_Ocomm__semiring__0(X4126)
| c_Polynomial_Osmult(X4126,X4125,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4126),X4124,X4123)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4126),c_Polynomial_Osmult(X4126,X4125,X4124),c_Polynomial_Osmult(X4126,X4125,X4123)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__right])]) ).
fof(i_0_1525,plain,
! [X2845,X2846,X2847,X2848] :
( ~ class_Rings_Olinordered__semidom(X2848)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2848),X2847),X2846) != hAPP(hAPP(c_Power_Opower__class_Opower(X2848),X2845),X2846)
| ~ c_Orderings_Oord__class_Oless__eq(X2848,c_Groups_Ozero__class_Ozero(X2848),X2847)
| ~ c_Orderings_Oord__class_Oless__eq(X2848,c_Groups_Ozero__class_Ozero(X2848),X2845)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2846)
| X2847 = X2845 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).
fof(i_0_1526,plain,
! [X4735,X4736,X4737] :
( ~ class_Rings_Ocomm__semiring__1(X4737)
| c_Groups_Oplus__class_Oplus(X4737,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4737),X4736),X4735),X4735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4737),c_Groups_Oplus__class_Oplus(X4737,X4736,c_Groups_Oone__class_Oone(X4737))),X4735) ),
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,
! [X4732,X4733,X4734] :
( ~ class_Rings_Ocomm__semiring__1(X4734)
| c_Groups_Oplus__class_Oplus(X4734,X4733,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4734),X4732),X4733)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4734),c_Groups_Oplus__class_Oplus(X4734,X4732,c_Groups_Oone__class_Oone(X4734))),X4733) ),
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,
! [X5246,X5247] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5247),X5246)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5246,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5247),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_RComplete_Onatfloor(X5246) = X5247 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__eq])]) ).
fof(i_0_1529,plain,
! [X3000,X3001,X3002] :
( ~ class_Rings_Olinordered__idom(X3002)
| ~ c_Orderings_Oord__class_Oless__eq(X3002,c_Groups_Ozero__class_Ozero(X3002),X3001)
| ~ c_Orderings_Oord__class_Oless__eq(X3002,c_Groups_Ozero__class_Ozero(X3002),X3000)
| ~ c_Orderings_Oord__class_Oless__eq(X3002,X3000,c_Groups_Oone__class_Oone(X3002))
| c_Orderings_Oord__class_Oless__eq(X3002,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3002),X3001),X3000),X3001) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).
fof(i_0_1530,plain,
! [X2997,X2998,X2999] :
( ~ class_Rings_Olinordered__idom(X2999)
| ~ c_Orderings_Oord__class_Oless__eq(X2999,c_Groups_Ozero__class_Ozero(X2999),X2998)
| ~ c_Orderings_Oord__class_Oless__eq(X2999,c_Groups_Ozero__class_Ozero(X2999),X2997)
| ~ c_Orderings_Oord__class_Oless__eq(X2999,X2997,c_Groups_Oone__class_Oone(X2999))
| c_Orderings_Oord__class_Oless__eq(X2999,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2999),X2997),X2998),X2998) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).
fof(i_0_1531,plain,
! [X2789,X2790,X2791,X2792] :
( ~ class_RealVector_Oreal__normed__vector(X2792)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2791,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2792,X2790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2791),c_RealVector_Onorm__class_Onorm(X2792,X2789)))
| X2790 = c_Groups_Ozero__class_Ozero(X2792) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma])]) ).
fof(i_0_1532,plain,
! [X3172,X3173,X3174,X3175] :
( ~ class_Rings_Oordered__semiring(X3175)
| ~ c_Orderings_Oord__class_Oless__eq(X3175,X3174,X3173)
| ~ c_Orderings_Oord__class_Oless__eq(X3175,c_Groups_Ozero__class_Ozero(X3175),X3172)
| c_Orderings_Oord__class_Oless__eq(X3175,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3175),X3174),X3172),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3175),X3173),X3172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).
fof(i_0_1533,plain,
! [X3180,X3181,X3182,X3183] :
( ~ class_Rings_Oordered__comm__semiring(X3183)
| ~ c_Orderings_Oord__class_Oless__eq(X3183,X3182,X3181)
| ~ c_Orderings_Oord__class_Oless__eq(X3183,c_Groups_Ozero__class_Ozero(X3183),X3180)
| c_Orderings_Oord__class_Oless__eq(X3183,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3183),X3180),X3182),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3183),X3180),X3181)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).
fof(i_0_1534,plain,
! [X3176,X3177,X3178,X3179] :
( ~ class_Rings_Oordered__semiring(X3179)
| ~ c_Orderings_Oord__class_Oless__eq(X3179,X3178,X3177)
| ~ c_Orderings_Oord__class_Oless__eq(X3179,c_Groups_Ozero__class_Ozero(X3179),X3176)
| c_Orderings_Oord__class_Oless__eq(X3179,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3179),X3176),X3178),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3179),X3176),X3177)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).
fof(i_0_1535,plain,
! [X2902,X2903,X2904,X2905] :
( ~ class_Rings_Olinordered__semidom(X2905)
| ~ c_Orderings_Oord__class_Oless__eq(X2905,X2904,X2903)
| ~ c_Orderings_Oord__class_Oless__eq(X2905,c_Groups_Ozero__class_Ozero(X2905),X2904)
| c_Orderings_Oord__class_Oless__eq(X2905,hAPP(hAPP(c_Power_Opower__class_Opower(X2905),X2904),X2902),hAPP(hAPP(c_Power_Opower__class_Opower(X2905),X2903),X2902)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).
fof(i_0_1536,plain,
! [X3247,X3248,X3249,X3250] :
( ~ class_Rings_Olinordered__semiring__strict(X3250)
| ~ c_Orderings_Oord__class_Oless(X3250,X3249,X3248)
| ~ c_Orderings_Oord__class_Oless(X3250,c_Groups_Ozero__class_Ozero(X3250),X3247)
| c_Orderings_Oord__class_Oless(X3250,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3250),X3249),X3247),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3250),X3248),X3247)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).
fof(i_0_1537,plain,
! [X3255,X3256,X3257,X3258] :
( ~ class_Rings_Olinordered__comm__semiring__strict(X3258)
| ~ c_Orderings_Oord__class_Oless(X3258,X3257,X3256)
| ~ c_Orderings_Oord__class_Oless(X3258,c_Groups_Ozero__class_Ozero(X3258),X3255)
| c_Orderings_Oord__class_Oless(X3258,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3258),X3255),X3257),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3258),X3255),X3256)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).
fof(i_0_1538,plain,
! [X3251,X3252,X3253,X3254] :
( ~ class_Rings_Olinordered__semiring__strict(X3254)
| ~ c_Orderings_Oord__class_Oless(X3254,X3253,X3252)
| ~ c_Orderings_Oord__class_Oless(X3254,c_Groups_Ozero__class_Ozero(X3254),X3251)
| c_Orderings_Oord__class_Oless(X3254,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3254),X3251),X3253),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3254),X3251),X3252)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).
fof(i_0_1539,plain,
! [X3184,X3185,X3186,X3187] :
( ~ class_Rings_Oordered__ring(X3187)
| ~ c_Orderings_Oord__class_Oless__eq(X3187,X3186,X3185)
| ~ c_Orderings_Oord__class_Oless__eq(X3187,X3184,c_Groups_Ozero__class_Ozero(X3187))
| c_Orderings_Oord__class_Oless__eq(X3187,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3187),X3185),X3184),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3187),X3186),X3184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).
fof(i_0_1540,plain,
! [X3188,X3189,X3190,X3191] :
( ~ class_Rings_Oordered__ring(X3191)
| ~ c_Orderings_Oord__class_Oless__eq(X3191,X3190,X3189)
| ~ c_Orderings_Oord__class_Oless__eq(X3191,X3188,c_Groups_Ozero__class_Ozero(X3191))
| c_Orderings_Oord__class_Oless__eq(X3191,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3191),X3188),X3189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3191),X3188),X3190)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).
fof(i_0_1541,plain,
! [X3259,X3260,X3261,X3262] :
( ~ class_Rings_Olinordered__ring__strict(X3262)
| ~ c_Orderings_Oord__class_Oless(X3262,X3261,X3260)
| ~ c_Orderings_Oord__class_Oless(X3262,X3259,c_Groups_Ozero__class_Ozero(X3262))
| c_Orderings_Oord__class_Oless(X3262,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3262),X3260),X3259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3262),X3261),X3259)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).
fof(i_0_1542,plain,
! [X3263,X3264,X3265,X3266] :
( ~ class_Rings_Olinordered__ring__strict(X3266)
| ~ c_Orderings_Oord__class_Oless(X3266,X3265,X3264)
| ~ c_Orderings_Oord__class_Oless(X3266,X3263,c_Groups_Ozero__class_Ozero(X3266))
| c_Orderings_Oord__class_Oless(X3266,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3266),X3263),X3264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3266),X3263),X3265)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).
fof(i_0_1543,plain,
! [X3824,X3825,X3826] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3826,X3825)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3824,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3825,X3824),X3826)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).
fof(i_0_1544,plain,
! [X4308,X4309,X4310,X4311,X4312] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4312)
| ~ c_Orderings_Oord__class_Oless__eq(X4312,X4311,X4310)
| ~ c_Orderings_Oord__class_Oless__eq(X4312,X4309,X4308)
| c_Orderings_Oord__class_Oless__eq(X4312,c_Groups_Oplus__class_Oplus(X4312,X4311,X4309),c_Groups_Oplus__class_Oplus(X4312,X4310,X4308)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).
fof(i_0_1545,plain,
! [X4476,X4477,X4478,X4479,X4480] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4480)
| ~ c_Orderings_Oord__class_Oless(X4480,X4479,X4478)
| ~ c_Orderings_Oord__class_Oless__eq(X4480,X4477,X4476)
| c_Orderings_Oord__class_Oless(X4480,c_Groups_Oplus__class_Oplus(X4480,X4479,X4477),c_Groups_Oplus__class_Oplus(X4480,X4478,X4476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).
fof(i_0_1546,plain,
! [X4481,X4482,X4483,X4484,X4485] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4485)
| ~ c_Orderings_Oord__class_Oless__eq(X4485,X4484,X4483)
| ~ c_Orderings_Oord__class_Oless(X4485,X4482,X4481)
| c_Orderings_Oord__class_Oless(X4485,c_Groups_Oplus__class_Oplus(X4485,X4484,X4482),c_Groups_Oplus__class_Oplus(X4485,X4483,X4481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).
fof(i_0_1547,plain,
! [X4337,X4338,X4339,X4340,X4341] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4341)
| ~ c_Orderings_Oord__class_Oless(X4341,X4340,X4339)
| ~ c_Orderings_Oord__class_Oless(X4341,X4338,X4337)
| c_Orderings_Oord__class_Oless(X4341,c_Groups_Oplus__class_Oplus(X4341,X4340,X4338),c_Groups_Oplus__class_Oplus(X4341,X4339,X4337)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).
fof(i_0_1548,plain,
! [X2914,X2915,X2916,X2917] :
( ~ class_Rings_Olinordered__semidom(X2917)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2916,X2915)
| ~ c_Orderings_Oord__class_Oless__eq(X2917,c_Groups_Oone__class_Oone(X2917),X2914)
| c_Orderings_Oord__class_Oless__eq(X2917,hAPP(hAPP(c_Power_Opower__class_Opower(X2917),X2914),X2916),hAPP(hAPP(c_Power_Opower__class_Opower(X2917),X2914),X2915)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).
fof(i_0_1549,plain,
! [X2921,X2922,X2923,X2924] :
( ~ class_Rings_Olinordered__semidom(X2924)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2923,X2922)
| ~ c_Orderings_Oord__class_Oless(X2924,c_Groups_Oone__class_Oone(X2924),X2921)
| c_Orderings_Oord__class_Oless(X2924,hAPP(hAPP(c_Power_Opower__class_Opower(X2924),X2921),X2923),hAPP(hAPP(c_Power_Opower__class_Opower(X2924),X2921),X2922)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).
fof(i_0_1550,plain,
! [X3836,X3837,X3838] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3838,c_Groups_Ozero__class_Ozero(X3838),X3836)
| ~ c_Orderings_Oord__class_Oless__eq(X3838,c_Groups_Ozero__class_Ozero(X3838),X3837)
| c_Groups_Oabs__class_Oabs(X3838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),c_Groups_Oabs__class_Oabs(X3838,X3837)),c_Groups_Oabs__class_Oabs(X3838,X3836))
| ~ class_Rings_Oordered__ring__abs(X3838) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3838,X3836,c_Groups_Ozero__class_Ozero(X3838))
| ~ c_Orderings_Oord__class_Oless__eq(X3838,c_Groups_Ozero__class_Ozero(X3838),X3837)
| c_Groups_Oabs__class_Oabs(X3838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),c_Groups_Oabs__class_Oabs(X3838,X3837)),c_Groups_Oabs__class_Oabs(X3838,X3836))
| ~ class_Rings_Oordered__ring__abs(X3838) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3838,c_Groups_Ozero__class_Ozero(X3838),X3836)
| ~ c_Orderings_Oord__class_Oless__eq(X3838,X3837,c_Groups_Ozero__class_Ozero(X3838))
| c_Groups_Oabs__class_Oabs(X3838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),c_Groups_Oabs__class_Oabs(X3838,X3837)),c_Groups_Oabs__class_Oabs(X3838,X3836))
| ~ class_Rings_Oordered__ring__abs(X3838) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3838,X3836,c_Groups_Ozero__class_Ozero(X3838))
| ~ c_Orderings_Oord__class_Oless__eq(X3838,X3837,c_Groups_Ozero__class_Ozero(X3838))
| c_Groups_Oabs__class_Oabs(X3838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),X3837),X3836)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3838),c_Groups_Oabs__class_Oabs(X3838,X3837)),c_Groups_Oabs__class_Oabs(X3838,X3836))
| ~ class_Rings_Oordered__ring__abs(X3838) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).
fof(i_0_1551,plain,
! [X4061,X4062,X4063,X4064] :
( ~ class_Groups_Oab__group__add(X4064)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4064),c_Polynomial_Omonom(X4064,X4063,X4062),c_Polynomial_Omonom(X4064,X4061,X4062)) = c_Polynomial_Omonom(X4064,c_Groups_Ominus__class_Ominus(X4064,X4063,X4061),X4062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__monom])]) ).
fof(i_0_1552,plain,
! [X4053,X4054,X4055,X4056] :
( ~ class_Groups_Ocomm__monoid__add(X4056)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4056),c_Polynomial_Omonom(X4056,X4055,X4054),c_Polynomial_Omonom(X4056,X4053,X4054)) = c_Polynomial_Omonom(X4056,c_Groups_Oplus__class_Oplus(X4056,X4055,X4053),X4054) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__monom])]) ).
fof(i_0_1553,plain,
! [X4178,X4179,X4180,X4181] :
( ~ class_Rings_Ocomm__ring(X4181)
| c_Polynomial_Osmult(X4181,c_Groups_Ominus__class_Ominus(X4181,X4180,X4179),X4178) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4181),c_Polynomial_Osmult(X4181,X4180,X4178),c_Polynomial_Osmult(X4181,X4179,X4178)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__diff__left])]) ).
fof(i_0_1554,plain,
! [X4166,X4167,X4168,X4169] :
( ~ class_Rings_Ocomm__semiring__0(X4169)
| c_Polynomial_Osmult(X4169,c_Groups_Oplus__class_Oplus(X4169,X4168,X4167),X4166) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4169),c_Polynomial_Osmult(X4169,X4168,X4166),c_Polynomial_Osmult(X4169,X4167,X4166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__add__left])]) ).
fof(i_0_1555,plain,
! [X3915,X3916,X3917] :
( ( X3916 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3917),X3915),X3916) = c_Groups_Oone__class_Oone(X3917)
| ~ class_Power_Opower(X3917) )
& ( X3916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X3917),X3915),X3916) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3917),X3915),hAPP(hAPP(c_Power_Opower__class_Opower(X3917),X3915),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3916,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ class_Power_Opower(X3917) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if])])]) ).
fof(i_0_1556,plain,
! [X4213,X4214,X4215,X4216] :
( ~ class_Rings_Ocomm__semiring__0(X4216)
| c_Polynomial_Osmult(X4216,X4215,c_Polynomial_OpCons(X4216,X4214,X4213)) = c_Polynomial_OpCons(X4216,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4216),X4215),X4214),c_Polynomial_Osmult(X4216,X4215,X4213)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__pCons])]) ).
fof(i_0_1557,plain,
! [X3619,X3620,X3621,X3622] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3622,X3621)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3620,X3619)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3622,X3620),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3621,X3619)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).
fof(i_0_1558,plain,
! [X4776,X4777,X4778,X4779] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4779,X4778)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4777,X4776)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4779,X4777),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4778,X4776)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).
fof(i_0_1559,plain,
! [X3796,X3797,X3798] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3798,X3797)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3796,X3798)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3798,X3796),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3797,X3796)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).
fof(i_0_1560,plain,
! [X3723,X3724,X3725] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3725,X3724)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3725,X3723)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3723,X3724),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3723,X3725)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).
fof(i_0_1561,plain,
! [X3567,X3568,X3569,X3570] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3570,X3569)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3568,X3567)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3570,X3568),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3569,X3567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).
fof(i_0_1562,plain,
! [X4023,X4024,X4025] :
( ( X4024 = c_Groups_Ozero__class_Ozero(X4025)
| c_Groups_Oplus__class_Oplus(X4025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)) != c_Groups_Ozero__class_Ozero(X4025)
| ~ class_Rings_Olinordered__ring__strict(X4025) )
& ( X4023 = c_Groups_Ozero__class_Ozero(X4025)
| c_Groups_Oplus__class_Oplus(X4025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)) != c_Groups_Ozero__class_Ozero(X4025)
| ~ class_Rings_Olinordered__ring__strict(X4025) )
& ( X4024 != c_Groups_Ozero__class_Ozero(X4025)
| X4023 != c_Groups_Ozero__class_Ozero(X4025)
| c_Groups_Oplus__class_Oplus(X4025,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4024),X4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4025),X4023),X4023)) = c_Groups_Ozero__class_Ozero(X4025)
| ~ class_Rings_Olinordered__ring__strict(X4025) ) ),
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,
! [X3842,X3843,X3844] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3844,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,X3843),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3844),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3842)))
| X3843 = 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,
! [X3393,X3394,X3395,X3396] :
( ~ class_RealVector_Oreal__normed__algebra(X3396)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3396),X3395),c_Groups_Ominus__class_Ominus(X3396,X3394,X3393)) = c_Groups_Ominus__class_Ominus(X3396,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3396),X3395),X3394),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3396),X3395),X3393)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Odiff__right])]) ).
fof(i_0_1565,plain,
! [X3389,X3390,X3391,X3392] :
( ~ class_RealVector_Oreal__normed__algebra(X3392)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3392),X3391),c_Groups_Ominus__class_Ominus(X3392,X3390,X3389)) = c_Groups_Ominus__class_Ominus(X3392,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3392),X3391),X3390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3392),X3391),X3389)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Odiff])]) ).
fof(i_0_1566,plain,
! [X4688,X4689,X4690,X4691] :
( ~ class_Rings_Ocomm__semiring__1(X4691)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4691),X4690),c_Groups_Oplus__class_Oplus(X4691,X4689,X4688)) = c_Groups_Oplus__class_Oplus(X4691,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4691),X4690),X4689),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4691),X4690),X4688)) ),
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,
! [X3087,X3088,X3089,X3090] :
( ~ class_RealVector_Oreal__normed__algebra(X3090)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3090),X3089),c_Groups_Oplus__class_Oplus(X3090,X3088,X3087)) = c_Groups_Oplus__class_Oplus(X3090,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3090),X3089),X3088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3090),X3089),X3087)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Oadd])]) ).
fof(i_0_1568,plain,
! [X3083,X3084,X3085,X3086] :
( ~ class_RealVector_Oreal__normed__algebra(X3086)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3086),X3085),c_Groups_Oplus__class_Oplus(X3086,X3084,X3083)) = c_Groups_Oplus__class_Oplus(X3086,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3086),X3085),X3084),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3086),X3085),X3083)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Oadd__right])]) ).
fof(i_0_1569,plain,
! [X3664,X3665,X3666] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3664)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3665,X3664)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3664)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3666)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3665,X3664)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3666),X3664)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).
fof(i_0_1570,plain,
! [X3667,X3668,X3669] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3668)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3669),X3668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3667),X3668)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3669,X3667)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3669),X3668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3667),X3668)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3668)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3669,X3667)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3669),X3668),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3667),X3668)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).
fof(i_0_1571,plain,
! [X3234,X3235,X3236] :
( ~ class_Rings_Olinordered__semiring__strict(X3236)
| ~ c_Orderings_Oord__class_Oless(X3236,c_Groups_Ozero__class_Ozero(X3236),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3236),X3235),X3234))
| ~ c_Orderings_Oord__class_Oless(X3236,c_Groups_Ozero__class_Ozero(X3236),X3234)
| c_Orderings_Oord__class_Oless(X3236,c_Groups_Ozero__class_Ozero(X3236),X3235) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).
fof(i_0_1572,plain,
! [X3231,X3232,X3233] :
( ~ class_Rings_Olinordered__semiring__strict(X3233)
| ~ c_Orderings_Oord__class_Oless(X3233,c_Groups_Ozero__class_Ozero(X3233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3233),X3232),X3231))
| ~ c_Orderings_Oord__class_Oless(X3233,c_Groups_Ozero__class_Ozero(X3233),X3232)
| c_Orderings_Oord__class_Oless(X3233,c_Groups_Ozero__class_Ozero(X3233),X3231) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).
fof(i_0_1573,plain,
! [X4234,X4235,X4236,X4237] :
( ~ class_Groups_Oab__semigroup__mult(X4237)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4237),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4237),X4236),X4235)),X4234) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4237),X4236),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4237),X4235),X4234)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).
fof(i_0_1574,plain,
! [X4630,X4631,X4632,X4633] :
( ~ class_Rings_Ocomm__semiring__1(X4633)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4633),X4632),X4631)),X4630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4633),X4632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4633),X4631),X4630)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).
fof(i_0_1575,plain,
! [X2886,X2887,X2888] :
( ~ class_Groups_Omonoid__mult(X2888)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2888),hAPP(hAPP(c_Power_Opower__class_Opower(X2888),X2887),X2886)),X2887) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2888),X2887),hAPP(hAPP(c_Power_Opower__class_Opower(X2888),X2887),X2886)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).
fof(i_0_1576,plain,
! [X4626,X4627,X4628,X4629] :
( ~ class_Rings_Ocomm__semiring__1(X4629)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),X4628),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),X4627),X4626)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4629),X4628),X4627)),X4626) ),
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,
! [X5224,X5225] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5225,X5224)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5225),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5224)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5225),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,X5224))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5225,X5224) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__real__le])]) ).
fof(i_0_1578,plain,
! [X5226,X5227] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5227,X5226)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5227),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5226),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5227),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5226),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5227,X5226) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__real__less])]) ).
fof(i_0_1579,plain,
! [X4079,X4080,X4081,X4082] :
( ~ class_Rings_Ocomm__semiring__1(X4082)
| hAPP(c_Polynomial_Opoly(X4082,c_Polynomial_Omonom(X4082,X4081,X4080)),X4079) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4082),X4081),hAPP(hAPP(c_Power_Opower__class_Opower(X4082),X4079),X4080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__monom])]) ).
fof(i_0_1580,plain,
! [X4604,X4605,X4606,X4607,X4608] :
( ( X4604 = hAPP(c_Polynomial_Opoly(X4608,X4607),X4606)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4608),X4607,c_Polynomial_Osmult(X4608,X4606,X4605)) != c_Polynomial_OpCons(X4608,X4604,X4605)
| ~ class_Rings_Ocomm__semiring__0(X4608) )
& ( X4605 = c_Polynomial_Osynthetic__div(X4608,X4607,X4606)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4608),X4607,c_Polynomial_Osmult(X4608,X4606,X4605)) != c_Polynomial_OpCons(X4608,X4604,X4605)
| ~ class_Rings_Ocomm__semiring__0(X4608) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique])])]) ).
fof(i_0_1581,plain,
! [X5255] :
( ( 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(X5255),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5255)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5255) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5255,c_RealDef_Oreal(tc_Nat_Onat,esk32_1(X5255)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5255) ) ),
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,
! [X4600,X4601,X4602,X4603] :
( ~ class_Rings_Ocomm__semiring__0(X4603)
| c_Polynomial_Osynthetic__div(X4603,c_Polynomial_OpCons(X4603,X4602,X4601),X4600) = c_Polynomial_OpCons(X4603,hAPP(c_Polynomial_Opoly(X4603,X4601),X4600),c_Polynomial_Osynthetic__div(X4603,X4601,X4600)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons])]) ).
fof(i_0_1583,plain,
! [X2827,X2828,X2829,X2830] :
( ~ class_Groups_Omonoid__mult(X2830)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2830),X2829),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2828),X2827)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2830),hAPP(hAPP(c_Power_Opower__class_Opower(X2830),X2829),X2828)),X2827) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).
fof(i_0_1584,plain,
! [X4718,X4719,X4720,X4721] :
( ~ class_Rings_Ocomm__semiring__1(X4721)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4721),hAPP(hAPP(c_Power_Opower__class_Opower(X4721),X4720),X4719)),X4718) = hAPP(hAPP(c_Power_Opower__class_Opower(X4721),X4720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4719),X4718)) ),
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,
! [X4829,X4830,X4831] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4831,X4830)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4829)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4829),X4831),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4829),X4830)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).
fof(i_0_1586,plain,
! [X3676,X3677,X3678] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3678,X3677)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3676)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3678),X3676),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3677),X3676)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).
fof(i_0_1587,plain,
! [X3679,X3680,X3681] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3681,X3680)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3679)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3679),X3681),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3679),X3680)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).
fof(i_0_1588,plain,
! [X2947,X2948,X2949] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2949)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2948,X2947)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2949),X2948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2949),X2947)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__less__mono2])]) ).
fof(i_0_1589,plain,
! [X4015,X4016] :
( ( X4016 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4015),X4016) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X4016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4015),X4016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4015),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X4015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X4016,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,
! [X3827,X3828,X3829] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3829,X3828),X3827)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3827,X3828)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3829,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3827,X3828))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3829,X3828),X3827) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).
fof(i_0_1591,plain,
! [X3789,X3790,X3791] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3791,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3790,X3789))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3791,X3789),X3790) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3791,X3789),X3790)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3791,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3790,X3789)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).
fof(i_0_1592,plain,
! [X3642,X3643,X3644,X3645] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3645,X3644)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3643,X3642)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3645),X3643),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3644),X3642)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).
fof(i_0_1593,plain,
! [X3805,X3806,X3807] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3807,X3806)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3806,X3807),X3805) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3806,X3805),X3807) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).
fof(i_0_1594,plain,
! [X3802,X3803,X3804] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3804,X3803)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3803,X3802),X3804) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3803,X3804),X3802) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).
fof(i_0_1595,plain,
! [X3808,X3809,X3810] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3810,X3809)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3808,X3809),X3810) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3808,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3809,X3810)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).
fof(i_0_1596,plain,
! [X3830,X3831,X3832] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3832,X3831)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3830,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3831,X3832)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3830,X3832),X3831) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).
fof(i_0_1597,plain,
! [X3819,X3820,X3821] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3821,X3820)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3819,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3820,X3821)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3819,X3820),X3821) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).
fof(i_0_1598,plain,
! [X4112,X4113,X4114,X4115] :
( ~ class_Rings_Ocomm__semiring__0(X4115)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4115)),X4114),c_Polynomial_Osmult(X4115,X4113,X4112)) = c_Polynomial_Osmult(X4115,X4113,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4115)),X4114),X4112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__smult__right])]) ).
fof(i_0_1599,plain,
! [X4201,X4202,X4203,X4204] :
( ~ class_Rings_Ocomm__semiring__0(X4204)
| hAPP(c_Polynomial_Opoly(X4204,c_Polynomial_Osmult(X4204,X4203,X4202)),X4201) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4204),X4203),hAPP(c_Polynomial_Opoly(X4204,X4202),X4201)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__smult])]) ).
fof(i_0_1600,plain,
! [X3154,X3155,X3156] :
( ( c_Orderings_Oord__class_Oless__eq(X3156,X3155,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3155)
| ~ c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3155)
| ~ c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless__eq(X3156,X3155,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless__eq(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| ~ c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| c_Orderings_Oord__class_Oless__eq(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| ~ c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3155)
| ~ c_Orderings_Oord__class_Oless__eq(X3156,X3154,c_Groups_Ozero__class_Ozero(X3156))
| c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3156,X3155,c_Groups_Ozero__class_Ozero(X3156))
| ~ c_Orderings_Oord__class_Oless__eq(X3156,c_Groups_Ozero__class_Ozero(X3156),X3154)
| c_Orderings_Oord__class_Oless__eq(X3156,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3156),X3155),X3154),c_Groups_Ozero__class_Ozero(X3156))
| ~ class_Rings_Olinordered__ring__strict(X3156) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).
fof(i_0_1601,plain,
! [X3151,X3152,X3153] :
( ( c_Orderings_Oord__class_Oless__eq(X3153,X3152,c_Groups_Ozero__class_Ozero(X3153))
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3152)
| ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) )
& ( c_Orderings_Oord__class_Oless__eq(X3153,X3151,c_Groups_Ozero__class_Ozero(X3153))
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3152)
| ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) )
& ( c_Orderings_Oord__class_Oless__eq(X3153,X3152,c_Groups_Ozero__class_Ozero(X3153))
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3151)
| ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) )
& ( c_Orderings_Oord__class_Oless__eq(X3153,X3151,c_Groups_Ozero__class_Ozero(X3153))
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3151)
| ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3152)
| ~ c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),X3151)
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3153,X3152,c_Groups_Ozero__class_Ozero(X3153))
| ~ c_Orderings_Oord__class_Oless__eq(X3153,X3151,c_Groups_Ozero__class_Ozero(X3153))
| c_Orderings_Oord__class_Oless__eq(X3153,c_Groups_Ozero__class_Ozero(X3153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3153),X3152),X3151))
| ~ class_Rings_Olinordered__ring__strict(X3153) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).
fof(i_0_1602,plain,
! [X4758,X4759] :
( ( ~ 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,X4759)),X4758))
| X4759 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| X4758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X4759 = 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,X4759)),X4758)) )
& ( X4758 != 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,X4759)),X4758)) ) ),
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,
! [X4802,X4803,X4804] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4804),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4803,X4802)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4804),X4803),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4804),X4802)),
inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(i_0_1604,plain,
! [X4790,X4791,X4792] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4792),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4791,X4790)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4792),X4791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4792),X4790)),
inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(i_0_1605,plain,
! [X3758,X3759,X3760] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3760),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3759,X3758)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3760),X3759),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3760),X3758)),
inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(i_0_1606,plain,
! [X3639,X3640,X3641] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3641),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3640,X3639)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3641),X3640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3641),X3639)),
inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).
fof(i_0_1607,plain,
! [X4754,X4755,X4756,X4757] :
( ~ class_Rings_Ocomm__semiring__0(X4757)
| hAPP(c_Polynomial_Opoly(X4757,c_Polynomial_Opcompose(X4757,X4756,X4755)),X4754) = hAPP(c_Polynomial_Opoly(X4757,X4756),hAPP(c_Polynomial_Opoly(X4757,X4755),X4754)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__pcompose])]) ).
fof(i_0_1608,plain,
! [X4730,X4731] :
( ~ class_Rings_Ocomm__semiring__1(X4731)
| c_Groups_Oplus__class_Oplus(X4731,X4730,X4730) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4731),c_Groups_Oplus__class_Oplus(X4731,c_Groups_Oone__class_Oone(X4731),c_Groups_Oone__class_Oone(X4731))),X4730) ),
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,
! [X3697,X3698,X3699] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3699)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3698,c_RealVector_Onorm__class_Onorm(X3699,X3697))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3698)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3699,c_Rings_Oinverse__class_Oinverse(X3699,X3697)),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3698)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bseq__inverse__lemma])]) ).
fof(i_0_1610,plain,
! [X3443,X3444] :
( ( X3444 = 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),X3444),X3444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3443),X3443)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3443 = 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),X3444),X3444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3443),X3443)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X3444 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3443 != 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),X3444),X3444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3443),X3443)) = 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,
! [X3702] : 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____),X3702))),
inference(variable_rename,[status(thm)],[fact_cq0]) ).
fof(i_0_1612,plain,
! [X4463,X4464,X4465] :
( ~ class_Groups_Oordered__comm__monoid__add(X4465)
| ~ c_Orderings_Oord__class_Oless__eq(X4465,X4464,c_Groups_Ozero__class_Ozero(X4465))
| ~ c_Orderings_Oord__class_Oless__eq(X4465,X4463,c_Groups_Ozero__class_Ozero(X4465))
| c_Orderings_Oord__class_Oless__eq(X4465,c_Groups_Oplus__class_Oplus(X4465,X4464,X4463),c_Groups_Ozero__class_Ozero(X4465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).
fof(i_0_1613,plain,
! [X4578,X4579,X4580] :
( ~ class_Groups_Oordered__comm__monoid__add(X4580)
| ~ c_Orderings_Oord__class_Oless(X4580,X4579,c_Groups_Ozero__class_Ozero(X4580))
| ~ c_Orderings_Oord__class_Oless__eq(X4580,X4578,c_Groups_Ozero__class_Ozero(X4580))
| c_Orderings_Oord__class_Oless(X4580,c_Groups_Oplus__class_Oplus(X4580,X4579,X4578),c_Groups_Ozero__class_Ozero(X4580)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).
fof(i_0_1614,plain,
! [X4581,X4582,X4583] :
( ~ class_Groups_Oordered__comm__monoid__add(X4583)
| ~ c_Orderings_Oord__class_Oless__eq(X4583,X4582,c_Groups_Ozero__class_Ozero(X4583))
| ~ c_Orderings_Oord__class_Oless(X4583,X4581,c_Groups_Ozero__class_Ozero(X4583))
| c_Orderings_Oord__class_Oless(X4583,c_Groups_Oplus__class_Oplus(X4583,X4582,X4581),c_Groups_Ozero__class_Ozero(X4583)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).
fof(i_0_1615,plain,
! [X4473,X4474,X4475] :
( ~ class_Groups_Oordered__comm__monoid__add(X4475)
| ~ c_Orderings_Oord__class_Oless(X4475,X4474,c_Groups_Ozero__class_Ozero(X4475))
| ~ c_Orderings_Oord__class_Oless(X4475,X4473,c_Groups_Ozero__class_Ozero(X4475))
| c_Orderings_Oord__class_Oless(X4475,c_Groups_Oplus__class_Oplus(X4475,X4474,X4473),c_Groups_Ozero__class_Ozero(X4475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).
fof(i_0_1616,plain,
! [X4449,X4450,X4451] :
( ~ class_Groups_Oordered__comm__monoid__add(X4451)
| ~ c_Orderings_Oord__class_Oless__eq(X4451,c_Groups_Ozero__class_Ozero(X4451),X4450)
| ~ c_Orderings_Oord__class_Oless__eq(X4451,c_Groups_Ozero__class_Ozero(X4451),X4449)
| c_Orderings_Oord__class_Oless__eq(X4451,c_Groups_Ozero__class_Ozero(X4451),c_Groups_Oplus__class_Oplus(X4451,X4450,X4449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).
fof(i_0_1617,plain,
! [X4564,X4565,X4566] :
( ~ class_Groups_Oordered__comm__monoid__add(X4566)
| ~ c_Orderings_Oord__class_Oless(X4566,c_Groups_Ozero__class_Ozero(X4566),X4565)
| ~ c_Orderings_Oord__class_Oless__eq(X4566,c_Groups_Ozero__class_Ozero(X4566),X4564)
| c_Orderings_Oord__class_Oless(X4566,c_Groups_Ozero__class_Ozero(X4566),c_Groups_Oplus__class_Oplus(X4566,X4565,X4564)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).
fof(i_0_1618,plain,
! [X4567,X4568,X4569] :
( ~ class_Groups_Oordered__comm__monoid__add(X4569)
| ~ c_Orderings_Oord__class_Oless__eq(X4569,c_Groups_Ozero__class_Ozero(X4569),X4568)
| ~ c_Orderings_Oord__class_Oless(X4569,c_Groups_Ozero__class_Ozero(X4569),X4567)
| c_Orderings_Oord__class_Oless(X4569,c_Groups_Ozero__class_Ozero(X4569),c_Groups_Oplus__class_Oplus(X4569,X4568,X4567)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).
fof(i_0_1619,plain,
! [X4470,X4471,X4472] :
( ~ class_Groups_Oordered__comm__monoid__add(X4472)
| ~ c_Orderings_Oord__class_Oless(X4472,c_Groups_Ozero__class_Ozero(X4472),X4471)
| ~ c_Orderings_Oord__class_Oless(X4472,c_Groups_Ozero__class_Ozero(X4472),X4470)
| c_Orderings_Oord__class_Oless(X4472,c_Groups_Ozero__class_Ozero(X4472),c_Groups_Oplus__class_Oplus(X4472,X4471,X4470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).
fof(i_0_1620,plain,
! [X3660,X3661] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3661)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3660) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3661)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3660)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3661,X3660)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).
fof(i_0_1621,plain,
! [X4815,X4816,X4817] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4817),X4816)),X4815) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4816),X4815)),
inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).
fof(i_0_1622,plain,
! [X3528,X3529,X3530] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3530),X3529)),X3528) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3529),X3528)),
inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).
fof(i_0_1623,plain,
! [X2860,X2861,X2862] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2862),X2861)),X2860) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2861),X2860)),
inference(variable_rename,[status(thm)],[fact_real__mult__assoc]) ).
fof(i_0_1624,plain,
! [X4763,X4764,X4765] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4765),X4764)),X4763) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X4765),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4764),X4763)),
inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).
fof(i_0_1625,plain,
! [X3205,X3206,X3207] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3207,c_Groups_Ozero__class_Ozero(X3207),X3206)
| ~ c_Orderings_Oord__class_Oless__eq(X3207,X3205,c_Groups_Ozero__class_Ozero(X3207))
| c_Orderings_Oord__class_Oless__eq(X3207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3207),X3206),X3205),c_Groups_Ozero__class_Ozero(X3207))
| ~ class_Rings_Oordered__cancel__semiring(X3207) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3207,X3206,c_Groups_Ozero__class_Ozero(X3207))
| ~ c_Orderings_Oord__class_Oless__eq(X3207,c_Groups_Ozero__class_Ozero(X3207),X3205)
| c_Orderings_Oord__class_Oless__eq(X3207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3207),X3206),X3205),c_Groups_Ozero__class_Ozero(X3207))
| ~ class_Rings_Oordered__cancel__semiring(X3207) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).
fof(i_0_1626,plain,
! [X3166,X3167,X3168] :
( ~ class_Rings_Oordered__cancel__semiring(X3168)
| ~ c_Orderings_Oord__class_Oless__eq(X3168,X3167,c_Groups_Ozero__class_Ozero(X3168))
| ~ c_Orderings_Oord__class_Oless__eq(X3168,c_Groups_Ozero__class_Ozero(X3168),X3166)
| c_Orderings_Oord__class_Oless__eq(X3168,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3168),X3167),X3166),c_Groups_Ozero__class_Ozero(X3168)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).
fof(i_0_1627,plain,
! [X3160,X3161,X3162] :
( ~ class_Rings_Oordered__cancel__semiring(X3162)
| ~ c_Orderings_Oord__class_Oless__eq(X3162,c_Groups_Ozero__class_Ozero(X3162),X3161)
| ~ c_Orderings_Oord__class_Oless__eq(X3162,X3160,c_Groups_Ozero__class_Ozero(X3162))
| c_Orderings_Oord__class_Oless__eq(X3162,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3162),X3161),X3160),c_Groups_Ozero__class_Ozero(X3162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).
fof(i_0_1628,plain,
! [X3163,X3164,X3165] :
( ~ class_Rings_Oordered__cancel__semiring(X3165)
| ~ c_Orderings_Oord__class_Oless__eq(X3165,c_Groups_Ozero__class_Ozero(X3165),X3164)
| ~ c_Orderings_Oord__class_Oless__eq(X3165,X3163,c_Groups_Ozero__class_Ozero(X3165))
| c_Orderings_Oord__class_Oless__eq(X3165,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3165),X3163),X3164),c_Groups_Ozero__class_Ozero(X3165)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).
fof(i_0_1629,plain,
! [X3241,X3242,X3243] :
( ~ class_Rings_Olinordered__semiring__strict(X3243)
| ~ c_Orderings_Oord__class_Oless(X3243,X3242,c_Groups_Ozero__class_Ozero(X3243))
| ~ c_Orderings_Oord__class_Oless(X3243,c_Groups_Ozero__class_Ozero(X3243),X3241)
| c_Orderings_Oord__class_Oless(X3243,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3243),X3242),X3241),c_Groups_Ozero__class_Ozero(X3243)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).
fof(i_0_1630,plain,
! [X3225,X3226,X3227] :
( ~ class_Rings_Olinordered__semiring__strict(X3227)
| ~ c_Orderings_Oord__class_Oless(X3227,c_Groups_Ozero__class_Ozero(X3227),X3226)
| ~ c_Orderings_Oord__class_Oless(X3227,X3225,c_Groups_Ozero__class_Ozero(X3227))
| c_Orderings_Oord__class_Oless(X3227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3227),X3226),X3225),c_Groups_Ozero__class_Ozero(X3227)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).
fof(i_0_1631,plain,
! [X3228,X3229,X3230] :
( ~ class_Rings_Olinordered__semiring__strict(X3230)
| ~ c_Orderings_Oord__class_Oless(X3230,c_Groups_Ozero__class_Ozero(X3230),X3229)
| ~ c_Orderings_Oord__class_Oless(X3230,X3228,c_Groups_Ozero__class_Ozero(X3230))
| c_Orderings_Oord__class_Oless(X3230,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3230),X3228),X3229),c_Groups_Ozero__class_Ozero(X3230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).
fof(i_0_1632,plain,
! [X3202,X3203,X3204] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3204,c_Groups_Ozero__class_Ozero(X3204),X3203)
| ~ c_Orderings_Oord__class_Oless__eq(X3204,c_Groups_Ozero__class_Ozero(X3204),X3202)
| c_Orderings_Oord__class_Oless__eq(X3204,c_Groups_Ozero__class_Ozero(X3204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3204),X3203),X3202))
| ~ class_Rings_Oordered__ring(X3204) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3204,X3203,c_Groups_Ozero__class_Ozero(X3204))
| ~ c_Orderings_Oord__class_Oless__eq(X3204,X3202,c_Groups_Ozero__class_Ozero(X3204))
| c_Orderings_Oord__class_Oless__eq(X3204,c_Groups_Ozero__class_Ozero(X3204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3204),X3203),X3202))
| ~ class_Rings_Oordered__ring(X3204) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).
fof(i_0_1633,plain,
! [X3157,X3158,X3159] :
( ~ class_Rings_Oordered__cancel__semiring(X3159)
| ~ c_Orderings_Oord__class_Oless__eq(X3159,c_Groups_Ozero__class_Ozero(X3159),X3158)
| ~ c_Orderings_Oord__class_Oless__eq(X3159,c_Groups_Ozero__class_Ozero(X3159),X3157)
| c_Orderings_Oord__class_Oless__eq(X3159,c_Groups_Ozero__class_Ozero(X3159),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3159),X3158),X3157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).
fof(i_0_1634,plain,
! [X3271,X3272,X3273] :
( ~ class_Rings_Olinordered__semidom(X3273)
| ~ c_Orderings_Oord__class_Oless(X3273,c_Groups_Oone__class_Oone(X3273),X3272)
| ~ c_Orderings_Oord__class_Oless(X3273,c_Groups_Oone__class_Oone(X3273),X3271)
| c_Orderings_Oord__class_Oless(X3273,c_Groups_Oone__class_Oone(X3273),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3273),X3272),X3271)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).
fof(i_0_1635,plain,
! [X3222,X3223,X3224] :
( ~ class_Rings_Olinordered__semiring__strict(X3224)
| ~ c_Orderings_Oord__class_Oless(X3224,c_Groups_Ozero__class_Ozero(X3224),X3223)
| ~ c_Orderings_Oord__class_Oless(X3224,c_Groups_Ozero__class_Ozero(X3224),X3222)
| c_Orderings_Oord__class_Oless(X3224,c_Groups_Ozero__class_Ozero(X3224),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3224),X3223),X3222)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).
fof(i_0_1636,plain,
! [X3169,X3170,X3171] :
( ~ class_Rings_Oordered__ring(X3171)
| ~ c_Orderings_Oord__class_Oless__eq(X3171,X3170,c_Groups_Ozero__class_Ozero(X3171))
| ~ c_Orderings_Oord__class_Oless__eq(X3171,X3169,c_Groups_Ozero__class_Ozero(X3171))
| c_Orderings_Oord__class_Oless__eq(X3171,c_Groups_Ozero__class_Ozero(X3171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3171),X3170),X3169)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).
fof(i_0_1637,plain,
! [X3244,X3245,X3246] :
( ~ class_Rings_Olinordered__ring__strict(X3246)
| ~ c_Orderings_Oord__class_Oless(X3246,X3245,c_Groups_Ozero__class_Ozero(X3246))
| ~ c_Orderings_Oord__class_Oless(X3246,X3244,c_Groups_Ozero__class_Ozero(X3246))
| c_Orderings_Oord__class_Oless(X3246,c_Groups_Ozero__class_Ozero(X3246),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3246),X3245),X3244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).
fof(i_0_1638,plain,
! [X4300,X4301,X4302,X4303] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4303)
| ~ c_Orderings_Oord__class_Oless__eq(X4303,X4302,X4301)
| c_Orderings_Oord__class_Oless__eq(X4303,c_Groups_Oplus__class_Oplus(X4303,X4302,X4300),c_Groups_Oplus__class_Oplus(X4303,X4301,X4300)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).
fof(i_0_1639,plain,
! [X4304,X4305,X4306,X4307] :
( ~ class_Groups_Oordered__ab__semigroup__add(X4307)
| ~ c_Orderings_Oord__class_Oless__eq(X4307,X4306,X4305)
| c_Orderings_Oord__class_Oless__eq(X4307,c_Groups_Oplus__class_Oplus(X4307,X4304,X4306),c_Groups_Oplus__class_Oplus(X4307,X4304,X4305)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).
fof(i_0_1640,plain,
! [X4329,X4330,X4331,X4332] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4332)
| ~ c_Orderings_Oord__class_Oless(X4332,X4331,X4330)
| c_Orderings_Oord__class_Oless(X4332,c_Groups_Oplus__class_Oplus(X4332,X4331,X4329),c_Groups_Oplus__class_Oplus(X4332,X4330,X4329)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).
fof(i_0_1641,plain,
! [X4333,X4334,X4335,X4336] :
( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X4336)
| ~ c_Orderings_Oord__class_Oless(X4336,X4335,X4334)
| c_Orderings_Oord__class_Oless(X4336,c_Groups_Oplus__class_Oplus(X4336,X4333,X4335),c_Groups_Oplus__class_Oplus(X4336,X4333,X4334)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).
fof(i_0_1642,plain,
! [X4908] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk21_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X4908),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____),X4908)),esk21_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,
! [X2788] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0)
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2788),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____),X2788)),esk2_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,
! [X2784] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X2784),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____),X2784)),v_m____) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_m_I2_J])]) ).
fof(i_0_1645,plain,
! [X3019] : 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____),X3019))),
inference(variable_rename,[status(thm)],[fact_c]) ).
fof(i_0_1646,plain,
! [X2849,X2850,X2851] :
( ~ class_Rings_Olinordered__semidom(X2851)
| ~ c_Orderings_Oord__class_Oless(X2851,c_Groups_Oone__class_Oone(X2851),X2850)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2849)
| c_Orderings_Oord__class_Oless(X2851,c_Groups_Oone__class_Oone(X2851),hAPP(hAPP(c_Power_Opower__class_Opower(X2851),X2850),X2849)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).
fof(i_0_1647,plain,
! [X5414,X5415,X5416,X5417] :
( ~ class_Rings_Ocomm__semiring__1(X5417)
| ~ c_Rings_Odvd__class_Odvd(X5417,X5416,X5415)
| c_Rings_Odvd__class_Odvd(X5417,hAPP(hAPP(c_Power_Opower__class_Opower(X5417),X5416),X5414),hAPP(hAPP(c_Power_Opower__class_Opower(X5417),X5415),X5414)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).
fof(i_0_1648,plain,
! [X5260,X5261,X5262,X5263] :
( ( ~ c_SEQ_Odecseq(X5261,X5260)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5262,X5263)
| c_Orderings_Oord__class_Oless__eq(X5261,hAPP(X5260,X5263),hAPP(X5260,X5262))
| ~ class_Orderings_Oorder(X5261) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk33_2(X5260,X5261),esk34_2(X5260,X5261))
| c_SEQ_Odecseq(X5261,X5260)
| ~ class_Orderings_Oorder(X5261) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5261,hAPP(X5260,esk34_2(X5260,X5261)),hAPP(X5260,esk33_2(X5260,X5261)))
| c_SEQ_Odecseq(X5261,X5260)
| ~ class_Orderings_Oorder(X5261) ) ),
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,
! [X5244,X5245] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5245),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5244)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5245,c_RealDef_Oreal(tc_Nat_Onat,X5244)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt])]) ).
fof(i_0_1650,plain,
! [X4455,X4456,X4457,X4458] :
( ~ class_Groups_Oordered__comm__monoid__add(X4458)
| ~ c_Orderings_Oord__class_Oless__eq(X4458,c_Groups_Ozero__class_Ozero(X4458),X4457)
| ~ c_Orderings_Oord__class_Oless__eq(X4458,X4456,X4455)
| c_Orderings_Oord__class_Oless__eq(X4458,X4456,c_Groups_Oplus__class_Oplus(X4458,X4457,X4455)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).
fof(i_0_1651,plain,
! [X4459,X4460,X4461,X4462] :
( ~ class_Groups_Oordered__comm__monoid__add(X4462)
| ~ c_Orderings_Oord__class_Oless__eq(X4462,c_Groups_Ozero__class_Ozero(X4462),X4461)
| ~ c_Orderings_Oord__class_Oless__eq(X4462,X4460,X4459)
| c_Orderings_Oord__class_Oless__eq(X4462,X4460,c_Groups_Oplus__class_Oplus(X4462,X4459,X4461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).
fof(i_0_1652,plain,
! [X4570,X4571,X4572,X4573] :
( ~ class_Groups_Oordered__comm__monoid__add(X4573)
| ~ c_Orderings_Oord__class_Oless(X4573,c_Groups_Ozero__class_Ozero(X4573),X4572)
| ~ c_Orderings_Oord__class_Oless__eq(X4573,X4571,X4570)
| c_Orderings_Oord__class_Oless(X4573,X4571,c_Groups_Oplus__class_Oplus(X4573,X4572,X4570)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).
fof(i_0_1653,plain,
! [X4574,X4575,X4576,X4577] :
( ~ class_Groups_Oordered__comm__monoid__add(X4577)
| ~ c_Orderings_Oord__class_Oless__eq(X4577,c_Groups_Ozero__class_Ozero(X4577),X4576)
| ~ c_Orderings_Oord__class_Oless(X4577,X4575,X4574)
| c_Orderings_Oord__class_Oless(X4577,X4575,c_Groups_Oplus__class_Oplus(X4577,X4576,X4574)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).
fof(i_0_1654,plain,
! [X3103,X3104,X3105,X3106] :
( ~ class_Rings_Olinordered__semidom(X3106)
| ~ c_Orderings_Oord__class_Oless(X3106,c_Groups_Ozero__class_Ozero(X3106),X3105)
| ~ c_Orderings_Oord__class_Oless(X3106,X3104,X3103)
| c_Orderings_Oord__class_Oless(X3106,X3104,c_Groups_Oplus__class_Oplus(X3106,X3105,X3103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).
fof(i_0_1655,plain,
! [X3441,X3442] : 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),X3442),X3442)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3441),X3441)),
inference(variable_rename,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(i_0_1656,plain,
! [X4849,X4850,X4851] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4851,X4850)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4849,X4851),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4849,X4850)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).
fof(i_0_1657,plain,
! [X3750,X3751,X3752] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3752,X3751)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3752,X3750),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3751,X3750)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).
fof(i_0_1658,plain,
! [X3753,X3754,X3755] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3755,X3754)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3753,X3754),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3753,X3755)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).
fof(i_0_1659,plain,
! [X3616,X3617,X3618] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3618,X3617)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3618,X3616),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3617,X3616)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).
fof(i_0_1660,plain,
! [X3400,X3401,X3402] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3402,X3401)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3400,X3402),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3400,X3401)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__left__mono])]) ).
fof(i_0_1661,plain,
! [X4780,X4781,X4782] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4782,X4781)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4782,X4780),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4781,X4780)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).
fof(i_0_1662,plain,
! [X3571,X3572,X3573] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3573,X3572)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3573,X3571),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3572,X3571)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).
fof(i_0_1663,plain,
! [X3772,X3773,X3774] :
( ~ class_Rings_Olinordered__idom(X3774)
| c_Groups_Oabs__class_Oabs(X3774,hAPP(hAPP(c_Power_Opower__class_Opower(X3774),c_Groups_Ouminus__class_Ouminus(X3774,X3773)),X3772)) = c_Groups_Oabs__class_Oabs(X3774,hAPP(hAPP(c_Power_Opower__class_Opower(X3774),X3773),X3772)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).
fof(i_0_1664,plain,
! [X5357,X5358,X5359,X5360] :
( ~ class_Rings_Ocomm__ring__1(X5360)
| ~ c_Rings_Odvd__class_Odvd(X5360,X5359,X5358)
| ~ c_Rings_Odvd__class_Odvd(X5360,X5359,X5357)
| c_Rings_Odvd__class_Odvd(X5360,X5359,c_Groups_Ominus__class_Ominus(X5360,X5358,X5357)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).
fof(i_0_1665,plain,
! [X5382,X5383,X5384,X5385] :
( ~ class_Rings_Ocomm__semiring__1(X5385)
| ~ c_Rings_Odvd__class_Odvd(X5385,X5384,X5383)
| ~ c_Rings_Odvd__class_Odvd(X5385,X5384,X5382)
| c_Rings_Odvd__class_Odvd(X5385,X5384,c_Groups_Oplus__class_Oplus(X5385,X5383,X5382)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).
fof(i_0_1666,plain,
! [X5298,X5300] :
( ~ class_RealVector_Oreal__algebra__1(X5298)
| ~ class_RealVector_Oreal__normed__vector(X5298)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5298,c_RealVector_Oof__real(X5298,X5300)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5300)),esk36_1(X5298))) ),
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,
! [X5122,X5124] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk26_1(X5122))
| ~ class_RealVector_Oreal__algebra__1(X5122)
| ~ class_RealVector_Oreal__normed__vector(X5122) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X5122,c_RealVector_Oof__real(X5122,X5124)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X5124)),esk26_1(X5122)))
| ~ class_RealVector_Oreal__algebra__1(X5122)
| ~ class_RealVector_Oreal__normed__vector(X5122) ) ),
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,
! [X4749,X4751] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk20_1(X4749))
| ~ class_RealVector_Oreal__algebra__1(X4749)
| ~ class_RealVector_Oreal__normed__vector(X4749) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4749,c_RealVector_Oof__real(X4749,X4751)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X4751)),esk20_1(X4749)))
| ~ class_RealVector_Oreal__algebra__1(X4749)
| ~ class_RealVector_Oreal__normed__vector(X4749) ) ),
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,
! [X4437,X4438,X4439] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4439)
| c_Groups_Oabs__class_Oabs(X4439,c_Groups_Oplus__class_Oplus(X4439,c_Groups_Oabs__class_Oabs(X4439,X4438),c_Groups_Oabs__class_Oabs(X4439,X4437))) = c_Groups_Oplus__class_Oplus(X4439,c_Groups_Oabs__class_Oabs(X4439,X4438),c_Groups_Oabs__class_Oabs(X4439,X4437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).
fof(i_0_1670,plain,
! [X4905,X4906] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4906)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4905)
| 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,X4906,X4905)) ),
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,
! [X3745,X3746,X3747] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3746,X3747) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3745,X3747)
| X3746 = X3745
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3747,X3745)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3747,X3746) )
& ( X3746 != X3745
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3746,X3747) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3745,X3747)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3747,X3745)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3747,X3746) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).
fof(i_0_1672,plain,
! [X3779,X3780] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3780)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3779)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3779,X3780),X3779) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).
fof(i_0_1673,plain,
! [X5235,X5236] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5236),X5235)
| c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5235,c_RealDef_Oreal(tc_Nat_Onat,X5236))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X5235),X5236) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__subtract])]) ).
fof(i_0_1674,plain,
! [X5238,X5239] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5239),X5238)
| c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5238,c_RealDef_Oreal(tc_Nat_Onat,X5239))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X5238),X5239) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__subtract])]) ).
fof(i_0_1675,plain,
! [X5391,X5392,X5393,X5394] :
( ~ class_Rings_Ocomm__semiring__1(X5394)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5394),c_Polynomial_Osmult(X5394,X5393,X5392),X5391)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5394),X5392,X5391) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__dvd__cancel])]) ).
fof(i_0_1676,plain,
! [X4445,X4446] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4446,c_Groups_Ozero__class_Ozero(X4446),c_Groups_Oplus__class_Oplus(X4446,X4445,X4445))
| c_Orderings_Oord__class_Oless__eq(X4446,c_Groups_Ozero__class_Ozero(X4446),X4445)
| ~ class_Groups_Olinordered__ab__group__add(X4446) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4446,c_Groups_Ozero__class_Ozero(X4446),X4445)
| c_Orderings_Oord__class_Oless__eq(X4446,c_Groups_Ozero__class_Ozero(X4446),c_Groups_Oplus__class_Oplus(X4446,X4445,X4445))
| ~ class_Groups_Olinordered__ab__group__add(X4446) ) ),
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,
! [X4466,X4467] :
( ( ~ c_Orderings_Oord__class_Oless(X4467,c_Groups_Ozero__class_Ozero(X4467),c_Groups_Oplus__class_Oplus(X4467,X4466,X4466))
| c_Orderings_Oord__class_Oless(X4467,c_Groups_Ozero__class_Ozero(X4467),X4466)
| ~ class_Groups_Olinordered__ab__group__add(X4467) )
& ( ~ c_Orderings_Oord__class_Oless(X4467,c_Groups_Ozero__class_Ozero(X4467),X4466)
| c_Orderings_Oord__class_Oless(X4467,c_Groups_Ozero__class_Ozero(X4467),c_Groups_Oplus__class_Oplus(X4467,X4466,X4466))
| ~ class_Groups_Olinordered__ab__group__add(X4467) ) ),
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,
! [X4447,X4448] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4448,c_Groups_Oplus__class_Oplus(X4448,X4447,X4447),c_Groups_Ozero__class_Ozero(X4448))
| c_Orderings_Oord__class_Oless__eq(X4448,X4447,c_Groups_Ozero__class_Ozero(X4448))
| ~ class_Groups_Olinordered__ab__group__add(X4448) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4448,X4447,c_Groups_Ozero__class_Ozero(X4448))
| c_Orderings_Oord__class_Oless__eq(X4448,c_Groups_Oplus__class_Oplus(X4448,X4447,X4447),c_Groups_Ozero__class_Ozero(X4448))
| ~ class_Groups_Olinordered__ab__group__add(X4448) ) ),
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,
! [X4468,X4469] :
( ( ~ c_Orderings_Oord__class_Oless(X4469,c_Groups_Oplus__class_Oplus(X4469,X4468,X4468),c_Groups_Ozero__class_Ozero(X4469))
| c_Orderings_Oord__class_Oless(X4469,X4468,c_Groups_Ozero__class_Ozero(X4469))
| ~ class_Groups_Olinordered__ab__group__add(X4469) )
& ( ~ c_Orderings_Oord__class_Oless(X4469,X4468,c_Groups_Ozero__class_Ozero(X4469))
| c_Orderings_Oord__class_Oless(X4469,c_Groups_Oplus__class_Oplus(X4469,X4468,X4468),c_Groups_Ozero__class_Ozero(X4469))
| ~ class_Groups_Olinordered__ab__group__add(X4469) ) ),
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,
! [X4747,X4748] :
( ( ~ c_Orderings_Oord__class_Oless(X4748,c_Groups_Oplus__class_Oplus(X4748,X4747,X4747),c_Groups_Ozero__class_Ozero(X4748))
| c_Orderings_Oord__class_Oless(X4748,X4747,c_Groups_Ozero__class_Ozero(X4748))
| ~ class_Rings_Olinordered__idom(X4748) )
& ( ~ c_Orderings_Oord__class_Oless(X4748,X4747,c_Groups_Ozero__class_Ozero(X4748))
| c_Orderings_Oord__class_Oless(X4748,c_Groups_Oplus__class_Oplus(X4748,X4747,X4747),c_Groups_Ozero__class_Ozero(X4748))
| ~ class_Rings_Olinordered__idom(X4748) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).
fof(i_0_1681,plain,
! [X4658,X4659,X4660,X4661] :
( ~ class_Rings_Ocomm__semiring__1(X4661)
| c_Groups_Oplus__class_Oplus(X4661,c_Groups_Oplus__class_Oplus(X4661,X4660,X4659),X4658) = c_Groups_Oplus__class_Oplus(X4661,c_Groups_Oplus__class_Oplus(X4661,X4660,X4658),X4659) ),
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,
! [X4258,X4259,X4260,X4261] :
( ~ class_Groups_Oab__semigroup__add(X4261)
| c_Groups_Oplus__class_Oplus(X4261,c_Groups_Oplus__class_Oplus(X4261,X4260,X4259),X4258) = c_Groups_Oplus__class_Oplus(X4261,X4260,c_Groups_Oplus__class_Oplus(X4261,X4259,X4258)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).
fof(i_0_1683,plain,
! [X4662,X4663,X4664,X4665] :
( ~ class_Rings_Ocomm__semiring__1(X4665)
| c_Groups_Oplus__class_Oplus(X4665,c_Groups_Oplus__class_Oplus(X4665,X4664,X4663),X4662) = c_Groups_Oplus__class_Oplus(X4665,X4664,c_Groups_Oplus__class_Oplus(X4665,X4663,X4662)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).
fof(i_0_1684,plain,
! [X4666,X4667,X4668,X4669] :
( ~ class_Rings_Ocomm__semiring__1(X4669)
| c_Groups_Oplus__class_Oplus(X4669,X4668,c_Groups_Oplus__class_Oplus(X4669,X4667,X4666)) = c_Groups_Oplus__class_Oplus(X4669,c_Groups_Oplus__class_Oplus(X4669,X4668,X4667),X4666) ),
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,
! [X4670,X4671,X4672,X4673] :
( ~ class_Rings_Ocomm__semiring__1(X4673)
| c_Groups_Oplus__class_Oplus(X4673,X4672,c_Groups_Oplus__class_Oplus(X4673,X4671,X4670)) = c_Groups_Oplus__class_Oplus(X4673,X4671,c_Groups_Oplus__class_Oplus(X4673,X4672,X4670)) ),
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,
! [X3847] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3847),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3847),
inference(variable_rename,[status(thm)],[i_0_1283]) ).
fof(i_0_1687,plain,
! [X3354,X3355] :
( ( ~ 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,X3355,X3354))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3355),X3354) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3355),X3354)
| 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,X3355,X3354)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff])]) ).
fof(i_0_1688,plain,
! [X3361,X3362] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3362,X3361))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3362),X3361) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3362),X3361)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3362,X3361)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff])]) ).
fof(i_0_1689,plain,
! [X3352,X3353] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3353,X3352),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3352,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3353)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3352,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3353))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3353,X3352),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,
! [X3359,X3360] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3360,X3359),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3359,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3360)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3359,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3360))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3360,X3359),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,
! [X3980,X3981,X3982] :
( ~ class_Fields_Olinordered__field(X3982)
| ~ c_Orderings_Oord__class_Oless__eq(X3982,c_Rings_Oinverse__class_Oinverse(X3982,X3981),c_Rings_Oinverse__class_Oinverse(X3982,X3980))
| ~ c_Orderings_Oord__class_Oless(X3982,c_Groups_Ozero__class_Ozero(X3982),X3981)
| c_Orderings_Oord__class_Oless__eq(X3982,X3980,X3981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le])]) ).
fof(i_0_1692,plain,
! [X3951,X3952,X3953] :
( ~ class_Fields_Olinordered__field(X3953)
| ~ c_Orderings_Oord__class_Oless(X3953,c_Rings_Oinverse__class_Oinverse(X3953,X3952),c_Rings_Oinverse__class_Oinverse(X3953,X3951))
| ~ c_Orderings_Oord__class_Oless(X3953,c_Groups_Ozero__class_Ozero(X3953),X3952)
| c_Orderings_Oord__class_Oless(X3953,X3951,X3952) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less])]) ).
fof(i_0_1693,plain,
! [X3977,X3978,X3979] :
( ~ class_Fields_Olinordered__field(X3979)
| ~ c_Orderings_Oord__class_Oless__eq(X3979,c_Rings_Oinverse__class_Oinverse(X3979,X3978),c_Rings_Oinverse__class_Oinverse(X3979,X3977))
| ~ c_Orderings_Oord__class_Oless(X3979,X3977,c_Groups_Ozero__class_Ozero(X3979))
| c_Orderings_Oord__class_Oless__eq(X3979,X3977,X3978) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__imp__le__neg])]) ).
fof(i_0_1694,plain,
! [X3948,X3949,X3950] :
( ~ class_Fields_Olinordered__field(X3950)
| ~ c_Orderings_Oord__class_Oless(X3950,c_Rings_Oinverse__class_Oinverse(X3950,X3949),c_Rings_Oinverse__class_Oinverse(X3950,X3948))
| ~ c_Orderings_Oord__class_Oless(X3950,X3948,c_Groups_Ozero__class_Ozero(X3950))
| c_Orderings_Oord__class_Oless(X3950,X3948,X3949) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__imp__less__neg])]) ).
fof(i_0_1695,plain,
! [X4486,X4487,X4488] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4488,X4487,X4486)
| c_Orderings_Oord__class_Oless__eq(X4488,c_Groups_Ominus__class_Ominus(X4488,X4487,X4486),c_Groups_Ozero__class_Ozero(X4488))
| ~ class_Groups_Oordered__ab__group__add(X4488) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4488,c_Groups_Ominus__class_Ominus(X4488,X4487,X4486),c_Groups_Ozero__class_Ozero(X4488))
| c_Orderings_Oord__class_Oless__eq(X4488,X4487,X4486)
| ~ class_Groups_Oordered__ab__group__add(X4488) ) ),
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,
! [X4489,X4490,X4491] :
( ( ~ c_Orderings_Oord__class_Oless(X4491,X4490,X4489)
| c_Orderings_Oord__class_Oless(X4491,c_Groups_Ominus__class_Ominus(X4491,X4490,X4489),c_Groups_Ozero__class_Ozero(X4491))
| ~ class_Groups_Oordered__ab__group__add(X4491) )
& ( ~ c_Orderings_Oord__class_Oless(X4491,c_Groups_Ominus__class_Ominus(X4491,X4490,X4489),c_Groups_Ozero__class_Ozero(X4491))
| c_Orderings_Oord__class_Oless(X4491,X4490,X4489)
| ~ class_Groups_Oordered__ab__group__add(X4491) ) ),
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,
! [X4075,X4076,X4077,X4078] :
( ~ class_Rings_Ocomm__semiring__0(X4078)
| c_Polynomial_Osmult(X4078,X4077,c_Polynomial_Omonom(X4078,X4076,X4075)) = c_Polynomial_Omonom(X4078,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4078),X4077),X4076),X4075) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__monom])]) ).
fof(i_0_1698,plain,
! [X4162,X4163,X4164,X4165] :
( ~ class_Rings_Ocomm__semiring__0(X4165)
| c_Polynomial_Osmult(X4165,X4164,c_Polynomial_Osmult(X4165,X4163,X4162)) = c_Polynomial_Osmult(X4165,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4165),X4164),X4163),X4162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__smult])]) ).
fof(i_0_1699,plain,
! [X3794,X3795] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3795,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3794))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3794,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3795))),
inference(variable_rename,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(i_0_1700,plain,
! [X4903,X4904] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4903)
| 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),X4904),X4903)) ),
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,
! [X3662,X3663] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3663)
| ~ 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),X3663),X3662)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3662)
| ~ 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),X3663),X3662)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3663)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3662)
| 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),X3663),X3662)) ) ),
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,
! [X2950,X2951] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2951)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2950)
| 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),X2951),X2950)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__mult__order])]) ).
fof(i_0_1703,plain,
! [X3833,X3834,X3835] :
( ~ class_Rings_Olinordered__idom(X3835)
| ~ c_Orderings_Oord__class_Oless__eq(X3835,c_Groups_Ozero__class_Ozero(X3835),X3834)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3835),c_Groups_Oabs__class_Oabs(X3835,X3833)),X3834) = c_Groups_Oabs__class_Oabs(X3835,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3835),X3833),X3834)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).
fof(i_0_1704,plain,
! [X3652] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3652,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3652),X3652))),
inference(variable_rename,[status(thm)],[fact_le__cube]) ).
fof(i_0_1705,plain,
! [X4360,X4361,X4362,X4363,X4364] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4364,X4363,X4362)
| c_Orderings_Oord__class_Oless__eq(X4364,X4361,X4360)
| c_Groups_Ominus__class_Ominus(X4364,X4363,X4362) != c_Groups_Ominus__class_Ominus(X4364,X4361,X4360)
| ~ class_Groups_Oordered__ab__group__add(X4364) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4364,X4361,X4360)
| c_Orderings_Oord__class_Oless__eq(X4364,X4363,X4362)
| c_Groups_Ominus__class_Ominus(X4364,X4363,X4362) != c_Groups_Ominus__class_Ominus(X4364,X4361,X4360)
| ~ class_Groups_Oordered__ab__group__add(X4364) ) ),
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,
! [X4365,X4366,X4367,X4368,X4369] :
( ( ~ c_Orderings_Oord__class_Oless(X4369,X4368,X4367)
| c_Orderings_Oord__class_Oless(X4369,X4366,X4365)
| c_Groups_Ominus__class_Ominus(X4369,X4368,X4367) != c_Groups_Ominus__class_Ominus(X4369,X4366,X4365)
| ~ class_Groups_Oordered__ab__group__add(X4369) )
& ( ~ c_Orderings_Oord__class_Oless(X4369,X4366,X4365)
| c_Orderings_Oord__class_Oless(X4369,X4368,X4367)
| c_Groups_Ominus__class_Ominus(X4369,X4368,X4367) != c_Groups_Ominus__class_Ominus(X4369,X4366,X4365)
| ~ class_Groups_Oordered__ab__group__add(X4369) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).
fof(i_0_1707,plain,
! [X3649,X3650,X3651] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3651,X3650)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3651),X3649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3650),X3649)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).
fof(i_0_1708,plain,
! [X3646,X3647,X3648] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3648,X3647)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3646),X3648),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3646),X3647)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).
fof(i_0_1709,plain,
! [X4622,X4623,X4624,X4625] :
( ~ class_Rings_Ocomm__semiring__1(X4625)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4623),X4622)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4625),X4624),X4622)) ),
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,
! [X3729,X3730,X3731] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3731,X3730),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3731,X3729)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3730,X3729),
inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).
fof(i_0_1711,plain,
! [X3726,X3727,X3728] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3728,X3727),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3726,X3727)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3728,X3726),
inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).
fof(i_0_1712,plain,
! [X3928,X3929,X3930] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3930,X3929),X3928) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3930,X3928),X3929),
inference(variable_rename,[status(thm)],[fact_diff__commute]) ).
fof(i_0_1713,plain,
! [X3732,X3733,X3734] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3734,X3733),X3732) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3734,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3733,X3732)),
inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).
fof(i_0_1714,plain,
! [X4846,X4847,X4848] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4848,X4847),X4846) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4848,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4847,X4846)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
fof(i_0_1715,plain,
! [X3509,X3510,X3511] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3511,X3510),X3509) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3511,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3510,X3509)),
inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).
fof(i_0_1716,plain,
! [X4843,X4844,X4845] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4845,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4844,X4843)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4844,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4845,X4843)),
inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).
fof(i_0_1717,plain,
! [X3506,X3507,X3508] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3508,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3507,X3506)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3507,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3508,X3506)),
inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).
fof(i_0_1718,plain,
! [X4793,X4794] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4794,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4793,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4794,X4793)
| X4794 = X4793 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4794,X4793)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4794,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4793,c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( X4794 != X4793
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4794,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4793,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,
! [X4788,X4789] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4789,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4788)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4789,X4788) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4789,X4788)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4789,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4788) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).
fof(i_0_1720,plain,
! [X4795,X4796] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4795,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4796,X4795) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4796,X4795)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4796,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4795,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,
! [X4800,X4801] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4801,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4800,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4801,X4800) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4801,X4800)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4801,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4800,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,
! [X5418,X5419,X5420,X5421] :
( ~ class_Rings_Ocomm__semiring__1(X5421)
| ~ c_Rings_Odvd__class_Odvd(X5421,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5421),X5420),X5419),X5418)
| c_Rings_Odvd__class_Odvd(X5421,X5419,X5418) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).
fof(i_0_1723,plain,
! [X3439,X3440] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3440,X3439)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3440,X3439),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,X3440,X3439),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3440,X3439) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff])]) ).
fof(i_0_1724,plain,
! [X4798,X4799] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4799,X4798)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4799,X4798),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4799,X4798),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4799,X4798) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).
fof(i_0_1725,plain,
! [X3781,X3782] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3782,X3781))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3781,X3782) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3781,X3782)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3782,X3781)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).
fof(i_0_1726,plain,
! [X3563,X3564,X3565,X3566] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3566,X3565)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3564,X3565) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3566,X3563)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3564,X3563) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).
fof(i_0_1727,plain,
! [X5242,X5243] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5243)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5243,c_RealDef_Oreal(tc_Nat_Onat,X5242))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5243),X5242) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__add])]) ).
fof(i_0_1728,plain,
! [X5248,X5249] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5249)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5249,c_RealDef_Oreal(tc_Nat_Onat,X5248))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5249),X5248) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__add])]) ).
fof(i_0_1729,plain,
! [X4559,X4560,X4561] :
( ( c_Orderings_Oord__class_Oless__eq(X4561,X4560,X4559)
| ~ c_Orderings_Oord__class_Oless__eq(X4561,c_Groups_Oabs__class_Oabs(X4561,X4560),X4559)
| ~ class_Groups_Oordered__ab__group__add__abs(X4561) )
& ( c_Orderings_Oord__class_Oless__eq(X4561,c_Groups_Ouminus__class_Ouminus(X4561,X4560),X4559)
| ~ c_Orderings_Oord__class_Oless__eq(X4561,c_Groups_Oabs__class_Oabs(X4561,X4560),X4559)
| ~ class_Groups_Oordered__ab__group__add__abs(X4561) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4561,X4560,X4559)
| ~ c_Orderings_Oord__class_Oless__eq(X4561,c_Groups_Ouminus__class_Ouminus(X4561,X4560),X4559)
| c_Orderings_Oord__class_Oless__eq(X4561,c_Groups_Oabs__class_Oabs(X4561,X4560),X4559)
| ~ class_Groups_Oordered__ab__group__add__abs(X4561) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).
fof(i_0_1730,plain,
! [X4556,X4557,X4558] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4558)
| ~ c_Orderings_Oord__class_Oless__eq(X4558,X4557,X4556)
| ~ c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Ouminus__class_Ouminus(X4558,X4557),X4556)
| c_Orderings_Oord__class_Oless__eq(X4558,c_Groups_Oabs__class_Oabs(X4558,X4557),X4556) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).
fof(i_0_1731,plain,
! [X3769,X3770,X3771] :
( ( c_Orderings_Oord__class_Oless(X3771,X3770,X3769)
| ~ c_Orderings_Oord__class_Oless(X3771,c_Groups_Oabs__class_Oabs(X3771,X3770),X3769)
| ~ class_Rings_Olinordered__idom(X3771) )
& ( c_Orderings_Oord__class_Oless(X3771,c_Groups_Ouminus__class_Ouminus(X3771,X3770),X3769)
| ~ c_Orderings_Oord__class_Oless(X3771,c_Groups_Oabs__class_Oabs(X3771,X3770),X3769)
| ~ class_Rings_Olinordered__idom(X3771) )
& ( ~ c_Orderings_Oord__class_Oless(X3771,X3770,X3769)
| ~ c_Orderings_Oord__class_Oless(X3771,c_Groups_Ouminus__class_Ouminus(X3771,X3770),X3769)
| c_Orderings_Oord__class_Oless(X3771,c_Groups_Oabs__class_Oabs(X3771,X3770),X3769)
| ~ class_Rings_Olinordered__idom(X3771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).
fof(i_0_1732,plain,
! [X3629,X3630,X3631] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3631,X3629)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3630),X3629) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3630,X3629)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3631,X3630),X3629) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1284])])]) ).
fof(i_0_1733,plain,
! [X3626,X3627,X3628] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3628,X3627),X3626)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3628,X3626) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).
fof(i_0_1734,plain,
! [X3623,X3624,X3625] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3625,X3624),X3623)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3624,X3623) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).
fof(i_0_1735,plain,
! [X3560,X3561,X3562] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3562,X3561),X3560)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3562,X3560) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).
fof(i_0_1736,plain,
! [X5183,X5184] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5184,X5183)
| c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5183,X5184)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5183),c_RealDef_Oreal(tc_Nat_Onat,X5184)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff])]) ).
fof(i_0_1737,plain,
! [X4452,X4453,X4454] :
( ( X4453 = c_Groups_Ozero__class_Ozero(X4454)
| c_Groups_Oplus__class_Oplus(X4454,X4453,X4452) != c_Groups_Ozero__class_Ozero(X4454)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4452)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4453)
| ~ class_Groups_Oordered__comm__monoid__add(X4454) )
& ( X4452 = c_Groups_Ozero__class_Ozero(X4454)
| c_Groups_Oplus__class_Oplus(X4454,X4453,X4452) != c_Groups_Ozero__class_Ozero(X4454)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4452)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4453)
| ~ class_Groups_Oordered__comm__monoid__add(X4454) )
& ( X4453 != c_Groups_Ozero__class_Ozero(X4454)
| X4452 != c_Groups_Ozero__class_Ozero(X4454)
| c_Groups_Oplus__class_Oplus(X4454,X4453,X4452) = c_Groups_Ozero__class_Ozero(X4454)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4452)
| ~ c_Orderings_Oord__class_Oless__eq(X4454,c_Groups_Ozero__class_Ozero(X4454),X4453)
| ~ class_Groups_Oordered__comm__monoid__add(X4454) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).
fof(i_0_1738,plain,
! [X3986,X3987,X3988] :
( ~ class_Fields_Olinordered__field(X3988)
| ~ c_Orderings_Oord__class_Oless__eq(X3988,X3987,X3986)
| ~ c_Orderings_Oord__class_Oless(X3988,c_Groups_Ozero__class_Ozero(X3988),X3987)
| c_Orderings_Oord__class_Oless__eq(X3988,c_Rings_Oinverse__class_Oinverse(X3988,X3986),c_Rings_Oinverse__class_Oinverse(X3988,X3987)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le])]) ).
fof(i_0_1739,plain,
! [X3959,X3960,X3961] :
( ~ class_Fields_Olinordered__field(X3961)
| ~ c_Orderings_Oord__class_Oless(X3961,X3960,X3959)
| ~ c_Orderings_Oord__class_Oless(X3961,c_Groups_Ozero__class_Ozero(X3961),X3960)
| c_Orderings_Oord__class_Oless(X3961,c_Rings_Oinverse__class_Oinverse(X3961,X3959),c_Rings_Oinverse__class_Oinverse(X3961,X3960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less])]) ).
fof(i_0_1740,plain,
! [X3983,X3984,X3985] :
( ~ class_Fields_Olinordered__field(X3985)
| ~ c_Orderings_Oord__class_Oless__eq(X3985,X3984,X3983)
| ~ c_Orderings_Oord__class_Oless(X3985,X3983,c_Groups_Ozero__class_Ozero(X3985))
| c_Orderings_Oord__class_Oless__eq(X3985,c_Rings_Oinverse__class_Oinverse(X3985,X3983),c_Rings_Oinverse__class_Oinverse(X3985,X3984)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__inverse__le__neg])]) ).
fof(i_0_1741,plain,
! [X3956,X3957,X3958] :
( ~ class_Fields_Olinordered__field(X3958)
| ~ c_Orderings_Oord__class_Oless(X3958,X3957,X3956)
| ~ c_Orderings_Oord__class_Oless(X3958,X3956,c_Groups_Ozero__class_Ozero(X3958))
| c_Orderings_Oord__class_Oless(X3958,c_Rings_Oinverse__class_Oinverse(X3958,X3956),c_Rings_Oinverse__class_Oinverse(X3958,X3957)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__inverse__less__neg])]) ).
fof(i_0_1742,plain,
! [X5112,X5113,X5114,X5115] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X5114,X5115),X5113,X5112)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5114,X5115),X5113,X5112)
| ~ class_Orderings_Oord(X5115) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5114,X5115),X5112,X5113)
| ~ c_Orderings_Oord__class_Oless(tc_fun(X5114,X5115),X5113,X5112)
| ~ class_Orderings_Oord(X5115) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X5114,X5115),X5113,X5112)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X5114,X5115),X5112,X5113)
| c_Orderings_Oord__class_Oless(tc_fun(X5114,X5115),X5113,X5112)
| ~ class_Orderings_Oord(X5115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1285])])]) ).
fof(i_0_1743,plain,
! [X4596,X4597] :
( ( ~ 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),X4597),X4596))
| X4596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4597) )
& ( X4596 != 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),X4597),X4596)) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X4597)
| 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),X4597),X4596)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq])])]) ).
fof(i_0_1744,plain,
! [X2822,X2823] :
( ( ~ 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),X2823),X2822))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2823)
| X2822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2823)
| 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),X2823),X2822)) )
& ( X2822 != 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),X2823),X2822)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).
fof(i_0_1745,plain,
! [X5277,X5278,X5279,X5280,X5281] :
( ~ class_Groups_Ominus(X5281)
| hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X5280,X5281),X5279,X5278),X5277) = c_Groups_Ominus__class_Ominus(X5281,hAPP(X5279,X5277),hAPP(X5278,X5277)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).
fof(i_0_1746,plain,
! [X4010,X4011] :
( ~ class_Fields_Olinordered__field(X4011)
| ~ c_Orderings_Oord__class_Oless(X4011,c_Groups_Ozero__class_Ozero(X4011),X4010)
| ~ c_Orderings_Oord__class_Oless__eq(X4011,X4010,c_Groups_Oone__class_Oone(X4011))
| c_Orderings_Oord__class_Oless__eq(X4011,c_Groups_Oone__class_Oone(X4011),c_Rings_Oinverse__class_Oinverse(X4011,X4010)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse])]) ).
fof(i_0_1747,plain,
! [X3921,X3922] :
( ( c_Orderings_Oord__class_Oless(X3922,c_Groups_Ozero__class_Ozero(X3922),X3921)
| ~ c_Orderings_Oord__class_Oless__eq(X3922,c_Groups_Oone__class_Oone(X3922),c_Rings_Oinverse__class_Oinverse(X3922,X3921))
| ~ class_Fields_Olinordered__field__inverse__zero(X3922) )
& ( c_Orderings_Oord__class_Oless__eq(X3922,X3921,c_Groups_Oone__class_Oone(X3922))
| ~ c_Orderings_Oord__class_Oless__eq(X3922,c_Groups_Oone__class_Oone(X3922),c_Rings_Oinverse__class_Oinverse(X3922,X3921))
| ~ class_Fields_Olinordered__field__inverse__zero(X3922) )
& ( ~ c_Orderings_Oord__class_Oless(X3922,c_Groups_Ozero__class_Ozero(X3922),X3921)
| ~ c_Orderings_Oord__class_Oless__eq(X3922,X3921,c_Groups_Oone__class_Oone(X3922))
| c_Orderings_Oord__class_Oless__eq(X3922,c_Groups_Oone__class_Oone(X3922),c_Rings_Oinverse__class_Oinverse(X3922,X3921))
| ~ class_Fields_Olinordered__field__inverse__zero(X3922) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__inverse__iff])])]) ).
fof(i_0_1748,plain,
! [X3994,X3995] :
( ~ class_Fields_Olinordered__field(X3995)
| ~ c_Orderings_Oord__class_Oless(X3995,c_Groups_Ozero__class_Ozero(X3995),X3994)
| ~ c_Orderings_Oord__class_Oless(X3995,X3994,c_Groups_Oone__class_Oone(X3995))
| c_Orderings_Oord__class_Oless(X3995,c_Groups_Oone__class_Oone(X3995),c_Rings_Oinverse__class_Oinverse(X3995,X3994)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse])]) ).
fof(i_0_1749,plain,
! [X3996,X3997] :
( ( c_Orderings_Oord__class_Oless(X3997,c_Groups_Ozero__class_Ozero(X3997),X3996)
| ~ c_Orderings_Oord__class_Oless(X3997,c_Groups_Oone__class_Oone(X3997),c_Rings_Oinverse__class_Oinverse(X3997,X3996))
| ~ class_Fields_Olinordered__field__inverse__zero(X3997) )
& ( c_Orderings_Oord__class_Oless(X3997,X3996,c_Groups_Oone__class_Oone(X3997))
| ~ c_Orderings_Oord__class_Oless(X3997,c_Groups_Oone__class_Oone(X3997),c_Rings_Oinverse__class_Oinverse(X3997,X3996))
| ~ class_Fields_Olinordered__field__inverse__zero(X3997) )
& ( ~ c_Orderings_Oord__class_Oless(X3997,c_Groups_Ozero__class_Ozero(X3997),X3996)
| ~ c_Orderings_Oord__class_Oless(X3997,X3996,c_Groups_Oone__class_Oone(X3997))
| c_Orderings_Oord__class_Oless(X3997,c_Groups_Oone__class_Oone(X3997),c_Rings_Oinverse__class_Oinverse(X3997,X3996))
| ~ class_Fields_Olinordered__field__inverse__zero(X3997) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__inverse__iff])])]) ).
fof(i_0_1750,plain,
! [X3775,X3776] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3775),X3776)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3776),X3775) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3776,X3775)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3776),X3775) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3775),X3776)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3776,X3775)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3776),X3775) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff])])]) ).
fof(i_0_1751,plain,
! [X5211,X5212,X5213] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5213),X5212,X5211)
| X5212 = X5211
| c_Polynomial_Opos__poly(X5213,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5213),X5211,X5212))
| ~ class_Rings_Olinordered__idom(X5213) )
& ( X5212 != X5211
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5213),X5212,X5211)
| ~ class_Rings_Olinordered__idom(X5213) )
& ( ~ c_Polynomial_Opos__poly(X5213,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5213),X5211,X5212))
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X5213),X5212,X5211)
| ~ class_Rings_Olinordered__idom(X5213) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def])])]) ).
fof(i_0_1752,plain,
! [X5250,X5251,X5252] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5252),X5251,X5250)
| c_Polynomial_Opos__poly(X5252,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5252),X5250,X5251))
| ~ class_Rings_Olinordered__idom(X5252) )
& ( ~ c_Polynomial_Opos__poly(X5252,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X5252),X5250,X5251))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5252),X5251,X5250)
| ~ class_Rings_Olinordered__idom(X5252) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__poly__def])])]) ).
fof(i_0_1753,plain,
! [X3839,X3840,X3841] :
( ~ class_Rings_Olinordered__idom(X3841)
| c_Orderings_Oord__class_Oless__eq(X3841,c_Groups_Ozero__class_Ozero(X3841),hAPP(hAPP(c_Power_Opower__class_Opower(X3841),c_Groups_Oabs__class_Oabs(X3841,X3840)),X3839)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).
fof(i_0_1754,plain,
! [X5179,X5180,X5181] :
( ( X5179 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5181))
| c_Polynomial_Opos__poly(X5181,X5179)
| ~ c_Polynomial_Opos__poly(X5181,c_Polynomial_OpCons(X5181,X5180,X5179))
| ~ class_Rings_Olinordered__idom(X5181) )
& ( c_Orderings_Oord__class_Oless(X5181,c_Groups_Ozero__class_Ozero(X5181),X5180)
| c_Polynomial_Opos__poly(X5181,X5179)
| ~ c_Polynomial_Opos__poly(X5181,c_Polynomial_OpCons(X5181,X5180,X5179))
| ~ class_Rings_Olinordered__idom(X5181) )
& ( ~ c_Polynomial_Opos__poly(X5181,X5179)
| c_Polynomial_Opos__poly(X5181,c_Polynomial_OpCons(X5181,X5180,X5179))
| ~ class_Rings_Olinordered__idom(X5181) )
& ( X5179 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5181))
| ~ c_Orderings_Oord__class_Oless(X5181,c_Groups_Ozero__class_Ozero(X5181),X5180)
| c_Polynomial_Opos__poly(X5181,c_Polynomial_OpCons(X5181,X5180,X5179))
| ~ class_Rings_Olinordered__idom(X5181) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons])])]) ).
fof(i_0_1755,plain,
! [X3692] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,X3692),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,X3692))
| hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,X3692),esk10_1(X3692)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1286])])]) ).
fof(i_0_1756,plain,
! [X5395,X5396,X5397,X5398] :
( ~ class_Rings_Ocomm__semiring__1(X5398)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5398),X5397,X5396)
| c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X5398),X5397,c_Polynomial_Osmult(X5398,X5395,X5396)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__smult])]) ).
fof(i_0_1757,plain,
! [X2933,X2934,X2935,X2936] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(X2936),X2935),X2934) != hAPP(hAPP(c_Power_Opower__class_Opower(X2936),X2935),X2933)
| X2934 = X2933
| ~ c_Orderings_Oord__class_Oless(X2936,c_Groups_Oone__class_Oone(X2936),X2935)
| ~ class_Rings_Olinordered__semidom(X2936) )
& ( X2934 != X2933
| hAPP(hAPP(c_Power_Opower__class_Opower(X2936),X2935),X2934) = hAPP(hAPP(c_Power_Opower__class_Opower(X2936),X2935),X2933)
| ~ c_Orderings_Oord__class_Oless(X2936,c_Groups_Oone__class_Oone(X2936),X2935)
| ~ class_Rings_Olinordered__semidom(X2936) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).
fof(i_0_1758,plain,
! [X5232,X5233] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5233),X5232)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5233,c_RealDef_Oreal(tc_Nat_Onat,X5232))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5233) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5233,c_RealDef_Oreal(tc_Nat_Onat,X5232))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5233),X5232)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5233) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq])])]) ).
fof(i_0_1759,plain,
! [X5240,X5241] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5241)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5241,c_RealDef_Oreal(tc_Nat_Onat,X5240))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X5241),X5240) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__natfloor])]) ).
fof(i_0_1760,plain,
! [X5228,X5229] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5228,c_RComplete_Onatfloor(X5229))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5228),X5229)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5229) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5228),X5229)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5228,c_RComplete_Onatfloor(X5229))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5229) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq])])]) ).
fof(i_0_1761,plain,
! [X2918,X2919,X2920] :
( ~ class_Rings_Olinordered__semidom(X2920)
| ~ c_Orderings_Oord__class_Oless__eq(X2920,c_Groups_Oone__class_Oone(X2920),X2919)
| c_Orderings_Oord__class_Oless__eq(X2920,c_Groups_Oone__class_Oone(X2920),hAPP(hAPP(c_Power_Opower__class_Opower(X2920),X2919),X2918)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).
fof(i_0_1762,plain,
! [X2906,X2907,X2908] :
( ~ class_Rings_Olinordered__semidom(X2908)
| ~ c_Orderings_Oord__class_Oless__eq(X2908,c_Groups_Ozero__class_Ozero(X2908),X2907)
| c_Orderings_Oord__class_Oless__eq(X2908,c_Groups_Ozero__class_Ozero(X2908),hAPP(hAPP(c_Power_Opower__class_Opower(X2908),X2907),X2906)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).
fof(i_0_1763,plain,
! [X2909,X2910,X2911] :
( ~ class_Rings_Olinordered__semidom(X2911)
| ~ c_Orderings_Oord__class_Oless(X2911,c_Groups_Ozero__class_Ozero(X2911),X2910)
| c_Orderings_Oord__class_Oless(X2911,c_Groups_Ozero__class_Ozero(X2911),hAPP(hAPP(c_Power_Opower__class_Opower(X2911),X2910),X2909)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).
fof(i_0_1764,plain,
! [X3989,X3990] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3990,c_Rings_Oinverse__class_Oinverse(X3990,X3989),c_Groups_Oone__class_Oone(X3990))
| c_Orderings_Oord__class_Oless__eq(X3990,X3989,c_Groups_Ozero__class_Ozero(X3990))
| c_Orderings_Oord__class_Oless__eq(X3990,c_Groups_Oone__class_Oone(X3990),X3989)
| ~ class_Fields_Olinordered__field__inverse__zero(X3990) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3990,X3989,c_Groups_Ozero__class_Ozero(X3990))
| c_Orderings_Oord__class_Oless__eq(X3990,c_Rings_Oinverse__class_Oinverse(X3990,X3989),c_Groups_Oone__class_Oone(X3990))
| ~ class_Fields_Olinordered__field__inverse__zero(X3990) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3990,c_Groups_Oone__class_Oone(X3990),X3989)
| c_Orderings_Oord__class_Oless__eq(X3990,c_Rings_Oinverse__class_Oinverse(X3990,X3989),c_Groups_Oone__class_Oone(X3990))
| ~ class_Fields_Olinordered__field__inverse__zero(X3990) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__le__1__iff])])]) ).
fof(i_0_1765,plain,
! [X3923,X3924] :
( ( ~ c_Orderings_Oord__class_Oless(X3924,c_Rings_Oinverse__class_Oinverse(X3924,X3923),c_Groups_Oone__class_Oone(X3924))
| c_Orderings_Oord__class_Oless__eq(X3924,X3923,c_Groups_Ozero__class_Ozero(X3924))
| c_Orderings_Oord__class_Oless(X3924,c_Groups_Oone__class_Oone(X3924),X3923)
| ~ class_Fields_Olinordered__field__inverse__zero(X3924) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3924,X3923,c_Groups_Ozero__class_Ozero(X3924))
| c_Orderings_Oord__class_Oless(X3924,c_Rings_Oinverse__class_Oinverse(X3924,X3923),c_Groups_Oone__class_Oone(X3924))
| ~ class_Fields_Olinordered__field__inverse__zero(X3924) )
& ( ~ c_Orderings_Oord__class_Oless(X3924,c_Groups_Oone__class_Oone(X3924),X3923)
| c_Orderings_Oord__class_Oless(X3924,c_Rings_Oinverse__class_Oinverse(X3924,X3923),c_Groups_Oone__class_Oone(X3924))
| ~ class_Fields_Olinordered__field__inverse__zero(X3924) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__less__1__iff])])]) ).
fof(i_0_1766,plain,
! [X5149] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5149)
| c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5149,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X5149),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_1767,plain,
! [X5111] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5111)
| c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X5111,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(X5111),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_1768,plain,
! [X3406,X3407,X3408] :
( ~ class_Rings_Odivision__ring(X3408)
| X3407 = c_Groups_Ozero__class_Ozero(X3408)
| X3406 = c_Groups_Ozero__class_Ozero(X3408)
| c_Rings_Oinverse__class_Oinverse(X3408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3408),X3407),X3406)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3408),c_Rings_Oinverse__class_Oinverse(X3408,X3406)),c_Rings_Oinverse__class_Oinverse(X3408,X3407)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__mult__distrib])]) ).
fof(i_0_1769,plain,
! [X3208,X3209] :
( ~ class_Rings_Olinordered__ring(X3209)
| ~ c_Orderings_Oord__class_Oless(X3209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3209),X3208),X3208),c_Groups_Ozero__class_Ozero(X3209)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1287])]) ).
fof(i_0_1770,plain,
! [X4772] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4772),X4772) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).
fof(i_0_1771,plain,
! [X5162,X5163] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5163)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X5162)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X5163,X5162)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).
fof(i_0_1772,plain,
! [X5125,X5126,X5127,X5128] : hAPP(hAPP(c_Power_Opower_Opower(X5128,X5127,X5126),X5125),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X5127,
inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(i_0_1773,plain,
! [X4775] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4775)
| 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),X4775)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).
fof(i_0_1774,plain,
! [X5316,X5317,X5318] :
( ~ class_Rings_Olinordered__idom(X5318)
| c_Groups_Osgn__class_Osgn(X5318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5318),X5317),X5316)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5318),c_Groups_Osgn__class_Osgn(X5318,X5317)),c_Groups_Osgn__class_Osgn(X5318,X5316)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).
fof(i_0_1775,plain,
! [X5319,X5320,X5321] :
( ~ class_RealVector_Oreal__normed__div__algebra(X5321)
| c_Groups_Osgn__class_Osgn(X5321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5321),X5320),X5319)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5321),c_Groups_Osgn__class_Osgn(X5321,X5320)),c_Groups_Osgn__class_Osgn(X5321,X5319)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__mult])]) ).
fof(i_0_1776,plain,
! [X3704,X3705,X3706] :
( ~ class_Rings_Olinordered__idom(X3706)
| c_Groups_Oabs__class_Oabs(X3706,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3706),X3705),X3704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3706),c_Groups_Oabs__class_Oabs(X3706,X3705)),c_Groups_Oabs__class_Oabs(X3706,X3704)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).
fof(i_0_1777,plain,
! [X3937,X3938,X3939] :
( ~ class_Fields_Ofield__inverse__zero(X3939)
| c_Rings_Oinverse__class_Oinverse(X3939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3939),X3938),X3937)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3939),c_Rings_Oinverse__class_Oinverse(X3939,X3938)),c_Rings_Oinverse__class_Oinverse(X3939,X3937)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__mult__distrib])]) ).
fof(i_0_1778,plain,
! [X4175,X4176,X4177] :
( ~ class_Groups_Oab__group__add(X4177)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4177),c_Polynomial_OpCons(X4177,X4176,X4175)) = c_Polynomial_OpCons(X4177,c_Groups_Ouminus__class_Ouminus(X4177,X4176),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4177),X4175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J])]) ).
fof(i_0_1779,plain,
! [X4172,X4173,X4174] :
( ~ class_Groups_Oab__group__add(X4174)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4174),c_Polynomial_OpCons(X4174,X4173,X4172)) = c_Polynomial_OpCons(X4174,c_Groups_Ouminus__class_Ouminus(X4174,X4173),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4174),X4172)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__pCons])]) ).
fof(i_0_1780,plain,
! [X4440,X4441,X4442] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4442)
| c_Groups_Oabs__class_Oabs(X4442,c_Groups_Ominus__class_Ominus(X4442,X4441,X4440)) = c_Groups_Oabs__class_Oabs(X4442,c_Groups_Ominus__class_Ominus(X4442,X4440,X4441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).
fof(i_0_1781,plain,
! [X3397,X3398,X3399] :
( ~ class_RealVector_Oreal__normed__vector(X3399)
| c_RealVector_Onorm__class_Onorm(X3399,c_Groups_Ominus__class_Ominus(X3399,X3398,X3397)) = c_RealVector_Onorm__class_Onorm(X3399,c_Groups_Ominus__class_Ominus(X3399,X3397,X3398)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__commute])]) ).
fof(i_0_1782,plain,
! [X2940,X2941,X2942] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2942)
| c_RealVector_Onorm__class_Onorm(X2942,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2942),X2941),X2940)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2942,X2941)),c_RealVector_Onorm__class_Onorm(X2942,X2940)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__mult])]) ).
fof(i_0_1783,plain,
! [X4783,X4784] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4784,X4783)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4784,c_Groups_Oone__class_Oone(tc_Int_Oint)),X4783) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).
fof(i_0_1784,plain,
! [X3585,X3586] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3586,X3585),X3586),
inference(variable_rename,[status(thm)],[i_0_1288]) ).
fof(i_0_1785,plain,
! [X3583,X3584] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3584,X3583),X3583),
inference(variable_rename,[status(thm)],[i_0_1289]) ).
fof(i_0_1786,plain,
! [X3814,X3815] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3815,X3814)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3814,X3815),X3815) = X3814 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).
fof(i_0_1787,plain,
! [X3748,X3749] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3749,X3748)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3748,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3748,X3749)) = X3749 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).
fof(i_0_1788,plain,
! [X3822,X3823] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3823,X3822)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3823,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3822,X3823)) = X3822 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).
fof(i_0_1789,plain,
! [X2960,X2961,X2962] :
( ~ class_RealVector_Oreal__algebra__1(X2962)
| c_RealVector_Oof__real(X2962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2961),X2960)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2962),c_RealVector_Oof__real(X2962,X2961)),c_RealVector_Oof__real(X2962,X2960)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__mult])]) ).
fof(i_0_1790,plain,
! [X4964,X4965,X4966,X4967,X4968] :
( ~ class_Orderings_Oord(X4968)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4967,X4968),X4966,X4965)
| c_Orderings_Oord__class_Oless__eq(X4968,hAPP(X4966,X4964),hAPP(X4965,X4964)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).
fof(i_0_1791,plain,
! [X4926,X4927,X4928,X4929,X4930] :
( ~ class_Orderings_Oord(X4930)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4929,X4930),X4928,X4927)
| c_Orderings_Oord__class_Oless__eq(X4930,hAPP(X4928,X4926),hAPP(X4927,X4926)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).
fof(i_0_1792,plain,
! [X3720,X3721,X3722] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3722,X3721)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3722,X3720),X3721) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).
fof(i_0_1793,plain,
! [X5159,X5160,X5161] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5161,X5160)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5161,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5160,X5159)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).
fof(i_0_1794,plain,
! [X3610,X3611,X3612] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3612,X3611)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3612,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3611,X3610)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).
fof(i_0_1795,plain,
! [X5174,X5175,X5176] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5176,X5175)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5176,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5174,X5175)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).
fof(i_0_1796,plain,
! [X3613,X3614,X3615] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3615,X3614)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3615,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3613,X3614)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).
fof(i_0_1797,plain,
! [X5166,X5167,X5168] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5168,X5167)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5168,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5167,X5166)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).
fof(i_0_1798,plain,
! [X3577,X3578,X3579] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3579,X3578)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3579,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3578,X3577)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).
fof(i_0_1799,plain,
! [X5169,X5170,X5171] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5171,X5170)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5171,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5169,X5170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).
fof(i_0_1800,plain,
! [X3574,X3575,X3576] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3576,X3575)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3576,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3574,X3575)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).
fof(i_0_1801,plain,
! [X3336,X3337,X3338] :
( ~ class_RealVector_Oreal__algebra__1(X3338)
| ~ class_RealVector_Oreal__normed__vector(X3338)
| c_RealVector_Oof__real(X3338,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3337,X3336)) = c_Groups_Ominus__class_Ominus(X3338,c_RealVector_Oof__real(X3338,X3337),c_RealVector_Oof__real(X3338,X3336)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Odiff])]) ).
fof(i_0_1802,plain,
! [X3033,X3034,X3035] :
( ~ class_RealVector_Oreal__algebra__1(X3035)
| ~ class_RealVector_Oreal__normed__vector(X3035)
| c_RealVector_Oof__real(X3035,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3034,X3033)) = c_Groups_Oplus__class_Oplus(X3035,c_RealVector_Oof__real(X3035,X3034),c_RealVector_Oof__real(X3035,X3033)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Oadd])]) ).
fof(i_0_1803,plain,
! [X4811,X4812] : 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,X4812)),X4811)),
inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).
fof(i_0_1804,plain,
! [X4612] :
( ( 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),X4612),X4612))
| X4612 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X4612 != 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),X4612),X4612)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1290])]) ).
fof(i_0_1805,plain,
! [X3670,X3671,X3672] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3672),X3671) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3672),X3670)
| X3671 = X3670
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3672) )
& ( X3671 != X3670
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3672),X3671) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3672),X3670)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3672) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).
fof(i_0_1806,plain,
! [X4901,X4902] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4902)
| 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),X4902),X4901)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).
fof(i_0_1807,plain,
! [X5401,X5402,X5403,X5404] :
( ~ class_Rings_Ocomm__semiring__1(X5404)
| ~ c_Rings_Odvd__class_Odvd(X5404,X5403,X5402)
| ~ c_Rings_Odvd__class_Odvd(X5404,X5402,X5401)
| c_Rings_Odvd__class_Odvd(X5404,X5403,X5401) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).
fof(i_0_1808,plain,
! [X4953,X4954,X4955,X4956] :
( ~ class_Orderings_Opreorder(X4956)
| ~ c_Orderings_Oord__class_Oless__eq(X4956,X4955,X4954)
| ~ c_Orderings_Oord__class_Oless__eq(X4956,X4954,X4953)
| c_Orderings_Oord__class_Oless__eq(X4956,X4955,X4953) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).
fof(i_0_1809,plain,
! [X4960,X4961,X4962,X4963] :
( ~ class_Orderings_Oorder(X4963)
| ~ c_Orderings_Oord__class_Oless__eq(X4963,X4962,X4961)
| ~ c_Orderings_Oord__class_Oless__eq(X4963,X4960,X4962)
| c_Orderings_Oord__class_Oless__eq(X4963,X4960,X4961) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).
fof(i_0_1810,plain,
! [X5091,X5092,X5093,X5094] :
( ~ class_Orderings_Opreorder(X5094)
| ~ c_Orderings_Oord__class_Oless(X5094,X5093,X5092)
| ~ c_Orderings_Oord__class_Oless__eq(X5094,X5092,X5091)
| c_Orderings_Oord__class_Oless(X5094,X5093,X5091) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).
fof(i_0_1811,plain,
! [X5099,X5100,X5101,X5102] :
( ~ class_Orderings_Opreorder(X5102)
| ~ c_Orderings_Oord__class_Oless__eq(X5102,X5101,X5100)
| ~ c_Orderings_Oord__class_Oless(X5102,X5100,X5099)
| c_Orderings_Oord__class_Oless(X5102,X5101,X5099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).
fof(i_0_1812,plain,
! [X5026,X5027,X5028,X5029] :
( ~ class_Orderings_Opreorder(X5029)
| ~ c_Orderings_Oord__class_Oless(X5029,X5028,X5027)
| ~ c_Orderings_Oord__class_Oless(X5029,X5027,X5026)
| c_Orderings_Oord__class_Oless(X5029,X5028,X5026) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).
fof(i_0_1813,plain,
! [X5095,X5096,X5097,X5098] :
( ~ class_Orderings_Oorder(X5098)
| ~ c_Orderings_Oord__class_Oless(X5098,X5097,X5096)
| ~ c_Orderings_Oord__class_Oless__eq(X5098,X5095,X5097)
| c_Orderings_Oord__class_Oless(X5098,X5095,X5096) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).
fof(i_0_1814,plain,
! [X5103,X5104,X5105,X5106] :
( ~ class_Orderings_Oorder(X5106)
| ~ c_Orderings_Oord__class_Oless__eq(X5106,X5105,X5104)
| ~ c_Orderings_Oord__class_Oless(X5106,X5103,X5105)
| c_Orderings_Oord__class_Oless(X5106,X5103,X5104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).
fof(i_0_1815,plain,
! [X5030,X5031,X5032,X5033] :
( ~ class_Orderings_Oorder(X5033)
| ~ c_Orderings_Oord__class_Oless(X5033,X5032,X5031)
| ~ c_Orderings_Oord__class_Oless(X5033,X5030,X5032)
| c_Orderings_Oord__class_Oless(X5033,X5030,X5031) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).
fof(i_0_1816,plain,
! [X5257,X5258,X5259] :
( ~ class_Groups_Oab__group__add(X5259)
| c_Groups_Ominus__class_Ominus(X5259,c_Groups_Ouminus__class_Ouminus(X5259,X5258),c_Groups_Ouminus__class_Ouminus(X5259,X5257)) = c_Groups_Ouminus__class_Ouminus(X5259,c_Groups_Ominus__class_Ominus(X5259,X5258,X5257)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Limits_Ominus__diff__minus])]) ).
fof(i_0_1817,plain,
! [X4423,X4424,X4425] :
( ~ class_Groups_Oab__group__add(X4425)
| c_Groups_Ouminus__class_Ouminus(X4425,c_Groups_Oplus__class_Oplus(X4425,X4424,X4423)) = c_Groups_Oplus__class_Oplus(X4425,c_Groups_Ouminus__class_Ouminus(X4425,X4424),c_Groups_Ouminus__class_Ouminus(X4425,X4423)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).
fof(i_0_1818,plain,
! [X4420,X4421,X4422] :
( ~ class_Groups_Ogroup__add(X4422)
| c_Groups_Ouminus__class_Ouminus(X4422,c_Groups_Oplus__class_Oplus(X4422,X4421,X4420)) = c_Groups_Oplus__class_Oplus(X4422,c_Groups_Ouminus__class_Ouminus(X4422,X4420),c_Groups_Ouminus__class_Ouminus(X4422,X4421)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).
fof(i_0_1819,plain,
! [X5234] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X5234,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5234)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(i_0_1820,plain,
! [X3414,X3415,X3416] :
( ~ class_Rings_Odivision__ring(X3416)
| X3415 = c_Groups_Ozero__class_Ozero(X3416)
| c_Rings_Oinverse__class_Oinverse(X3416,hAPP(hAPP(c_Power_Opower__class_Opower(X3416),X3415),X3414)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3416),c_Rings_Oinverse__class_Oinverse(X3416,X3415)),X3414) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__inverse])]) ).
fof(i_0_1821,plain,
! [X3339,X3340,X3341] :
( ~ class_RealVector_Oreal__algebra__1(X3341)
| c_RealVector_Oof__real(X3341,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3340,X3339)) = c_Groups_Ominus__class_Ominus(X3341,c_RealVector_Oof__real(X3341,X3340),c_RealVector_Oof__real(X3341,X3339)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__diff])]) ).
fof(i_0_1822,plain,
! [X3036,X3037,X3038] :
( ~ class_RealVector_Oreal__algebra__1(X3038)
| c_RealVector_Oof__real(X3038,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3037,X3036)) = c_Groups_Oplus__class_Oplus(X3038,c_RealVector_Oof__real(X3038,X3037),c_RealVector_Oof__real(X3038,X3036)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__add])]) ).
fof(i_0_1823,plain,
! [X5274,X5275,X5276] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5276,c_Groups_Ouminus__class_Ouminus(X5276,X5275),c_Groups_Ouminus__class_Ouminus(X5276,X5274))
| c_Orderings_Oord__class_Oless__eq(X5276,X5274,X5275)
| ~ class_Lattices_Oboolean__algebra(X5276) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5276,X5274,X5275)
| c_Orderings_Oord__class_Oless__eq(X5276,c_Groups_Ouminus__class_Ouminus(X5276,X5275),c_Groups_Ouminus__class_Ouminus(X5276,X5274))
| ~ class_Lattices_Oboolean__algebra(X5276) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).
fof(i_0_1824,plain,
! [X4393,X4394,X4395] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4395,c_Groups_Ouminus__class_Ouminus(X4395,X4394),c_Groups_Ouminus__class_Ouminus(X4395,X4393))
| c_Orderings_Oord__class_Oless__eq(X4395,X4393,X4394)
| ~ class_Groups_Oordered__ab__group__add(X4395) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4395,X4393,X4394)
| c_Orderings_Oord__class_Oless__eq(X4395,c_Groups_Ouminus__class_Ouminus(X4395,X4394),c_Groups_Ouminus__class_Ouminus(X4395,X4393))
| ~ class_Groups_Oordered__ab__group__add(X4395) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).
fof(i_0_1825,plain,
! [X4411,X4412,X4413] :
( ( ~ c_Orderings_Oord__class_Oless(X4413,c_Groups_Ouminus__class_Ouminus(X4413,X4412),c_Groups_Ouminus__class_Ouminus(X4413,X4411))
| c_Orderings_Oord__class_Oless(X4413,X4411,X4412)
| ~ class_Groups_Oordered__ab__group__add(X4413) )
& ( ~ c_Orderings_Oord__class_Oless(X4413,X4411,X4412)
| c_Orderings_Oord__class_Oless(X4413,c_Groups_Ouminus__class_Ouminus(X4413,X4412),c_Groups_Ouminus__class_Ouminus(X4413,X4411))
| ~ class_Groups_Oordered__ab__group__add(X4413) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).
fof(i_0_1826,plain,
! [X3080,X3081,X3082] :
( ~ class_RealVector_Oreal__normed__algebra(X3082)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3082),c_Groups_Ouminus__class_Ouminus(X3082,X3081)),X3080) = c_Groups_Ouminus__class_Ouminus(X3082,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3082),X3081),X3080)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus])]) ).
fof(i_0_1827,plain,
! [X3077,X3078,X3079] :
( ~ class_RealVector_Oreal__normed__algebra(X3079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),c_Groups_Ouminus__class_Ouminus(X3079,X3078)),X3077) = c_Groups_Ouminus__class_Ouminus(X3079,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3079),X3078),X3077)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left])]) ).
fof(i_0_1828,plain,
! [X3710,X3711,X3712] :
( ~ class_Rings_Olinordered__idom(X3712)
| c_Groups_Oabs__class_Oabs(X3712,hAPP(hAPP(c_Power_Opower__class_Opower(X3712),X3711),X3710)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3712),c_Groups_Oabs__class_Oabs(X3712,X3711)),X3710) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).
fof(i_0_1829,plain,
! [X3378,X3379,X3380] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3380)
| c_Rings_Oinverse__class_Oinverse(X3380,hAPP(hAPP(c_Power_Opower__class_Opower(X3380),X3379),X3378)) = hAPP(hAPP(c_Power_Opower__class_Opower(X3380),c_Rings_Oinverse__class_Oinverse(X3380,X3379)),X3378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inverse])]) ).
fof(i_0_1830,plain,
! [X3042,X3043,X3044] :
( ~ class_Rings_Oring(X3044)
| c_Groups_Ouminus__class_Ouminus(X3044,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3044),X3043),X3042)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3044),c_Groups_Ouminus__class_Ouminus(X3044,X3043)),X3042) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).
fof(i_0_1831,plain,
! [X4120,X4121,X4122] :
( ~ class_Rings_Ocomm__ring(X4122)
| c_Polynomial_Osmult(X4122,X4121,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4122),X4120)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4122),c_Polynomial_Osmult(X4122,X4121,X4120)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__right])]) ).
fof(i_0_1832,plain,
! [X3811,X3812,X3813] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3812,X3813) != X3811
| X3812 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3811,X3813)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3813,X3812) )
& ( X3812 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3811,X3813)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3812,X3813) = X3811
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3813,X3812) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).
fof(i_0_1833,plain,
! [X2963,X2964,X2965] :
( ~ class_RealVector_Oreal__normed__div__algebra(X2965)
| c_RealVector_Onorm__class_Onorm(X2965,hAPP(hAPP(c_Power_Opower__class_Opower(X2965),X2964),X2963)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2965,X2964)),X2963) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__power])]) ).
fof(i_0_1834,plain,
! [X4417,X4418,X4419] :
( ~ class_Groups_Ogroup__add(X4419)
| c_Groups_Oplus__class_Oplus(X4419,X4418,c_Groups_Oplus__class_Oplus(X4419,c_Groups_Ouminus__class_Ouminus(X4419,X4418),X4417)) = X4417 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).
fof(i_0_1835,plain,
! [X4855,X4856,X4857] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4857,X4856)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4856,X4855)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4857,X4855) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).
fof(i_0_1836,plain,
! [X3523,X3524,X3525] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3525,X3524)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3524,X3523)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3525,X3523) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).
fof(i_0_1837,plain,
! [X2854,X2855,X2856] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2856,X2855)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2855,X2854)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2856,X2854) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__trans])]) ).
fof(i_0_1838,plain,
! [X5197,X5198,X5199] :
( ~ class_Rings_Olinordered__idom(X5199)
| ~ c_Polynomial_Opos__poly(X5199,X5198)
| ~ c_Polynomial_Opos__poly(X5199,X5197)
| c_Polynomial_Opos__poly(X5199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X5199)),X5198),X5197)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__mult])]) ).
fof(i_0_1839,plain,
! [X5193,X5194] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5194),X5193)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5194)),c_RealDef_Oreal(tc_Nat_Onat,X5193)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__mult]) ).
fof(i_0_1840,plain,
! [X2967,X2968,X2969] :
( ~ class_RealVector_Oreal__algebra__1(X2969)
| c_RealVector_Oof__real(X2969,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2968),X2967)) = hAPP(hAPP(c_Power_Opower__class_Opower(X2969),c_RealVector_Oof__real(X2969,X2968)),X2967) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__power])]) ).
fof(i_0_1841,plain,
! [X4150,X4151,X4152] :
( ~ class_Rings_Ocomm__ring(X4152)
| hAPP(c_Polynomial_Opoly(X4152,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4152),X4151)),X4150) = c_Groups_Ouminus__class_Ouminus(X4152,hAPP(c_Polynomial_Opoly(X4152,X4151),X4150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__minus])]) ).
fof(i_0_1842,plain,
! [X4553,X4554,X4555] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4555)
| ~ c_Orderings_Oord__class_Oless__eq(X4555,c_Groups_Oabs__class_Oabs(X4555,X4554),X4553)
| c_Orderings_Oord__class_Oless__eq(X4555,c_Groups_Ouminus__class_Ouminus(X4555,X4554),X4553) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).
fof(i_0_1843,plain,
! [X4390,X4391,X4392] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ouminus__class_Ouminus(X4392,X4391),X4390)
| c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ouminus__class_Ouminus(X4392,X4390),X4391)
| ~ class_Groups_Oordered__ab__group__add(X4392) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ouminus__class_Ouminus(X4392,X4390),X4391)
| c_Orderings_Oord__class_Oless__eq(X4392,c_Groups_Ouminus__class_Ouminus(X4392,X4391),X4390)
| ~ class_Groups_Oordered__ab__group__add(X4392) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).
fof(i_0_1844,plain,
! [X4408,X4409,X4410] :
( ( ~ c_Orderings_Oord__class_Oless(X4410,c_Groups_Ouminus__class_Ouminus(X4410,X4409),X4408)
| c_Orderings_Oord__class_Oless(X4410,c_Groups_Ouminus__class_Ouminus(X4410,X4408),X4409)
| ~ class_Groups_Oordered__ab__group__add(X4410) )
& ( ~ c_Orderings_Oord__class_Oless(X4410,c_Groups_Ouminus__class_Ouminus(X4410,X4408),X4409)
| c_Orderings_Oord__class_Oless(X4410,c_Groups_Ouminus__class_Ouminus(X4410,X4409),X4408)
| ~ class_Groups_Oordered__ab__group__add(X4410) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).
fof(i_0_1845,plain,
! [X4387,X4388,X4389] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4389,X4388,c_Groups_Ouminus__class_Ouminus(X4389,X4387))
| c_Orderings_Oord__class_Oless__eq(X4389,X4387,c_Groups_Ouminus__class_Ouminus(X4389,X4388))
| ~ class_Groups_Oordered__ab__group__add(X4389) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4389,X4387,c_Groups_Ouminus__class_Ouminus(X4389,X4388))
| c_Orderings_Oord__class_Oless__eq(X4389,X4388,c_Groups_Ouminus__class_Ouminus(X4389,X4387))
| ~ class_Groups_Oordered__ab__group__add(X4389) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).
fof(i_0_1846,plain,
! [X4405,X4406,X4407] :
( ( ~ c_Orderings_Oord__class_Oless(X4407,X4406,c_Groups_Ouminus__class_Ouminus(X4407,X4405))
| c_Orderings_Oord__class_Oless(X4407,X4405,c_Groups_Ouminus__class_Ouminus(X4407,X4406))
| ~ class_Groups_Oordered__ab__group__add(X4407) )
& ( ~ c_Orderings_Oord__class_Oless(X4407,X4405,c_Groups_Ouminus__class_Ouminus(X4407,X4406))
| c_Orderings_Oord__class_Oless(X4407,X4406,c_Groups_Ouminus__class_Ouminus(X4407,X4405))
| ~ class_Groups_Oordered__ab__group__add(X4407) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).
fof(i_0_1847,plain,
! [X5202,X5203] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5203,X5202)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5203),c_RealDef_Oreal(tc_Nat_Onat,X5202)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__add]) ).
fof(i_0_1848,plain,
! [X4865,X4866] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4866,X4865)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4866),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4865)),
inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(i_0_1849,plain,
! [X4050,X4051,X4052] :
( ~ class_Groups_Oab__group__add(X4052)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4052),c_Polynomial_Omonom(X4052,X4051,X4050)) = c_Polynomial_Omonom(X4052,c_Groups_Ouminus__class_Ouminus(X4052,X4051),X4050) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__monom])]) ).
fof(i_0_1850,plain,
! [X4182,X4183,X4184] :
( ~ class_Rings_Ocomm__ring(X4184)
| c_Polynomial_Osmult(X4184,c_Groups_Ouminus__class_Ouminus(X4184,X4183),X4182) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4184),c_Polynomial_Osmult(X4184,X4183,X4182)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__minus__left])]) ).
fof(i_0_1851,plain,
! [X5282,X5283,X5284] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5284)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5284),X5283),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5284),X5283),X5282)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5284),X5283),X5282) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).
fof(i_0_1852,plain,
! [X3901] : 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,X3901))),
inference(variable_rename,[status(thm)],[fact_abs__add__one__gt__zero]) ).
fof(i_0_1853,plain,
! [X3792,X3793] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3793,X3792)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3792,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3793,X3792)) = X3793 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1291])]) ).
fof(i_0_1854,plain,
! [X3964,X3965] :
( ~ class_Fields_Olinordered__field(X3965)
| ~ c_Orderings_Oord__class_Oless(X3965,c_Groups_Ozero__class_Ozero(X3965),c_Rings_Oinverse__class_Oinverse(X3965,X3964))
| X3964 = c_Groups_Ozero__class_Ozero(X3965)
| c_Orderings_Oord__class_Oless(X3965,c_Groups_Ozero__class_Ozero(X3965),X3964) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__imp__positive])]) ).
fof(i_0_1855,plain,
! [X3954,X3955] :
( ~ class_Fields_Olinordered__field(X3955)
| ~ c_Orderings_Oord__class_Oless(X3955,c_Rings_Oinverse__class_Oinverse(X3955,X3954),c_Groups_Ozero__class_Ozero(X3955))
| X3954 = c_Groups_Ozero__class_Ozero(X3955)
| c_Orderings_Oord__class_Oless(X3955,X3954,c_Groups_Ozero__class_Ozero(X3955)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__imp__negative])]) ).
fof(i_0_1856,plain,
! [X5209,X5210] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5210),c_RealDef_Oreal(tc_Nat_Onat,X5209))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5210,X5209) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5210,X5209)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5210),c_RealDef_Oreal(tc_Nat_Onat,X5209)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff])]) ).
fof(i_0_1857,plain,
! [X5185,X5186] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5186),c_RealDef_Oreal(tc_Nat_Onat,X5185))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5186,X5185) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5186,X5185)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5186),c_RealDef_Oreal(tc_Nat_Onat,X5185)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff])]) ).
fof(i_0_1858,plain,
! [X4496,X4497] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4497,c_Groups_Ouminus__class_Ouminus(X4497,X4496),c_Groups_Ozero__class_Ozero(X4497))
| c_Orderings_Oord__class_Oless__eq(X4497,c_Groups_Ozero__class_Ozero(X4497),X4496)
| ~ class_Groups_Oordered__ab__group__add(X4497) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4497,c_Groups_Ozero__class_Ozero(X4497),X4496)
| c_Orderings_Oord__class_Oless__eq(X4497,c_Groups_Ouminus__class_Ouminus(X4497,X4496),c_Groups_Ozero__class_Ozero(X4497))
| ~ class_Groups_Oordered__ab__group__add(X4497) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).
fof(i_0_1859,plain,
! [X4502,X4503] :
( ( ~ c_Orderings_Oord__class_Oless(X4503,c_Groups_Ouminus__class_Ouminus(X4503,X4502),c_Groups_Ozero__class_Ozero(X4503))
| c_Orderings_Oord__class_Oless(X4503,c_Groups_Ozero__class_Ozero(X4503),X4502)
| ~ class_Groups_Oordered__ab__group__add(X4503) )
& ( ~ c_Orderings_Oord__class_Oless(X4503,c_Groups_Ozero__class_Ozero(X4503),X4502)
| c_Orderings_Oord__class_Oless(X4503,c_Groups_Ouminus__class_Ouminus(X4503,X4502),c_Groups_Ozero__class_Ozero(X4503))
| ~ class_Groups_Oordered__ab__group__add(X4503) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).
fof(i_0_1860,plain,
! [X3946,X3947] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3947,c_Groups_Ozero__class_Ozero(X3947),c_Rings_Oinverse__class_Oinverse(X3947,X3946))
| c_Orderings_Oord__class_Oless__eq(X3947,c_Groups_Ozero__class_Ozero(X3947),X3946)
| ~ class_Fields_Olinordered__field__inverse__zero(X3947) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3947,c_Groups_Ozero__class_Ozero(X3947),X3946)
| c_Orderings_Oord__class_Oless__eq(X3947,c_Groups_Ozero__class_Ozero(X3947),c_Rings_Oinverse__class_Oinverse(X3947,X3946))
| ~ class_Fields_Olinordered__field__inverse__zero(X3947) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonnegative__iff__nonnegative])])]) ).
fof(i_0_1861,plain,
! [X3970,X3971] :
( ( ~ c_Orderings_Oord__class_Oless(X3971,c_Groups_Ozero__class_Ozero(X3971),c_Rings_Oinverse__class_Oinverse(X3971,X3970))
| c_Orderings_Oord__class_Oless(X3971,c_Groups_Ozero__class_Ozero(X3971),X3970)
| ~ class_Fields_Olinordered__field__inverse__zero(X3971) )
& ( ~ c_Orderings_Oord__class_Oless(X3971,c_Groups_Ozero__class_Ozero(X3971),X3970)
| c_Orderings_Oord__class_Oless(X3971,c_Groups_Ozero__class_Ozero(X3971),c_Rings_Oinverse__class_Oinverse(X3971,X3970))
| ~ class_Fields_Olinordered__field__inverse__zero(X3971) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__positive__iff__positive])])]) ).
fof(i_0_1862,plain,
! [X5305,X5306] :
( ( ~ c_Orderings_Oord__class_Oless(X5306,c_Groups_Ozero__class_Ozero(X5306),c_Groups_Osgn__class_Osgn(X5306,X5305))
| c_Orderings_Oord__class_Oless(X5306,c_Groups_Ozero__class_Ozero(X5306),X5305)
| ~ class_Rings_Olinordered__idom(X5306) )
& ( ~ c_Orderings_Oord__class_Oless(X5306,c_Groups_Ozero__class_Ozero(X5306),X5305)
| c_Orderings_Oord__class_Oless(X5306,c_Groups_Ozero__class_Ozero(X5306),c_Groups_Osgn__class_Osgn(X5306,X5305))
| ~ class_Rings_Olinordered__idom(X5306) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).
fof(i_0_1863,plain,
! [X3944,X3945] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X3945,c_Rings_Oinverse__class_Oinverse(X3945,X3944),c_Groups_Ozero__class_Ozero(X3945))
| c_Orderings_Oord__class_Oless__eq(X3945,X3944,c_Groups_Ozero__class_Ozero(X3945))
| ~ class_Fields_Olinordered__field__inverse__zero(X3945) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X3945,X3944,c_Groups_Ozero__class_Ozero(X3945))
| c_Orderings_Oord__class_Oless__eq(X3945,c_Rings_Oinverse__class_Oinverse(X3945,X3944),c_Groups_Ozero__class_Ozero(X3945))
| ~ class_Fields_Olinordered__field__inverse__zero(X3945) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonpositive__iff__nonpositive])])]) ).
fof(i_0_1864,plain,
! [X3968,X3969] :
( ( ~ c_Orderings_Oord__class_Oless(X3969,c_Rings_Oinverse__class_Oinverse(X3969,X3968),c_Groups_Ozero__class_Ozero(X3969))
| c_Orderings_Oord__class_Oless(X3969,X3968,c_Groups_Ozero__class_Ozero(X3969))
| ~ class_Fields_Olinordered__field__inverse__zero(X3969) )
& ( ~ c_Orderings_Oord__class_Oless(X3969,X3968,c_Groups_Ozero__class_Ozero(X3969))
| c_Orderings_Oord__class_Oless(X3969,c_Rings_Oinverse__class_Oinverse(X3969,X3968),c_Groups_Ozero__class_Ozero(X3969))
| ~ class_Fields_Olinordered__field__inverse__zero(X3969) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__negative__iff__negative])])]) ).
fof(i_0_1865,plain,
! [X5303,X5304] :
( ( ~ c_Orderings_Oord__class_Oless(X5304,c_Groups_Osgn__class_Osgn(X5304,X5303),c_Groups_Ozero__class_Ozero(X5304))
| c_Orderings_Oord__class_Oless(X5304,X5303,c_Groups_Ozero__class_Ozero(X5304))
| ~ class_Rings_Olinordered__idom(X5304) )
& ( ~ c_Orderings_Oord__class_Oless(X5304,X5303,c_Groups_Ozero__class_Ozero(X5304))
| c_Orderings_Oord__class_Oless(X5304,c_Groups_Osgn__class_Osgn(X5304,X5303),c_Groups_Ozero__class_Ozero(X5304))
| ~ class_Rings_Olinordered__idom(X5304) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).
fof(i_0_1866,plain,
! [X4492,X4493] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4493,c_Groups_Ozero__class_Ozero(X4493),c_Groups_Ouminus__class_Ouminus(X4493,X4492))
| c_Orderings_Oord__class_Oless__eq(X4493,X4492,c_Groups_Ozero__class_Ozero(X4493))
| ~ class_Groups_Oordered__ab__group__add(X4493) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4493,X4492,c_Groups_Ozero__class_Ozero(X4493))
| c_Orderings_Oord__class_Oless__eq(X4493,c_Groups_Ozero__class_Ozero(X4493),c_Groups_Ouminus__class_Ouminus(X4493,X4492))
| ~ class_Groups_Oordered__ab__group__add(X4493) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).
fof(i_0_1867,plain,
! [X4500,X4501] :
( ( ~ c_Orderings_Oord__class_Oless(X4501,c_Groups_Ozero__class_Ozero(X4501),c_Groups_Ouminus__class_Ouminus(X4501,X4500))
| c_Orderings_Oord__class_Oless(X4501,X4500,c_Groups_Ozero__class_Ozero(X4501))
| ~ class_Groups_Oordered__ab__group__add(X4501) )
& ( ~ c_Orderings_Oord__class_Oless(X4501,X4500,c_Groups_Ozero__class_Ozero(X4501))
| c_Orderings_Oord__class_Oless(X4501,c_Groups_Ozero__class_Ozero(X4501),c_Groups_Ouminus__class_Ouminus(X4501,X4500))
| ~ class_Groups_Oordered__ab__group__add(X4501) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).
fof(i_0_1868,plain,
! [X5052,X5053,X5054] :
( ( c_Orderings_Oord__class_Oless__eq(X5054,X5053,X5052)
| ~ c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| ~ class_Orderings_Opreorder(X5054) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5054,X5052,X5053)
| ~ c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| ~ class_Orderings_Opreorder(X5054) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5054,X5053,X5052)
| c_Orderings_Oord__class_Oless__eq(X5054,X5052,X5053)
| c_Orderings_Oord__class_Oless(X5054,X5053,X5052)
| ~ class_Orderings_Opreorder(X5054) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1292])])]) ).
fof(i_0_1869,plain,
! [X3074,X3075,X3076] :
( ~ class_RealVector_Oreal__normed__algebra(X3076)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3076),X3075),c_Groups_Ouminus__class_Ouminus(X3076,X3074)) = c_Groups_Ouminus__class_Ouminus(X3076,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3076),X3075),X3074)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus])]) ).
fof(i_0_1870,plain,
! [X3071,X3072,X3073] :
( ~ class_RealVector_Oreal__normed__algebra(X3073)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3073),X3072),c_Groups_Ouminus__class_Ouminus(X3073,X3071)) = c_Groups_Ouminus__class_Ouminus(X3073,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3073),X3072),X3071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right])]) ).
fof(i_0_1871,plain,
! [X3039,X3040,X3041] :
( ~ class_Rings_Oring(X3041)
| c_Groups_Ouminus__class_Ouminus(X3041,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3041),X3040),X3039)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3041),X3040),c_Groups_Ouminus__class_Ouminus(X3041,X3039)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).
fof(i_0_1872,plain,
! [X5271,X5272,X5273] :
( ~ class_Lattices_Oboolean__algebra(X5273)
| ~ c_Orderings_Oord__class_Oless__eq(X5273,X5272,X5271)
| c_Orderings_Oord__class_Oless__eq(X5273,c_Groups_Ouminus__class_Ouminus(X5273,X5271),c_Groups_Ouminus__class_Ouminus(X5273,X5272)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).
fof(i_0_1873,plain,
! [X4396,X4397,X4398] :
( ~ class_Groups_Oordered__ab__group__add(X4398)
| ~ c_Orderings_Oord__class_Oless__eq(X4398,X4397,X4396)
| c_Orderings_Oord__class_Oless__eq(X4398,c_Groups_Ouminus__class_Ouminus(X4398,X4396),c_Groups_Ouminus__class_Ouminus(X4398,X4397)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).
fof(i_0_1874,plain,
! [X3111] :
( ~ class_Rings_Olinordered__semidom(X3111)
| c_Orderings_Oord__class_Oless(X3111,c_Groups_Ozero__class_Ozero(X3111),c_Groups_Oplus__class_Oplus(X3111,c_Groups_Oone__class_Oone(X3111),c_Groups_Oone__class_Oone(X3111))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
fof(i_0_1875,plain,
! [X5237] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X5237,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5237))),
inference(variable_rename,[status(thm)],[fact_real__natfloor__gt__diff__one]) ).
fof(i_0_1876,plain,
! [X4414,X4415,X4416] :
( ~ class_Groups_Ogroup__add(X4416)
| c_Groups_Oplus__class_Oplus(X4416,c_Groups_Ouminus__class_Ouminus(X4416,X4415),c_Groups_Oplus__class_Oplus(X4416,X4415,X4414)) = X4414 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).
fof(i_0_1877,plain,
! [X4498,X4499] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4499,c_Groups_Ouminus__class_Ouminus(X4499,X4498),X4498)
| c_Orderings_Oord__class_Oless__eq(X4499,c_Groups_Ozero__class_Ozero(X4499),X4498)
| ~ class_Groups_Olinordered__ab__group__add(X4499) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4499,c_Groups_Ozero__class_Ozero(X4499),X4498)
| c_Orderings_Oord__class_Oless__eq(X4499,c_Groups_Ouminus__class_Ouminus(X4499,X4498),X4498)
| ~ class_Groups_Olinordered__ab__group__add(X4499) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).
fof(i_0_1878,plain,
! [X4504,X4505] :
( ( ~ c_Orderings_Oord__class_Oless(X4505,c_Groups_Ouminus__class_Ouminus(X4505,X4504),X4504)
| c_Orderings_Oord__class_Oless(X4505,c_Groups_Ozero__class_Ozero(X4505),X4504)
| ~ class_Groups_Olinordered__ab__group__add(X4505) )
& ( ~ c_Orderings_Oord__class_Oless(X4505,c_Groups_Ozero__class_Ozero(X4505),X4504)
| c_Orderings_Oord__class_Oless(X4505,c_Groups_Ouminus__class_Ouminus(X4505,X4504),X4504)
| ~ class_Groups_Olinordered__ab__group__add(X4505) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).
fof(i_0_1879,plain,
! [X4494,X4495] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4495,X4494,c_Groups_Ouminus__class_Ouminus(X4495,X4494))
| c_Orderings_Oord__class_Oless__eq(X4495,X4494,c_Groups_Ozero__class_Ozero(X4495))
| ~ class_Groups_Olinordered__ab__group__add(X4495) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4495,X4494,c_Groups_Ozero__class_Ozero(X4495))
| c_Orderings_Oord__class_Oless__eq(X4495,X4494,c_Groups_Ouminus__class_Ouminus(X4495,X4494))
| ~ class_Groups_Olinordered__ab__group__add(X4495) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).
fof(i_0_1880,plain,
! [X3101,X3102] :
( ( ~ c_Orderings_Oord__class_Oless(X3102,X3101,c_Groups_Ouminus__class_Ouminus(X3102,X3101))
| c_Orderings_Oord__class_Oless(X3102,X3101,c_Groups_Ozero__class_Ozero(X3102))
| ~ class_Rings_Olinordered__idom(X3102) )
& ( ~ c_Orderings_Oord__class_Oless(X3102,X3101,c_Groups_Ozero__class_Ozero(X3102))
| c_Orderings_Oord__class_Oless(X3102,X3101,c_Groups_Ouminus__class_Ouminus(X3102,X3101))
| ~ class_Rings_Olinordered__idom(X3102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).
fof(i_0_1881,plain,
! [X4813,X4814] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4814)),X4813) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4814),X4813)),
inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).
fof(i_0_1882,plain,
! [X2785,X2786] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,X2786)),X2785) = c_RealVector_Oof__real(tc_Complex_Ocomplex,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2786),X2785)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__power]) ).
fof(i_0_1883,plain,
! [X5190,X5191] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5191)),X5190) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5191),X5190)),
inference(variable_rename,[status(thm)],[fact_power__real__of__nat]) ).
fof(i_0_1884,plain,
! [X5188,X5189] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X5189),X5188)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5189)),X5188),
inference(variable_rename,[status(thm)],[fact_real__of__nat__power]) ).
fof(i_0_1885,plain,
! [X3491,X3492,X3493] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3492,X3493)
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| X3493 = X3492
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3492) )
& ( ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| X3493 = X3492
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3492) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3492,X3493)
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3492) )
& ( ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3493,X3492) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3492,X3493)
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| X3493 = X3492
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493)) )
& ( ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| X3493 = X3492
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3492,X3493)
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493)) )
& ( ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493))
| ~ hBOOL(hAPP(hAPP(X3491,X3492),X3493)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).
fof(i_0_1886,plain,
! [X3962,X3963] :
( ~ class_Fields_Olinordered__field(X3963)
| ~ c_Orderings_Oord__class_Oless(X3963,X3962,c_Groups_Ozero__class_Ozero(X3963))
| c_Orderings_Oord__class_Oless(X3963,c_Rings_Oinverse__class_Oinverse(X3963,X3962),c_Groups_Ozero__class_Ozero(X3963)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__imp__inverse__negative])]) ).
fof(i_0_1887,plain,
! [X3966,X3967] :
( ~ class_Fields_Olinordered__field(X3967)
| ~ c_Orderings_Oord__class_Oless(X3967,c_Groups_Ozero__class_Ozero(X3967),X3966)
| c_Orderings_Oord__class_Oless(X3967,c_Groups_Ozero__class_Ozero(X3967),c_Rings_Oinverse__class_Oinverse(X3967,X3966)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_positive__imp__inverse__positive])]) ).
fof(i_0_1888,plain,
! [X4217,X4218,X4219,X4220] :
( ~ class_Rings_Ocomm__semiring__0(X4220)
| c_Polynomial_Osmult(X4220,X4219,X4218) != c_Polynomial_OpCons(X4220,X4217,X4218)
| X4218 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4220)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__unique__lemma])]) ).
fof(i_0_1889,plain,
! [X3707,X3708] :
( ~ class_Rings_Olinordered__idom(X3708)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3708),c_Groups_Oabs__class_Oabs(X3708,X3707)),c_Groups_Oabs__class_Oabs(X3708,X3707)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3708),X3707),X3707) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).
fof(i_0_1890,plain,
! [X3048,X3049,X3050] :
( ~ class_Rings_Oring(X3050)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3050),c_Groups_Ouminus__class_Ouminus(X3050,X3049)),c_Groups_Ouminus__class_Ouminus(X3050,X3048)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3050),X3049),X3048) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).
fof(i_0_1891,plain,
! [X3045,X3046,X3047] :
( ~ class_Rings_Oring(X3047)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3047),c_Groups_Ouminus__class_Ouminus(X3047,X3046)),X3045) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3047),X3046),c_Groups_Ouminus__class_Ouminus(X3047,X3045)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).
fof(i_0_1892,plain,
! [X5351,X5352,X5353] :
( ( ~ c_Rings_Odvd__class_Odvd(X5353,c_Groups_Ouminus__class_Ouminus(X5353,X5352),X5351)
| c_Rings_Odvd__class_Odvd(X5353,X5352,X5351)
| ~ class_Rings_Ocomm__ring__1(X5353) )
& ( ~ c_Rings_Odvd__class_Odvd(X5353,X5352,X5351)
| c_Rings_Odvd__class_Odvd(X5353,c_Groups_Ouminus__class_Ouminus(X5353,X5352),X5351)
| ~ class_Rings_Ocomm__ring__1(X5353) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).
fof(i_0_1893,plain,
! [X5408,X5409,X5410] :
( ( ~ c_Rings_Odvd__class_Odvd(X5410,c_Groups_Oabs__class_Oabs(X5410,X5409),X5408)
| c_Rings_Odvd__class_Odvd(X5410,X5409,X5408)
| ~ class_Rings_Olinordered__idom(X5410) )
& ( ~ c_Rings_Odvd__class_Odvd(X5410,X5409,X5408)
| c_Rings_Odvd__class_Odvd(X5410,c_Groups_Oabs__class_Oabs(X5410,X5409),X5408)
| ~ class_Rings_Olinordered__idom(X5410) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff])])]) ).
fof(i_0_1894,plain,
! [X4432,X4433,X4434] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4434)
| ~ c_Orderings_Oord__class_Oless__eq(X4434,c_Groups_Oabs__class_Oabs(X4434,X4433),X4432)
| c_Orderings_Oord__class_Oless__eq(X4434,X4433,X4432) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).
fof(i_0_1895,plain,
! [X5354,X5355,X5356] :
( ( ~ c_Rings_Odvd__class_Odvd(X5356,X5355,c_Groups_Ouminus__class_Ouminus(X5356,X5354))
| c_Rings_Odvd__class_Odvd(X5356,X5355,X5354)
| ~ class_Rings_Ocomm__ring__1(X5356) )
& ( ~ c_Rings_Odvd__class_Odvd(X5356,X5355,X5354)
| c_Rings_Odvd__class_Odvd(X5356,X5355,c_Groups_Ouminus__class_Ouminus(X5356,X5354))
| ~ class_Rings_Ocomm__ring__1(X5356) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).
fof(i_0_1896,plain,
! [X5405,X5406,X5407] :
( ( ~ c_Rings_Odvd__class_Odvd(X5407,X5406,c_Groups_Oabs__class_Oabs(X5407,X5405))
| c_Rings_Odvd__class_Odvd(X5407,X5406,X5405)
| ~ class_Rings_Olinordered__idom(X5407) )
& ( ~ c_Rings_Odvd__class_Odvd(X5407,X5406,X5405)
| c_Rings_Odvd__class_Odvd(X5407,X5406,c_Groups_Oabs__class_Oabs(X5407,X5405))
| ~ class_Rings_Olinordered__idom(X5407) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff])])]) ).
fof(i_0_1897,plain,
! [X3051,X3052,X3053] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3052),X3052) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3051),X3051)
| X3052 = X3051
| X3052 = c_Groups_Ouminus__class_Ouminus(X3053,X3051)
| ~ class_Rings_Oidom(X3053) )
& ( X3052 != X3051
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3052),X3052) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3051),X3051)
| ~ class_Rings_Oidom(X3053) )
& ( X3052 != c_Groups_Ouminus__class_Ouminus(X3053,X3051)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3052),X3052) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3053),X3051),X3051)
| ~ class_Rings_Oidom(X3053) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).
fof(i_0_1898,plain,
! [X5204,X5205,X5206] :
( ~ class_Rings_Olinordered__idom(X5206)
| ~ c_Polynomial_Opos__poly(X5206,X5205)
| ~ c_Polynomial_Opos__poly(X5206,X5204)
| c_Polynomial_Opos__poly(X5206,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X5206),X5205,X5204)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__add])]) ).
fof(i_0_1899,plain,
! [X4264,X4265,X4266,X4267,X4268] :
( ( X4267 != X4266
| X4265 = X4264
| c_Groups_Ominus__class_Ominus(X4268,X4267,X4266) != c_Groups_Ominus__class_Ominus(X4268,X4265,X4264)
| ~ class_Groups_Oab__group__add(X4268) )
& ( X4265 != X4264
| X4267 = X4266
| c_Groups_Ominus__class_Ominus(X4268,X4267,X4266) != c_Groups_Ominus__class_Ominus(X4268,X4265,X4264)
| ~ class_Groups_Oab__group__add(X4268) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).
fof(i_0_1900,plain,
! [X5221,X5222] :
( X5222 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5222))
| c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5222),X5221)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(X5222)),X5221) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__power])]) ).
fof(i_0_1901,plain,
! [X5079,X5080,X5081] :
( ( c_Orderings_Oord__class_Oless(X5081,X5080,X5079)
| X5080 = X5079
| ~ c_Orderings_Oord__class_Oless__eq(X5081,X5080,X5079)
| ~ class_Orderings_Olinorder(X5081) )
& ( X5080 != X5079
| ~ c_Orderings_Oord__class_Oless(X5081,X5080,X5079)
| ~ c_Orderings_Oord__class_Oless__eq(X5081,X5080,X5079)
| ~ class_Orderings_Olinorder(X5081) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1293])])]) ).
fof(i_0_1902,plain,
! [X4426,X4427,X4428] :
( ~ class_Groups_Oab__group__add(X4428)
| c_Groups_Ouminus__class_Ouminus(X4428,c_Groups_Ominus__class_Ominus(X4428,X4427,X4426)) = c_Groups_Ominus__class_Ominus(X4428,X4426,X4427) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).
fof(i_0_1903,plain,
! [X4957,X4958,X4959] :
( ~ class_Orderings_Oorder(X4959)
| ~ c_Orderings_Oord__class_Oless__eq(X4959,X4958,X4957)
| ~ c_Orderings_Oord__class_Oless__eq(X4959,X4957,X4958)
| X4957 = X4958 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).
fof(i_0_1904,plain,
! [X4950,X4951,X4952] :
( ~ class_Orderings_Oorder(X4952)
| ~ c_Orderings_Oord__class_Oless__eq(X4952,X4951,X4950)
| ~ c_Orderings_Oord__class_Oless__eq(X4952,X4950,X4951)
| X4951 = X4950 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).
fof(i_0_1905,plain,
! [X4931,X4932,X4933] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4933,X4931,X4932)
| X4931 = X4932
| ~ c_Orderings_Oord__class_Oless__eq(X4933,X4932,X4931)
| ~ class_Orderings_Oorder(X4933) )
& ( X4931 != X4932
| c_Orderings_Oord__class_Oless__eq(X4933,X4931,X4932)
| ~ c_Orderings_Oord__class_Oless__eq(X4933,X4932,X4931)
| ~ class_Orderings_Oorder(X4933) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).
fof(i_0_1906,plain,
! [X4920,X4921,X4922] :
( ( c_Orderings_Oord__class_Oless__eq(X4922,X4921,X4920)
| X4921 != X4920
| ~ class_Orderings_Oorder(X4922) )
& ( c_Orderings_Oord__class_Oless__eq(X4922,X4920,X4921)
| X4921 != X4920
| ~ class_Orderings_Oorder(X4922) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X4922,X4921,X4920)
| ~ c_Orderings_Oord__class_Oless__eq(X4922,X4920,X4921)
| X4921 = X4920
| ~ class_Orderings_Oorder(X4922) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).
fof(i_0_1907,plain,
! [X5223] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5223))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5223) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5223)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5223)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff])]) ).
fof(i_0_1908,plain,
! [X3109,X3110] :
( ~ class_Rings_Olinordered__semidom(X3110)
| c_Orderings_Oord__class_Oless(X3110,X3109,c_Groups_Oplus__class_Oplus(X3110,X3109,c_Groups_Oone__class_Oone(X3110))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).
fof(i_0_1909,plain,
! [X4103,X4104,X4105,X4106,X4107] :
( ( X4106 = X4104
| c_Polynomial_OpCons(X4107,X4106,X4105) != c_Polynomial_OpCons(X4107,X4104,X4103)
| ~ class_Groups_Ozero(X4107) )
& ( X4105 = X4103
| c_Polynomial_OpCons(X4107,X4106,X4105) != c_Polynomial_OpCons(X4107,X4104,X4103)
| ~ class_Groups_Ozero(X4107) )
& ( X4106 != X4104
| X4105 != X4103
| c_Polynomial_OpCons(X4107,X4106,X4105) = c_Polynomial_OpCons(X4107,X4104,X4103)
| ~ class_Groups_Ozero(X4107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff])])]) ).
fof(i_0_1910,plain,
! [X4046,X4047,X4048,X4049] :
( ( c_Polynomial_Omonom(X4049,X4048,X4047) != c_Polynomial_Omonom(X4049,X4046,X4047)
| X4048 = X4046
| ~ class_Groups_Ozero(X4049) )
& ( X4048 != X4046
| c_Polynomial_Omonom(X4049,X4048,X4047) = c_Polynomial_Omonom(X4049,X4046,X4047)
| ~ class_Groups_Ozero(X4049) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__iff])])]) ).
fof(i_0_1911,plain,
! [X4250,X4251,X4252,X4253] :
( ( c_Groups_Oplus__class_Oplus(X4253,X4252,X4251) != c_Groups_Oplus__class_Oplus(X4253,X4250,X4251)
| X4252 = X4250
| ~ class_Groups_Ocancel__semigroup__add(X4253) )
& ( X4252 != X4250
| c_Groups_Oplus__class_Oplus(X4253,X4252,X4251) = c_Groups_Oplus__class_Oplus(X4253,X4250,X4251)
| ~ class_Groups_Ocancel__semigroup__add(X4253) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).
fof(i_0_1912,plain,
! [X4238,X4239,X4240,X4241] :
( ~ class_Groups_Ocancel__semigroup__add(X4241)
| c_Groups_Oplus__class_Oplus(X4241,X4240,X4239) != c_Groups_Oplus__class_Oplus(X4241,X4238,X4239)
| X4240 = X4238 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).
fof(i_0_1913,plain,
! [X4242,X4243,X4244,X4245] :
( ~ class_Groups_Ocancel__ab__semigroup__add(X4245)
| c_Groups_Oplus__class_Oplus(X4245,X4244,X4243) != c_Groups_Oplus__class_Oplus(X4245,X4244,X4242)
| X4243 = X4242 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).
fof(i_0_1914,plain,
! [X4254,X4255,X4256,X4257] :
( ( c_Groups_Oplus__class_Oplus(X4257,X4256,X4255) != c_Groups_Oplus__class_Oplus(X4257,X4256,X4254)
| X4255 = X4254
| ~ class_Groups_Ocancel__semigroup__add(X4257) )
& ( X4255 != X4254
| c_Groups_Oplus__class_Oplus(X4257,X4256,X4255) = c_Groups_Oplus__class_Oplus(X4257,X4256,X4254)
| ~ class_Groups_Ocancel__semigroup__add(X4257) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).
fof(i_0_1915,plain,
! [X4246,X4247,X4248,X4249] :
( ~ class_Groups_Ocancel__semigroup__add(X4249)
| c_Groups_Oplus__class_Oplus(X4249,X4248,X4247) != c_Groups_Oplus__class_Oplus(X4249,X4248,X4246)
| X4247 = X4246 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).
fof(i_0_1916,plain,
! [X4808,X4809] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4809),X4808)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4809) = 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_1917,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_1294])]) ).
fof(i_0_1918,plain,
! [X5043,X5044,X5045] :
( ( c_Orderings_Oord__class_Oless__eq(X5045,X5044,X5043)
| c_Orderings_Oord__class_Oless(X5045,X5043,X5044)
| ~ class_Orderings_Olinorder(X5045) )
& ( ~ c_Orderings_Oord__class_Oless(X5045,X5043,X5044)
| ~ c_Orderings_Oord__class_Oless__eq(X5045,X5044,X5043)
| ~ class_Orderings_Olinorder(X5045) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1295])])]) ).
fof(i_0_1919,plain,
! [X5073,X5074,X5075] :
( ~ class_Orderings_Olinorder(X5075)
| ~ c_Orderings_Oord__class_Oless__eq(X5075,X5074,X5073)
| ~ c_Orderings_Oord__class_Oless(X5075,X5073,X5074) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1296])]) ).
fof(i_0_1920,plain,
! [X5040,X5041,X5042] :
( ( c_Orderings_Oord__class_Oless(X5042,X5041,X5040)
| c_Orderings_Oord__class_Oless__eq(X5042,X5040,X5041)
| ~ class_Orderings_Olinorder(X5042) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5042,X5040,X5041)
| ~ c_Orderings_Oord__class_Oless(X5042,X5041,X5040)
| ~ class_Orderings_Olinorder(X5042) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1297])])]) ).
fof(i_0_1921,plain,
! [X4977,X4978,X4979] :
( ( c_Orderings_Oord__class_Oless(X4979,X4978,X4977)
| c_Orderings_Oord__class_Oless(X4979,X4977,X4978)
| X4978 = X4977
| ~ class_Orderings_Olinorder(X4979) )
& ( ~ c_Orderings_Oord__class_Oless(X4979,X4977,X4978)
| ~ c_Orderings_Oord__class_Oless(X4979,X4978,X4977)
| ~ class_Orderings_Olinorder(X4979) )
& ( X4978 != X4977
| ~ c_Orderings_Oord__class_Oless(X4979,X4978,X4977)
| ~ class_Orderings_Olinorder(X4979) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1298])])]) ).
fof(i_0_1922,plain,
! [X5034,X5035,X5036] :
( ~ class_Orderings_Opreorder(X5036)
| ~ c_Orderings_Oord__class_Oless(X5036,X5035,X5034)
| ~ c_Orderings_Oord__class_Oless(X5036,X5034,X5035) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1299])]) ).
fof(i_0_1923,plain,
! [X5004,X5005,X5006] :
( ~ class_Orderings_Opreorder(X5006)
| ~ c_Orderings_Oord__class_Oless(X5006,X5005,X5004)
| ~ c_Orderings_Oord__class_Oless(X5006,X5004,X5005) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1300])]) ).
fof(i_0_1924,plain,
! [X4995,X4996,X4997] :
( ~ class_Orderings_Opreorder(X4997)
| ~ c_Orderings_Oord__class_Oless(X4997,X4996,X4995)
| ~ c_Orderings_Oord__class_Oless(X4997,X4995,X4996) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1301])]) ).
fof(i_0_1925,plain,
! [X4992,X4993,X4994] :
( ~ class_Orderings_Opreorder(X4994)
| ~ c_Orderings_Oord__class_Oless(X4994,X4993,X4992)
| ~ c_Orderings_Oord__class_Oless(X4994,X4992,X4993) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1302])]) ).
fof(i_0_1926,plain,
! [X5219,X5220] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5220,c_RealDef_Oreal(tc_Nat_Onat,X5219))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5220),X5219) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__le])]) ).
fof(i_0_1927,plain,
! [X5217,X5218] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5218),X5217)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5218,c_RComplete_Onatfloor(X5217)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor])]) ).
fof(i_0_1928,plain,
! [X4769,X4770,X4771] :
( ( hAPP(c_Polynomial_Opoly(X4771,X4770),X4769) != c_Groups_Ozero__class_Ozero(X4771)
| X4770 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4771))
| c_Polynomial_Oorder(X4771,X4769,X4770) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Oidom(X4771) )
& ( X4770 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4771))
| hAPP(c_Polynomial_Opoly(X4771,X4770),X4769) = c_Groups_Ozero__class_Ozero(X4771)
| ~ class_Rings_Oidom(X4771) )
& ( c_Polynomial_Oorder(X4771,X4769,X4770) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(c_Polynomial_Opoly(X4771,X4770),X4769) = c_Groups_Ozero__class_Ozero(X4771)
| ~ class_Rings_Oidom(X4771) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__root])])]) ).
fof(i_0_1929,plain,
! [X3715,X3716] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3716,X3715) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3715,X3716) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3716 = X3715 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).
fof(i_0_1930,plain,
! [X5216] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X5216)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(X5216)),X5216) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__natfloor__le])]) ).
fof(i_0_1931,plain,
! [X5301,X5302] :
( ( X5301 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302))
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5302),X5301) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302))
| ~ class_Rings_Olinordered__idom(X5302) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5302),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302)),X5301)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5302),X5301) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5302))
| X5301 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302))
| ~ class_Rings_Olinordered__idom(X5302) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X5302),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302)),X5301)
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X5302),X5301) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5302),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X5302)))
| X5301 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5302))
| ~ class_Rings_Olinordered__idom(X5302) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1303])])]) ).
fof(i_0_1932,plain,
! [X4085,X4086] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4086),X4085,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4086)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4086),X4085) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4086),X4085)
| ~ class_Rings_Olinordered__idom(X4086) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(X4086),X4085,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4086)))
| c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(X4086),X4085) = X4085
| ~ class_Rings_Olinordered__idom(X4086) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1304])])]) ).
fof(i_0_1933,plain,
! [X3149,X3150] :
( ~ class_Rings_Olinordered__ring(X3150)
| c_Orderings_Oord__class_Oless__eq(X3150,c_Groups_Ozero__class_Ozero(X3150),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3150),X3149),X3149)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).
fof(i_0_1934,plain,
! [X4858,X4859] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4859,X4858)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4858,X4859)
| X4859 = X4858 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).
fof(i_0_1935,plain,
! [X3526,X3527] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3527,X3526)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3526,X3527)
| X3527 = X3526 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).
fof(i_0_1936,plain,
! [X2852,X2853] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2853,X2852)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2852,X2853)
| X2853 = X2852 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
fof(i_0_1937,plain,
! [X4402,X4403,X4404] :
( ~ class_Groups_Ogroup__add(X4404)
| c_Groups_Ominus__class_Ominus(X4404,c_Groups_Oplus__class_Oplus(X4404,X4403,X4402),X4402) = X4403 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).
fof(i_0_1938,plain,
! [X4399,X4400,X4401] :
( ~ class_Groups_Ogroup__add(X4401)
| c_Groups_Oplus__class_Oplus(X4401,c_Groups_Ominus__class_Ominus(X4401,X4400,X4399),X4399) = X4400 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).
fof(i_0_1939,plain,
! [X4827,X4828] :
( ( X4828 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4828),X4827) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4828) )
& ( X4827 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4828),X4827) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4828) )
& ( X4828 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| X4827 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4828),X4827) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4828) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).
fof(i_0_1940,plain,
! [X3515,X3516,X3517] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3517,X3516) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3515,X3516)
| X3517 = X3515 )
& ( X3517 != X3515
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3517,X3516) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3515,X3516) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).
fof(i_0_1941,plain,
! [X3512,X3513,X3514] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3514,X3513) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3514,X3512)
| X3513 = X3512 )
& ( X3513 != X3512
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3514,X3513) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3514,X3512) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).
fof(i_0_1942,plain,
! [X5148] :
( 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),X5148) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X5148)) ),
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_1943,plain,
! [X3695] :
( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk11_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)
& hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk11_0),X3695) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3695)) ),
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_1944,plain,
! [X3691] : hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____),X3691) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_c____,X3691)),
inference(variable_rename,[status(thm)],[fact_q_I2_J]) ).
fof(i_0_1945,plain,
! [X3601,X3602,X3604,X3605,X3606] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3602,X3601)
| X3601 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3602,esk8_2(X3601,X3602)) )
& ( X3604 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3605,X3606)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3605,X3604) ) ),
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_1946,plain,
! [X3020,X3021,X3023,X3024,X3025] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3021,X3020)
| X3020 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3021,esk6_2(X3020,X3021)) )
& ( X3023 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3024,X3025)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3024,X3023) ) ),
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_1947,plain,
! [X3783,X3784] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3784,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3784,X3783)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).
fof(i_0_1948,plain,
! [X3735,X3736] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3736,X3735),X3736) = X3735,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).
fof(i_0_1949,plain,
! [X3737,X3738] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3738,X3737),X3737) = X3738,
inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).
fof(i_0_1950,plain,
! [X3756,X3757] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3757,X3756),X3757),
inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).
fof(i_0_1951,plain,
! [X3599,X3600] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3600,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3600,X3599)),
inference(variable_rename,[status(thm)],[fact_le__add1]) ).
fof(i_0_1952,plain,
! [X3597,X3598] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3598,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3597,X3598)),
inference(variable_rename,[status(thm)],[fact_le__add2]) ).
fof(i_0_1953,plain,
! [X5154] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5154))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5154) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5154)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X5154)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one])]) ).
fof(i_0_1954,plain,
! [X5120] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5120),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5120,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5120,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5120),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_1955,plain,
! [X4528,X4529] :
( ( ~ c_Orderings_Oord__class_Oless(X4529,c_Groups_Ozero__class_Ozero(X4529),c_Groups_Oabs__class_Oabs(X4529,X4528))
| X4528 != c_Groups_Ozero__class_Ozero(X4529)
| ~ class_Groups_Oordered__ab__group__add__abs(X4529) )
& ( X4528 = c_Groups_Ozero__class_Ozero(X4529)
| c_Orderings_Oord__class_Oless(X4529,c_Groups_Ozero__class_Ozero(X4529),c_Groups_Oabs__class_Oabs(X4529,X4528))
| ~ class_Groups_Oordered__ab__group__add__abs(X4529) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).
fof(i_0_1956,plain,
! [X2796] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X2796))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2796) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X2796),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2796) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X2796),X2796)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2796) ) ),
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_1957,plain,
! [X3557,X3558,X3559] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3559),X3558) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3557),X3558)
| X3559 = X3557
| X3558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3559 != X3557
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3559),X3558) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3557),X3558) )
& ( X3558 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3559),X3558) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3557),X3558) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).
fof(i_0_1958,plain,
! [X2898,X2899,X2900] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2899),X2900) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2898),X2900)
| X2899 = X2898
| X2900 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X2899 != X2898
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2899),X2900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2898),X2900)
| X2900 = 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_1959,plain,
! [X3554,X3555,X3556] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3555) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3554)
| X3555 = X3554
| X3556 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3555 != X3554
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3555) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3554) )
& ( X3556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3555) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3556),X3554) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).
fof(i_0_1960,plain,
! [X3551,X3552,X3553] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3552) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3551)
| X3553 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3552 = X3551 )
& ( X3553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3552) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3551) )
& ( X3552 != X3551
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3552) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3553),X3551) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).
fof(i_0_1961,plain,
! [X2895,X2896,X2897] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2897),X2896) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2897),X2895)
| X2896 = X2895
| X2897 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( X2896 != X2895
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2897),X2896) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2897),X2895)
| X2897 = 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_1962,plain,
! [X5164,X5165] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5165,X5164)
| c_Nat__Transfer_Otsub(X5164,X5165) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5164,X5165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).
fof(i_0_1963,plain,
! [X5157,X5158] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5158,X5157)
| c_Nat__Transfer_Otsub(X5157,X5158) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X5157,X5158) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X5158,X5157)
| c_Nat__Transfer_Otsub(X5157,X5158) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1305])]) ).
fof(i_0_1964,plain,
! [X5088,X5089,X5090] :
( ~ class_Orderings_Oorder(X5090)
| ~ c_Orderings_Oord__class_Oless__eq(X5090,X5089,X5088)
| X5088 = X5089
| c_Orderings_Oord__class_Oless(X5090,X5089,X5088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).
fof(i_0_1965,plain,
! [X5085,X5086,X5087] :
( ~ class_Orderings_Oorder(X5087)
| ~ c_Orderings_Oord__class_Oless__eq(X5087,X5086,X5085)
| X5086 = X5085
| c_Orderings_Oord__class_Oless(X5087,X5086,X5085) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).
fof(i_0_1966,plain,
! [X5082,X5083,X5084] :
( ~ class_Orderings_Oorder(X5084)
| ~ c_Orderings_Oord__class_Oless__eq(X5084,X5083,X5082)
| c_Orderings_Oord__class_Oless(X5084,X5083,X5082)
| X5083 = X5082 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).
fof(i_0_1967,plain,
! [X5067,X5068,X5069] :
( ~ class_Orderings_Oorder(X5069)
| X5068 = X5067
| ~ c_Orderings_Oord__class_Oless__eq(X5069,X5068,X5067)
| c_Orderings_Oord__class_Oless(X5069,X5068,X5067) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).
fof(i_0_1968,plain,
! [X5055,X5056,X5057] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5057,X5056,X5055)
| c_Orderings_Oord__class_Oless(X5057,X5056,X5055)
| X5056 = X5055
| ~ class_Orderings_Oorder(X5057) )
& ( ~ c_Orderings_Oord__class_Oless(X5057,X5056,X5055)
| c_Orderings_Oord__class_Oless__eq(X5057,X5056,X5055)
| ~ class_Orderings_Oorder(X5057) )
& ( X5056 != X5055
| c_Orderings_Oord__class_Oless__eq(X5057,X5056,X5055)
| ~ class_Orderings_Oorder(X5057) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).
fof(i_0_1969,plain,
! [X5049,X5050,X5051] :
( ( c_Orderings_Oord__class_Oless__eq(X5051,X5050,X5049)
| ~ c_Orderings_Oord__class_Oless(X5051,X5050,X5049)
| ~ class_Orderings_Oorder(X5051) )
& ( X5050 != X5049
| ~ c_Orderings_Oord__class_Oless(X5051,X5050,X5049)
| ~ class_Orderings_Oorder(X5051) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X5051,X5050,X5049)
| X5050 = X5049
| c_Orderings_Oord__class_Oless(X5051,X5050,X5049)
| ~ class_Orderings_Oorder(X5051) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).
fof(i_0_1970,plain,
! [X5064,X5065,X5066] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X5066,X5065,X5064)
| X5065 = X5064
| c_Orderings_Oord__class_Oless(X5066,X5065,X5064)
| ~ class_Orderings_Olinorder(X5066) )
& ( X5065 != X5064
| c_Orderings_Oord__class_Oless__eq(X5066,X5065,X5064)
| c_Orderings_Oord__class_Oless(X5066,X5065,X5064)
| ~ class_Orderings_Olinorder(X5066) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1306])])]) ).
fof(i_0_1971,plain,
! [X5070,X5071,X5072] :
( ~ class_Orderings_Oorder(X5072)
| X5071 = X5070
| ~ c_Orderings_Oord__class_Oless__eq(X5072,X5070,X5071)
| c_Orderings_Oord__class_Oless(X5072,X5070,X5071) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).
fof(i_0_1972,plain,
! [X4738,X4739] :
( ~ class_Rings_Ocomm__ring__1(X4739)
| c_Groups_Ouminus__class_Ouminus(X4739,X4738) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4739),c_Groups_Ouminus__class_Ouminus(X4739,c_Groups_Oone__class_Oone(X4739))),X4738) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).
fof(i_0_1973,plain,
! [X5150,X5151] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5151,X5150)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X5151),c_RComplete_Onatfloor(X5150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natfloor__mono])]) ).
fof(i_0_1974,plain,
! [X5117,X5118] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5118,X5117)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X5118),c_RComplete_Onatceiling(X5117)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_natceiling__mono])]) ).
fof(i_0_1975,plain,
! [X4522,X4523] :
( ( ~ c_Orderings_Oord__class_Oless__eq(X4523,c_Groups_Oabs__class_Oabs(X4523,X4522),c_Groups_Ozero__class_Ozero(X4523))
| X4522 = c_Groups_Ozero__class_Ozero(X4523)
| ~ class_Groups_Oordered__ab__group__add__abs(X4523) )
& ( X4522 != c_Groups_Ozero__class_Ozero(X4523)
| c_Orderings_Oord__class_Oless__eq(X4523,c_Groups_Oabs__class_Oabs(X4523,X4522),c_Groups_Ozero__class_Ozero(X4523))
| ~ class_Groups_Oordered__ab__group__add__abs(X4523) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).
fof(i_0_1976,plain,
! [X5076,X5077,X5078] :
( ~ class_Orderings_Opreorder(X5078)
| ~ c_Orderings_Oord__class_Oless(X5078,X5077,X5076)
| c_Orderings_Oord__class_Oless__eq(X5078,X5077,X5076) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).
fof(i_0_1977,plain,
! [X4584,X4585] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4585)
| c_Orderings_Oord__class_Oless__eq(X4585,c_Groups_Ouminus__class_Ouminus(X4585,c_Groups_Oabs__class_Oabs(X4585,X4584)),c_Groups_Ozero__class_Ozero(X4585)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).
fof(i_0_1978,plain,
! [X4826] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4826)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4826) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4826)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X4826) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).
fof(i_0_1979,plain,
! [X2815,X2816] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2816,X2815))
| X2815 != c_Groups_Ozero__class_Ozero(X2816)
| ~ class_RealVector_Oreal__normed__vector(X2816) )
& ( X2815 = c_Groups_Ozero__class_Ozero(X2816)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2816,X2815))
| ~ class_RealVector_Oreal__normed__vector(X2816) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff])])]) ).
fof(i_0_1980,plain,
! [X3974] : 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,X3974)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X3974)),
inference(variable_rename,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(i_0_1981,plain,
! [X4526,X4527] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4527)
| ~ c_Orderings_Oord__class_Oless(X4527,c_Groups_Oabs__class_Oabs(X4527,X4526),c_Groups_Ozero__class_Ozero(X4527)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1307])]) ).
fof(i_0_1982,plain,
! [X3653] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3653,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3653),X3653)),
inference(variable_rename,[status(thm)],[fact_le__square]) ).
fof(i_0_1983,plain,
! [X4532,X4533,X4534] :
( ~ class_Groups_Ogroup__add(X4534)
| c_Groups_Ominus__class_Ominus(X4534,X4533,c_Groups_Ouminus__class_Ouminus(X4534,X4532)) = c_Groups_Oplus__class_Oplus(X4534,X4533,X4532) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).
fof(i_0_1984,plain,
! [X4740,X4741,X4742] :
( ~ class_Rings_Ocomm__ring__1(X4742)
| c_Groups_Ominus__class_Ominus(X4742,X4741,X4740) = c_Groups_Oplus__class_Oplus(X4742,X4741,c_Groups_Ouminus__class_Ouminus(X4742,X4740)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).
fof(i_0_1985,plain,
! [X4535,X4536,X4537] :
( ~ class_Groups_Oab__group__add(X4537)
| c_Groups_Ominus__class_Ominus(X4537,X4536,X4535) = c_Groups_Oplus__class_Oplus(X4537,X4536,c_Groups_Ouminus__class_Ouminus(X4537,X4535)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).
fof(i_0_1986,plain,
! [X4538,X4539,X4540] :
( ~ class_Groups_Ogroup__add(X4540)
| c_Groups_Ominus__class_Ominus(X4540,X4539,X4538) = c_Groups_Oplus__class_Oplus(X4540,X4539,c_Groups_Ouminus__class_Ouminus(X4540,X4538)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).
fof(i_0_1987,plain,
! [X2817,X2818] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2818,X2817),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X2817 = c_Groups_Ozero__class_Ozero(X2818)
| ~ class_RealVector_Oreal__normed__vector(X2818) )
& ( X2817 != c_Groups_Ozero__class_Ozero(X2818)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2818,X2817),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(X2818) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff])])]) ).
fof(i_0_1988,plain,
! [X3785,X3786] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3786,X3785) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3786,X3785) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3786,X3785)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3786,X3785) = 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_1989,plain,
! [X4820,X4821] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4821,X4820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4821,X4820) )
& ( X4821 != X4820
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4821,X4820) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4821,X4820)
| X4821 = X4820
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4821,X4820) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).
fof(i_0_1990,plain,
! [X3595,X3596] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3596,X3595)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3596,X3595) )
& ( X3596 != X3595
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3596,X3595) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3596,X3595)
| X3596 = X3595
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3596,X3595) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).
fof(i_0_1991,plain,
! [X3593,X3594] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3594,X3593)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3594,X3593)
| X3594 = X3593 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3594,X3593)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3594,X3593) )
& ( X3594 != X3593
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3594,X3593) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).
fof(i_0_1992,plain,
! [X3589,X3590] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3590,X3589)
| X3590 = X3589
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3590,X3589) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).
fof(i_0_1993,plain,
! [X2893,X2894] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2894,X2893)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2894,X2893) )
& ( X2894 != X2893
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2894,X2893) )
& ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2894,X2893)
| X2894 = X2893
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2894,X2893) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__less__def])])]) ).
fof(i_0_1994,plain,
! [X2891,X2892] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2892,X2891)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2892,X2891)
| X2892 = X2891 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2892,X2891)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2892,X2891) )
& ( X2892 != X2891
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2892,X2891) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
fof(i_0_1995,plain,
! [X3787,X3788] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3788,X3787)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3788,X3787) = 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_1996,plain,
! [X4834] : 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),X4834)) = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X4834),
inference(variable_rename,[status(thm)],[fact_complex__i__mult__minus]) ).
fof(i_0_1997,plain,
! [X5292,X5293,X5294,X5295] :
( ~ class_Groups_Ouminus(X5295)
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X5294,X5295),X5293),X5292) = c_Groups_Ouminus__class_Ouminus(X5295,hAPP(X5293,X5292)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).
fof(i_0_1998,plain,
! [X5307,X5308] :
( ~ class_Rings_Olinordered__idom(X5308)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5308),c_Groups_Osgn__class_Osgn(X5308,X5307)),c_Groups_Oabs__class_Oabs(X5308,X5307)) = X5307 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).
fof(i_0_1999,plain,
! [X4083,X4084] :
( ~ class_Groups_Ozero(X4084)
| c_Polynomial_Omonom(X4084,X4083,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(X4084,X4083,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4084))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__0])]) ).
fof(i_0_2000,plain,
! [X5336,X5337] :
( ( c_Groups_Osgn__class_Osgn(X5337,X5336) != c_Groups_Ouminus__class_Ouminus(X5337,c_Groups_Oone__class_Oone(X5337))
| c_Orderings_Oord__class_Oless(X5337,X5336,c_Groups_Ozero__class_Ozero(X5337))
| ~ class_Rings_Olinordered__idom(X5337) )
& ( ~ c_Orderings_Oord__class_Oless(X5337,X5336,c_Groups_Ozero__class_Ozero(X5337))
| c_Groups_Osgn__class_Osgn(X5337,X5336) = c_Groups_Ouminus__class_Ouminus(X5337,c_Groups_Oone__class_Oone(X5337))
| ~ class_Rings_Olinordered__idom(X5337) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).
fof(i_0_2001,plain,
! [X5334,X5335] :
( ~ class_Rings_Olinordered__idom(X5335)
| ~ c_Orderings_Oord__class_Oless(X5335,X5334,c_Groups_Ozero__class_Ozero(X5335))
| c_Groups_Osgn__class_Osgn(X5335,X5334) = c_Groups_Ouminus__class_Ouminus(X5335,c_Groups_Oone__class_Oone(X5335)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).
fof(i_0_2002,plain,
! [X5172,X5173] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5173,X5172)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5173,X5172) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).
fof(i_0_2003,plain,
! [X3591,X3592] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3592,X3591)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3592,X3591) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).
fof(i_0_2004,plain,
! [X3587,X3588] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3588,X3587)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3588,X3587) )
& ( X3588 != X3587
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3588,X3587) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).
fof(i_0_2005,plain,
! [X2957,X2958] :
( ~ class_RealVector_Oreal__normed__vector(X2958)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X2958,X2957),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1308])]) ).
fof(i_0_2006,plain,
! [X4588,X4589] :
( ( ~ c_Orderings_Oord__class_Oless(X4589,X4588,c_Groups_Ozero__class_Ozero(X4589))
| c_Groups_Oabs__class_Oabs(X4589,X4588) = c_Groups_Ouminus__class_Ouminus(X4589,X4588)
| ~ class_Groups_Oabs__if(X4589) )
& ( c_Orderings_Oord__class_Oless(X4589,X4588,c_Groups_Ozero__class_Ozero(X4589))
| c_Groups_Oabs__class_Oabs(X4589,X4588) = X4588
| ~ class_Groups_Oabs__if(X4589) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1309])])]) ).
fof(i_0_2007,plain,
! [X4586,X4587] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4587)
| ~ c_Orderings_Oord__class_Oless__eq(X4587,X4586,c_Groups_Ozero__class_Ozero(X4587))
| c_Groups_Oabs__class_Oabs(X4587,X4586) = c_Groups_Ouminus__class_Ouminus(X4587,X4586) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).
fof(i_0_2008,plain,
! [X4230,X4231] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4231)
| ~ c_Orderings_Oord__class_Oless(X4231,X4230,c_Groups_Ozero__class_Ozero(X4231))
| c_Groups_Oabs__class_Oabs(X4231,X4230) = c_Groups_Ouminus__class_Ouminus(X4231,X4230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).
fof(i_0_2009,plain,
! [X4087,X4088] :
( ~ class_Rings_Ocomm__semiring__0(X4088)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4088)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4088))),X4087) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4088)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left])]) ).
fof(i_0_2010,plain,
! [X4861,X4862] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4862,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4861)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4862,X4861),
inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(i_0_2011,plain,
! [X4863,X4864] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4864,X4863) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4864,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4863)),
inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).
fof(i_0_2012,plain,
! [X3975,X3976] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X3976,X3975) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X3976,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,X3975)),
inference(variable_rename,[status(thm)],[fact_complex__diff__def]) ).
fof(i_0_2013,plain,
! [X3318,X3319] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3319,X3318) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3319,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3318)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
fof(i_0_2014,plain,
! [X3316,X3317] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3317,X3316) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3317,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3316)),
inference(variable_rename,[status(thm)],[fact_real__diff__def]) ).
fof(i_0_2015,plain,
! [X4810] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4810),c_Groups_Oone__class_Oone(tc_Int_Oint))
| X4810 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( X4810 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4810),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_2016,plain,
! [X5207] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5207),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| X5207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5207 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5207),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_2017,plain,
! [X2781,X2782] :
( hAPP(X2782,esk1_2(X2781,X2782)) != hAPP(X2781,esk1_2(X2781,X2782))
| X2782 = X2781 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).
fof(i_0_2018,plain,
! [X5338,X5339] :
( ( X5338 != c_Groups_Ozero__class_Ozero(X5339)
| c_Groups_Osgn__class_Osgn(X5339,X5338) = c_Groups_Ozero__class_Ozero(X5339)
| ~ class_Groups_Osgn__if(X5339) )
& ( ~ c_Orderings_Oord__class_Oless(X5339,c_Groups_Ozero__class_Ozero(X5339),X5338)
| c_Groups_Osgn__class_Osgn(X5339,X5338) = c_Groups_Oone__class_Oone(X5339)
| X5338 = c_Groups_Ozero__class_Ozero(X5339)
| ~ class_Groups_Osgn__if(X5339) )
& ( c_Orderings_Oord__class_Oless(X5339,c_Groups_Ozero__class_Ozero(X5339),X5338)
| c_Groups_Osgn__class_Osgn(X5339,X5338) = c_Groups_Ouminus__class_Ouminus(X5339,c_Groups_Oone__class_Oone(X5339))
| X5338 = c_Groups_Ozero__class_Ozero(X5339)
| ~ class_Groups_Osgn__if(X5339) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1310])])]) ).
fof(i_0_2019,plain,
! [X4197,X4198,X4199] :
( ( c_Polynomial_Osmult(X4199,X4198,X4197) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| X4198 = c_Groups_Ozero__class_Ozero(X4199)
| X4197 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| ~ class_Rings_Oidom(X4199) )
& ( X4198 != c_Groups_Ozero__class_Ozero(X4199)
| c_Polynomial_Osmult(X4199,X4198,X4197) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| ~ class_Rings_Oidom(X4199) )
& ( X4197 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| c_Polynomial_Osmult(X4199,X4198,X4197) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4199))
| ~ class_Rings_Oidom(X4199) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__eq__0__iff])])]) ).
fof(i_0_2020,plain,
! [X3332,X3333] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3333,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3332)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3333 = X3332 )
& ( X3333 != X3332
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3333,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3332)) = 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_2021,plain,
! [X5187] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5187),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[i_0_1311]) ).
fof(i_0_2022,plain,
! [X2879,X2880,X2881] :
( ( X2880 = c_Groups_Ozero__class_Ozero(X2881)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2881),X2880),X2879) != c_Groups_Ozero__class_Ozero(X2881)
| ~ class_Power_Opower(X2881)
| ~ class_Rings_Omult__zero(X2881)
| ~ class_Rings_Ono__zero__divisors(X2881)
| ~ class_Rings_Ozero__neq__one(X2881) )
& ( X2879 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2881),X2880),X2879) != c_Groups_Ozero__class_Ozero(X2881)
| ~ class_Power_Opower(X2881)
| ~ class_Rings_Omult__zero(X2881)
| ~ class_Rings_Ono__zero__divisors(X2881)
| ~ class_Rings_Ozero__neq__one(X2881) )
& ( X2880 != c_Groups_Ozero__class_Ozero(X2881)
| X2879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2881),X2880),X2879) = c_Groups_Ozero__class_Ozero(X2881)
| ~ class_Power_Opower(X2881)
| ~ class_Rings_Omult__zero(X2881)
| ~ class_Rings_Ono__zero__divisors(X2881)
| ~ class_Rings_Ozero__neq__one(X2881) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).
fof(i_0_2023,plain,
! [X3107,X3108] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),X3107),X3107) != c_Groups_Oone__class_Oone(X3108)
| X3107 = c_Groups_Oone__class_Oone(X3108)
| X3107 = c_Groups_Ouminus__class_Ouminus(X3108,c_Groups_Oone__class_Oone(X3108))
| ~ class_Rings_Oring__1__no__zero__divisors(X3108) )
& ( X3107 != c_Groups_Oone__class_Oone(X3108)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),X3107),X3107) = c_Groups_Oone__class_Oone(X3108)
| ~ class_Rings_Oring__1__no__zero__divisors(X3108) )
& ( X3107 != c_Groups_Ouminus__class_Ouminus(X3108,c_Groups_Oone__class_Oone(X3108))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3108),X3107),X3107) = c_Groups_Oone__class_Oone(X3108)
| ~ class_Rings_Oring__1__no__zero__divisors(X3108) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).
fof(i_0_2024,plain,
! [X5332,X5333] :
( ( c_Groups_Osgn__class_Osgn(X5333,X5332) != c_Groups_Oone__class_Oone(X5333)
| c_Orderings_Oord__class_Oless(X5333,c_Groups_Ozero__class_Ozero(X5333),X5332)
| ~ class_Rings_Olinordered__idom(X5333) )
& ( ~ c_Orderings_Oord__class_Oless(X5333,c_Groups_Ozero__class_Ozero(X5333),X5332)
| c_Groups_Osgn__class_Osgn(X5333,X5332) = c_Groups_Oone__class_Oone(X5333)
| ~ class_Rings_Olinordered__idom(X5333) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).
fof(i_0_2025,plain,
! [X5330,X5331] :
( ~ class_Rings_Olinordered__idom(X5331)
| ~ c_Orderings_Oord__class_Oless(X5331,c_Groups_Ozero__class_Ozero(X5331),X5330)
| c_Groups_Osgn__class_Osgn(X5331,X5330) = c_Groups_Oone__class_Oone(X5331) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).
fof(i_0_2026,plain,
! [X3998,X3999] :
( ~ class_Fields_Ofield(X3999)
| X3998 = c_Groups_Ozero__class_Ozero(X3999)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3999),c_Rings_Oinverse__class_Oinverse(X3999,X3998)),X3998) = c_Groups_Oone__class_Oone(X3999) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse])]) ).
fof(i_0_2027,plain,
! [X3450,X3451] :
( ~ class_Rings_Odivision__ring(X3451)
| X3450 = c_Groups_Ozero__class_Ozero(X3451)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3451),c_Rings_Oinverse__class_Oinverse(X3451,X3450)),X3450) = c_Groups_Oone__class_Oone(X3451) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__inverse])]) ).
fof(i_0_2028,plain,
! [X4191,X4192,X4193] :
( ( X4192 = c_Groups_Ozero__class_Ozero(X4193)
| c_Polynomial_OpCons(X4193,X4192,X4191) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4193))
| ~ class_Groups_Ozero(X4193) )
& ( X4191 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4193))
| c_Polynomial_OpCons(X4193,X4192,X4191) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4193))
| ~ class_Groups_Ozero(X4193) )
& ( X4192 != c_Groups_Ozero__class_Ozero(X4193)
| X4191 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4193))
| c_Polynomial_OpCons(X4193,X4192,X4191) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4193))
| ~ class_Groups_Ozero(X4193) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff])])]) ).
fof(i_0_2029,plain,
! [X5386,X5387,X5388] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5388,X5387,X5386) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5388))
| X5387 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5388))
| ~ class_Rings_Ocomm__semiring__0(X5388) )
& ( X5387 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5388))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5388,X5387,X5386) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5388))
| ~ class_Rings_Ocomm__semiring__0(X5388) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__eq__0__iff])])]) ).
fof(i_0_2030,plain,
! [X4974,X4975,X4976] :
( ( X4975 = X4974
| c_Orderings_Oord__class_Oless(X4976,X4975,X4974)
| c_Orderings_Oord__class_Oless(X4976,X4974,X4975)
| ~ class_Orderings_Olinorder(X4976) )
& ( ~ c_Orderings_Oord__class_Oless(X4976,X4975,X4974)
| X4975 != X4974
| ~ class_Orderings_Olinorder(X4976) )
& ( ~ c_Orderings_Oord__class_Oless(X4976,X4974,X4975)
| X4975 != X4974
| ~ class_Orderings_Olinorder(X4976) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).
fof(i_0_2031,plain,
! [X5037,X5038,X5039] :
( ~ class_Orderings_Olinorder(X5039)
| c_Orderings_Oord__class_Oless(X5039,X5038,X5037)
| X5038 = X5037
| c_Orderings_Oord__class_Oless(X5039,X5037,X5038) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1312])]) ).
fof(i_0_2032,plain,
! [X4986,X4987,X4988] :
( ~ class_Orderings_Olinorder(X4988)
| X4987 = X4986
| c_Orderings_Oord__class_Oless(X4988,X4987,X4986)
| c_Orderings_Oord__class_Oless(X4988,X4986,X4987) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1313])]) ).
fof(i_0_2033,plain,
! [X4983,X4984,X4985] :
( ( c_Orderings_Oord__class_Oless(X4985,X4983,X4984)
| X4983 = X4984
| c_Orderings_Oord__class_Oless(X4985,X4984,X4983)
| ~ class_Orderings_Olinorder(X4985) )
& ( X4983 != X4984
| ~ c_Orderings_Oord__class_Oless(X4985,X4983,X4984)
| c_Orderings_Oord__class_Oless(X4985,X4984,X4983)
| ~ class_Orderings_Olinorder(X4985) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1314])])]) ).
fof(i_0_2034,plain,
! [X4980,X4981,X4982] :
( ~ class_Orderings_Olinorder(X4982)
| c_Orderings_Oord__class_Oless(X4982,X4981,X4980)
| X4981 = X4980
| c_Orderings_Oord__class_Oless(X4982,X4980,X4981) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).
fof(i_0_2035,plain,
! [X3125,X3126,X3127] :
( ~ class_Rings_Olinordered__idom(X3127)
| X3126 = X3125
| c_Orderings_Oord__class_Oless(X3127,X3126,X3125)
| c_Orderings_Oord__class_Oless(X3127,X3125,X3126) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1315])]) ).
fof(i_0_2036,plain,
! [X2833,X2834,X2835,X2836,X2837,X2838,X2841,X2842] :
( ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2835,X2834,X2833)
| hAPP(X2833,X2836) = hAPP(X2833,X2837) )
& ( hAPP(X2838,esk4_1(X2838)) != hAPP(X2838,esk5_1(X2838))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2842,X2841,X2838) ) ),
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_2037,plain,
! [X4524,X4525] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4525)
| ~ c_Orderings_Oord__class_Oless__eq(X4525,c_Groups_Ozero__class_Ozero(X4525),X4524)
| c_Groups_Oabs__class_Oabs(X4525,X4524) = X4524 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).
fof(i_0_2038,plain,
! [X4530,X4531] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4531)
| ~ c_Orderings_Oord__class_Oless(X4531,c_Groups_Ozero__class_Ozero(X4531),X4530)
| c_Groups_Oabs__class_Oabs(X4531,X4530) = X4530 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
fof(i_0_2039,plain,
! [X4969,X4970,X4971] :
( ~ class_Orderings_Olinorder(X4971)
| c_Orderings_Oord__class_Oless__eq(X4971,X4970,X4969)
| c_Orderings_Oord__class_Oless__eq(X4971,X4969,X4970) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1316])]) ).
fof(i_0_2040,plain,
! [X4917,X4918,X4919] :
( ~ class_Orderings_Olinorder(X4919)
| c_Orderings_Oord__class_Oless__eq(X4919,X4918,X4917)
| c_Orderings_Oord__class_Oless__eq(X4919,X4917,X4918) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).
fof(i_0_2041,plain,
! [X5058,X5059,X5060] :
( ~ class_Orderings_Olinorder(X5060)
| c_Orderings_Oord__class_Oless(X5060,X5059,X5058)
| c_Orderings_Oord__class_Oless__eq(X5060,X5058,X5059) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1317])]) ).
fof(i_0_2042,plain,
! [X5061,X5062,X5063] :
( ~ class_Orderings_Olinorder(X5063)
| c_Orderings_Oord__class_Oless__eq(X5063,X5062,X5061)
| c_Orderings_Oord__class_Oless(X5063,X5061,X5062) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1318])]) ).
fof(i_0_2043,plain,
! [X5046,X5047,X5048] :
( ~ class_Orderings_Olinorder(X5048)
| c_Orderings_Oord__class_Oless__eq(X5048,X5047,X5046)
| c_Orderings_Oord__class_Oless(X5048,X5046,X5047) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).
fof(i_0_2044,plain,
! [X4674,X4675,X4676] :
( ~ class_Rings_Ocomm__semiring__1(X4676)
| c_Groups_Oplus__class_Oplus(X4676,X4675,X4674) = c_Groups_Oplus__class_Oplus(X4676,X4674,X4675) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
fof(i_0_2045,plain,
! [X4515,X4516,X4517] :
( ~ class_Groups_Ogroup__add(X4517)
| c_Groups_Oplus__class_Oplus(X4517,X4516,X4515) != c_Groups_Ozero__class_Ozero(X4517)
| c_Groups_Ouminus__class_Ouminus(X4517,X4516) = X4515 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).
fof(i_0_2046,plain,
! [X4508,X4509,X4510] :
( ( X4509 != c_Groups_Ouminus__class_Ouminus(X4510,X4508)
| c_Groups_Oplus__class_Oplus(X4510,X4509,X4508) = c_Groups_Ozero__class_Ozero(X4510)
| ~ class_Groups_Ogroup__add(X4510) )
& ( c_Groups_Oplus__class_Oplus(X4510,X4509,X4508) != c_Groups_Ozero__class_Ozero(X4510)
| X4509 = c_Groups_Ouminus__class_Ouminus(X4510,X4508)
| ~ class_Groups_Ogroup__add(X4510) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).
fof(i_0_2047,plain,
! [X3026,X3027,X3028] :
( ( c_Groups_Oplus__class_Oplus(X3028,X3027,X3026) != c_Groups_Ozero__class_Ozero(X3028)
| X3026 = c_Groups_Ouminus__class_Ouminus(X3028,X3027)
| ~ class_Groups_Ogroup__add(X3028) )
& ( X3026 != c_Groups_Ouminus__class_Ouminus(X3028,X3027)
| c_Groups_Oplus__class_Oplus(X3028,X3027,X3026) = c_Groups_Ozero__class_Ozero(X3028)
| ~ class_Groups_Ogroup__add(X3028) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff])])]) ).
fof(i_0_2048,plain,
! [X4072,X4073,X4074] :
( ( c_Polynomial_Omonom(X4074,X4073,X4072) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4074))
| X4073 = c_Groups_Ozero__class_Ozero(X4074)
| ~ class_Groups_Ozero(X4074) )
& ( X4073 != c_Groups_Ozero__class_Ozero(X4074)
| c_Polynomial_Omonom(X4074,X4073,X4072) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4074))
| ~ class_Groups_Ozero(X4074) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0__iff])])]) ).
fof(i_0_2049,plain,
! [X4562,X4563] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4563)
| c_Orderings_Oord__class_Oless__eq(X4563,c_Groups_Ouminus__class_Ouminus(X4563,X4562),c_Groups_Oabs__class_Oabs(X4563,X4562)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).
fof(i_0_2050,plain,
! [X4797] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X4797,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4797) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4797) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4797,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,X4797) = X4797 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1319])]) ).
fof(i_0_2051,plain,
! [X3846] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3846,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3846) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3846) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3846,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3846) = X3846 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1320])]) ).
fof(i_0_2052,plain,
! [X3845] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3845,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3845) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3845) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3845,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3845) = X3845 ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1321])]) ).
fof(i_0_2053,plain,
! [X3267] :
( ~ class_Rings_Olinordered__semidom(X3267)
| ~ c_Orderings_Oord__class_Oless__eq(X3267,c_Groups_Oone__class_Oone(X3267),c_Groups_Ozero__class_Ozero(X3267)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1322])]) ).
fof(i_0_2054,plain,
! [X3269] :
( ~ class_Rings_Olinordered__semidom(X3269)
| ~ c_Orderings_Oord__class_Oless(X3269,c_Groups_Oone__class_Oone(X3269),c_Groups_Ozero__class_Ozero(X3269)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1323])]) ).
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_q____)),
inference(fof_simplification,[status(thm)],[fact_qnc]) ).
fof(i_0_2057,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_2058,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_2059,plain,
! [X4089,X4090] :
( ~ class_Rings_Ocomm__semiring__0(X4090)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(X4090)),X4089),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4090))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4090)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right])]) ).
fof(i_0_2060,plain,
! [X4619,X4620,X4621] :
( ~ class_Rings_Ocomm__semiring__1(X4621)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4621),X4620),X4619) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4621),X4619),X4620) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).
fof(i_0_2061,plain,
! [X3409,X3410,X3411] :
( ~ class_Rings_Odivision__ring(X3411)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3411),X3410),X3409) != c_Groups_Oone__class_Oone(X3411)
| c_Rings_Oinverse__class_Oinverse(X3411,X3410) = X3409 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__unique])]) ).
fof(i_0_2062,plain,
! [X4818,X4819] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X4819,X4818)
| X4819 = X4818
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X4818,X4819) ),
inference(variable_rename,[status(thm)],[fact_zless__linear]) ).
fof(i_0_2063,plain,
! [X3501,X3502] :
( ( X3502 = X3501
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3502,X3501)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3501,X3502) )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3502,X3501)
| X3502 != X3501 )
& ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3501,X3502)
| X3502 != X3501 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).
fof(i_0_2064,plain,
! [X3499,X3500] :
( X3500 = X3499
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3500,X3499)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3499,X3500) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1324])]) ).
fof(i_0_2065,plain,
! [X4853,X4854] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4854,X4853)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4853,X4854) ),
inference(variable_rename,[status(thm)],[fact_zle__linear]) ).
fof(i_0_2066,plain,
! [X3519,X3520] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3520,X3519)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3519,X3520) ),
inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).
fof(i_0_2067,plain,
! [X2857,X2858] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2858,X2857)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2857,X2858) ),
inference(variable_rename,[status(thm)],[fact_real__le__linear]) ).
fof(i_0_2068,plain,
! [X3138,X3139,X3140] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3140),X3139),X3138) != c_Groups_Ozero__class_Ozero(X3140)
| X3139 = c_Groups_Ozero__class_Ozero(X3140)
| X3138 = c_Groups_Ozero__class_Ozero(X3140)
| ~ class_Rings_Oring__no__zero__divisors(X3140) )
& ( X3139 != c_Groups_Ozero__class_Ozero(X3140)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3140),X3139),X3138) = c_Groups_Ozero__class_Ozero(X3140)
| ~ class_Rings_Oring__no__zero__divisors(X3140) )
& ( X3138 != c_Groups_Ozero__class_Ozero(X3140)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3140),X3139),X3138) = c_Groups_Ozero__class_Ozero(X3140)
| ~ class_Rings_Oring__no__zero__divisors(X3140) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).
fof(i_0_2069,plain,
! [X3144,X3145,X3146] :
( ~ class_Rings_Ono__zero__divisors(X3146)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3146),X3145),X3144) != c_Groups_Ozero__class_Ozero(X3146)
| X3145 = c_Groups_Ozero__class_Ozero(X3146)
| X3144 = c_Groups_Ozero__class_Ozero(X3146) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).
fof(i_0_2070,plain,
! [X3141,X3142,X3143] :
( ~ class_Rings_Ono__zero__divisors(X3143)
| X3142 = c_Groups_Ozero__class_Ozero(X3143)
| X3141 = c_Groups_Ozero__class_Ozero(X3143)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3143),X3142),X3141) != c_Groups_Ozero__class_Ozero(X3143) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).
fof(i_0_2071,plain,
! [X5411,X5412,X5413] :
( ~ class_Rings_Olinordered__idom(X5413)
| c_Groups_Oabs__class_Oabs(X5413,X5412) != c_Groups_Oabs__class_Oabs(X5413,X5411)
| c_Rings_Odvd__class_Odvd(X5413,X5412,X5411) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq])]) ).
fof(i_0_2072,plain,
! [X4095,X4096] :
( ~ class_Groups_Oab__group__add(X4096)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4096),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4096)),X4095) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4096),X4095) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J])]) ).
fof(i_0_2073,plain,
! [X4841,X4842] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4842,X4841) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4841,X4842),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(i_0_2074,plain,
! [X3504,X3505] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3505,X3504) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3504,X3505),
inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).
fof(i_0_2075,plain,
! [X4766,X4767] :
( ( c_Groups_Oplus__class_Oplus(X4767,X4766,X4766) != c_Groups_Ozero__class_Ozero(X4767)
| X4766 = c_Groups_Ozero__class_Ozero(X4767)
| ~ class_Groups_Olinordered__ab__group__add(X4767) )
& ( X4766 != c_Groups_Ozero__class_Ozero(X4767)
| c_Groups_Oplus__class_Oplus(X4767,X4766,X4766) = c_Groups_Ozero__class_Ozero(X4767)
| ~ class_Groups_Olinordered__ab__group__add(X4767) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).
fof(i_0_2076,plain,
! [X4286,X4287] :
( ( c_Groups_Ozero__class_Ozero(X4287) != c_Groups_Oplus__class_Oplus(X4287,X4286,X4286)
| X4286 = c_Groups_Ozero__class_Ozero(X4287)
| ~ class_Groups_Olinordered__ab__group__add(X4287) )
& ( X4286 != c_Groups_Ozero__class_Ozero(X4287)
| c_Groups_Ozero__class_Ozero(X4287) = c_Groups_Oplus__class_Oplus(X4287,X4286,X4286)
| ~ class_Groups_Olinordered__ab__group__add(X4287) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).
fof(i_0_2077,plain,
! [X4353,X4354,X4355] :
( ( X4354 != X4353
| c_Groups_Ominus__class_Ominus(X4355,X4354,X4353) = c_Groups_Ozero__class_Ozero(X4355)
| ~ class_Groups_Oab__group__add(X4355) )
& ( c_Groups_Ominus__class_Ominus(X4355,X4354,X4353) != c_Groups_Ozero__class_Ozero(X4355)
| X4354 = X4353
| ~ class_Groups_Oab__group__add(X4355) ) ),
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,
! [X4350,X4351,X4352] :
( ( c_Groups_Ominus__class_Ominus(X4352,X4351,X4350) != c_Groups_Ozero__class_Ozero(X4352)
| X4351 = X4350
| ~ class_Groups_Ogroup__add(X4352) )
& ( X4351 != X4350
| c_Groups_Ominus__class_Ominus(X4352,X4351,X4350) = c_Groups_Ozero__class_Ozero(X4352)
| ~ class_Groups_Ogroup__add(X4352) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).
fof(i_0_2079,plain,
! [X2876,X2877,X2878] :
( ~ class_Rings_Oring__1__no__zero__divisors(X2878)
| X2877 = c_Groups_Ozero__class_Ozero(X2878)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2878),X2877),X2876) != c_Groups_Ozero__class_Ozero(X2878) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).
fof(i_0_2080,plain,
! [X3334,X3335] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3335,X3334) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3334 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3335) )
& ( X3334 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3335)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X3335,X3334) = 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,
! [X4685,X4686,X4687] :
( ( X4686 != c_Groups_Oplus__class_Oplus(X4687,X4686,X4685)
| X4685 = c_Groups_Ozero__class_Ozero(X4687)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4687) )
& ( X4685 != c_Groups_Ozero__class_Ozero(X4687)
| X4686 = c_Groups_Oplus__class_Oplus(X4687,X4686,X4685)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4687) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(i_0_2082,plain,
! [X5309,X5310] :
( ~ class_Rings_Olinordered__idom(X5310)
| c_Groups_Oabs__class_Oabs(X5310,X5309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5310),X5309),c_Groups_Osgn__class_Osgn(X5310,X5309)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).
fof(i_0_2083,plain,
! [X4185,X4186] :
( ( c_Polynomial_Opoly(X4186,X4185) != c_Polynomial_Opoly(X4186,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4186)))
| X4185 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4186))
| ~ class_Int_Oring__char__0(X4186)
| ~ class_Rings_Oidom(X4186) )
& ( X4185 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4186))
| c_Polynomial_Opoly(X4186,X4185) = c_Polynomial_Opoly(X4186,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4186)))
| ~ class_Int_Oring__char__0(X4186)
| ~ class_Rings_Oidom(X4186) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__zero])])]) ).
fof(i_0_2084,plain,
! [X3485] :
( X3485 = 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,X3485)),X3485) = 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,
! [X5001,X5002,X5003] :
( ~ class_Orderings_Oorder(X5003)
| ~ c_Orderings_Oord__class_Oless(X5003,X5002,X5001)
| X5001 != X5002 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).
fof(i_0_2086,plain,
! [X4998,X4999,X5000] :
( ~ class_Orderings_Oorder(X5000)
| ~ c_Orderings_Oord__class_Oless(X5000,X4999,X4998)
| X4999 != X4998 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).
fof(i_0_2087,plain,
! [X4989,X4990,X4991] :
( ~ class_Orderings_Oorder(X4991)
| ~ c_Orderings_Oord__class_Oless(X4991,X4990,X4989)
| X4990 != X4989 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).
fof(i_0_2088,plain,
! [X4194] :
( ~ class_Groups_Ozero(X4194)
| c_Polynomial_OpCons(X4194,c_Groups_Ozero__class_Ozero(X4194),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4194))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4194)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pCons__0__0])]) ).
fof(i_0_2089,plain,
! [X4200] :
( ~ class_Rings_Ocomm__semiring__1(X4200)
| c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4200)) = c_Polynomial_OpCons(X4200,c_Groups_Oone__class_Oone(X4200),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4200))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__poly__def])]) ).
fof(i_0_2090,plain,
! [X5153] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5153,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X5153) = 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,
! [X5119] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5119,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X5119) = 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,
! [X3452,X3453] :
( ~ class_Rings_Odivision__ring(X3453)
| X3452 = c_Groups_Ozero__class_Ozero(X3453)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3453),X3452),c_Rings_Oinverse__class_Oinverse(X3453,X3452)) = c_Groups_Oone__class_Oone(X3453) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse])]) ).
fof(i_0_2093,plain,
! [X3534] :
( ( X3534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| 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),X3534)
| X3534 != 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,
! [X4520,X4521] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4521)
| c_Orderings_Oord__class_Oless__eq(X4521,c_Groups_Ozero__class_Ozero(X4521),c_Groups_Oabs__class_Oabs(X4521,X4520)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).
fof(i_0_2095,plain,
! [X4972,X4973] :
( ~ class_Orderings_Opreorder(X4973)
| ~ c_Orderings_Oord__class_Oless(X4973,X4972,X4972) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1325])]) ).
fof(i_0_2096,plain,
! [X3328,X3329] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3329)
| ~ class_Rings_Odivision__ring__inverse__zero(X3329)
| c_RealVector_Onorm__class_Onorm(X3329,c_Rings_Oinverse__class_Oinverse(X3329,X3328)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3329,X3328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__inverse])]) ).
fof(i_0_2097,plain,
! [X3972,X3973] :
( ~ class_Fields_Olinordered__field(X3973)
| X3972 = c_Groups_Ozero__class_Ozero(X3973)
| c_Groups_Oabs__class_Oabs(X3973,c_Rings_Oinverse__class_Oinverse(X3973,X3972)) = c_Rings_Oinverse__class_Oinverse(X3973,c_Groups_Oabs__class_Oabs(X3973,X3972)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__inverse])]) ).
fof(i_0_2098,plain,
! [X3412,X3413] :
( ~ class_Rings_Odivision__ring(X3413)
| X3412 = c_Groups_Ozero__class_Ozero(X3413)
| c_Rings_Oinverse__class_Oinverse(X3413,c_Groups_Ouminus__class_Ouminus(X3413,X3412)) = c_Groups_Ouminus__class_Ouminus(X3413,c_Rings_Oinverse__class_Oinverse(X3413,X3412)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__minus__eq])]) ).
fof(i_0_2099,plain,
! [X3546] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3546,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X3546 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3546 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3546,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,
! [X4822,X4823] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4823),X4822) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4822),X4823),
inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).
fof(i_0_2101,plain,
! [X3531,X3532] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3532),X3531) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3531),X3532),
inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).
fof(i_0_2102,plain,
! [X2863,X2864] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2864),X2863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2863),X2864),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(i_0_2103,plain,
! [X4513,X4514] :
( ~ class_Groups_Oab__group__add(X4514)
| c_Groups_Oplus__class_Oplus(X4514,c_Groups_Ouminus__class_Ouminus(X4514,X4513),X4513) = c_Groups_Ozero__class_Ozero(X4514) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).
fof(i_0_2104,plain,
! [X4511,X4512] :
( ~ class_Groups_Ogroup__add(X4512)
| c_Groups_Oplus__class_Oplus(X4512,c_Groups_Ouminus__class_Ouminus(X4512,X4511),X4511) = c_Groups_Ozero__class_Ozero(X4512) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).
fof(i_0_2105,plain,
! [X4506,X4507] :
( ~ class_Groups_Ogroup__add(X4507)
| c_Groups_Oplus__class_Oplus(X4507,X4506,c_Groups_Ouminus__class_Ouminus(X4507,X4506)) = c_Groups_Ozero__class_Ozero(X4507) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).
fof(i_0_2106,plain,
! [X3330,X3331] :
( ~ class_RealVector_Oreal__div__algebra(X3331)
| ~ class_Rings_Odivision__ring__inverse__zero(X3331)
| c_RealVector_Oof__real(X3331,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3330)) = c_Rings_Oinverse__class_Oinverse(X3331,c_RealVector_Oof__real(X3331,X3330)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__inverse])]) ).
fof(i_0_2107,plain,
! [X3029,X3030] :
( ~ class_RealVector_Oreal__algebra__1(X3030)
| ~ class_RealVector_Oreal__normed__vector(X3030)
| c_RealVector_Oof__real(X3030,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3029)) = c_Groups_Ouminus__class_Ouminus(X3030,c_RealVector_Oof__real(X3030,X3029)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ominus])]) ).
fof(i_0_2108,plain,
! [X3541,X3542] :
( ( X3542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3542,X3541) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3542,X3541) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3542 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3541 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3542,X3541) = 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,
! [X3345,X3346] :
( ~ class_RealVector_Oreal__normed__div__algebra(X3346)
| X3345 = c_Groups_Ozero__class_Ozero(X3346)
| c_RealVector_Onorm__class_Onorm(X3346,c_Rings_Oinverse__class_Oinverse(X3346,X3345)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3346,X3345)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__norm__inverse])]) ).
fof(i_0_2110,plain,
! [X5389,X5390] :
( ~ class_Rings_Ocomm__semiring__0(X5390)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X5390,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5390)),X5389) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5390)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_offset__poly__0])]) ).
fof(i_0_2111,plain,
! [X4752,X4753] :
( ~ class_Rings_Ocomm__semiring__0(X4753)
| c_Polynomial_Opcompose(X4753,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4753)),X4752) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4753)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pcompose__0])]) ).
fof(i_0_2112,plain,
! [X4598,X4599] :
( ~ class_Rings_Ocomm__semiring__0(X4599)
| c_Polynomial_Osynthetic__div(X4599,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4599)),X4598) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4599)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_synthetic__div__0])]) ).
fof(i_0_2113,plain,
! [X4187,X4188] :
( ~ class_Rings_Ocomm__semiring__0(X4188)
| c_Polynomial_Osmult(X4188,X4187,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4188))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4188)) ),
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____),esk12_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,
! [X3536,X3537] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3537,X3536)
| X3536 != 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,
! [X2955,X2956] :
( ~ class_RealVector_Oreal__normed__vector(X2956)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2956,X2955)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__ge__zero])]) ).
fof(i_0_2117,plain,
! [X2912,X2913] :
( ( X2912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2913),c_Groups_Ozero__class_Ozero(X2913)),X2912) = c_Groups_Oone__class_Oone(X2913)
| ~ class_Power_Opower(X2913)
| ~ class_Rings_Osemiring__0(X2913) )
& ( X2912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2913),c_Groups_Ozero__class_Ozero(X2913)),X2912) = c_Groups_Ozero__class_Ozero(X2913)
| ~ class_Power_Opower(X2913)
| ~ class_Rings_Osemiring__0(X2913) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).
fof(i_0_2118,plain,
! [X3543,X3544] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3544,X3543) != X3544
| X3543 = 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,
! [X3535] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3535,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1326]) ).
fof(i_0_2120,plain,
! [X3533] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3533,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1327]) ).
fof(i_0_2121,plain,
! [X3312] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3312,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[i_0_1328]) ).
fof(i_0_2122,plain,
! [X5208] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X5208,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X5208))),
inference(variable_rename,[status(thm)],[fact_real__natceiling__ge]) ).
fof(i_0_2123,plain,
! [X3347,X3348] :
( ~ class_RealVector_Oreal__div__algebra(X3348)
| X3347 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X3348,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,X3347)) = c_Rings_Oinverse__class_Oinverse(X3348,c_RealVector_Oof__real(X3348,X3347)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__of__real__inverse])]) ).
fof(i_0_2124,plain,
! [X4139,X4140] :
( ~ class_Rings_Ocomm__semiring__1(X4140)
| hAPP(c_Polynomial_Opoly(X4140,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(X4140))),X4139) = c_Groups_Oone__class_Oone(X4140) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__1])]) ).
fof(i_0_2125,plain,
! [X4189,X4190] :
( ~ class_Rings_Ocomm__semiring__0(X4190)
| hAPP(c_Polynomial_Opoly(X4190,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4190))),X4189) = c_Groups_Ozero__class_Ozero(X4190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__0])]) ).
fof(i_0_2126,plain,
! [X4435,X4436] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4436)
| c_Orderings_Oord__class_Oless__eq(X4436,X4435,c_Groups_Oabs__class_Oabs(X4436,X4435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).
fof(i_0_2127,plain,
! [X3496,X3497] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3497,X3496)
| X3496 != X3497 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).
fof(i_0_2128,plain,
! [X3494,X3495] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3495,X3494)
| X3495 != X3494 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).
fof(i_0_2129,plain,
! [X5328,X5329] :
( ~ class_RealVector_Oreal__normed__vector(X5329)
| c_Groups_Osgn__class_Osgn(X5329,c_Groups_Ouminus__class_Ouminus(X5329,X5328)) = c_Groups_Ouminus__class_Ouminus(X5329,c_Groups_Osgn__class_Osgn(X5329,X5328)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__minus])]) ).
fof(i_0_2130,plain,
! [X3942,X3943] :
( ~ class_Fields_Olinordered__field__inverse__zero(X3943)
| c_Groups_Oabs__class_Oabs(X3943,c_Rings_Oinverse__class_Oinverse(X3943,X3942)) = c_Rings_Oinverse__class_Oinverse(X3943,c_Groups_Oabs__class_Oabs(X3943,X3942)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__inverse])]) ).
fof(i_0_2131,plain,
! [X3376,X3377] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3377)
| c_Rings_Oinverse__class_Oinverse(X3377,c_Groups_Ouminus__class_Ouminus(X3377,X3376)) = c_Groups_Ouminus__class_Ouminus(X3377,c_Rings_Oinverse__class_Oinverse(X3377,X3376)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__minus__eq])]) ).
fof(i_0_2132,plain,
! [X4097,X4098] :
( ~ class_Groups_Ocomm__monoid__add(X4098)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4098),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4098)),X4097) = X4097 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J])]) ).
fof(i_0_2133,plain,
! [X4091,X4092] :
( ~ class_Groups_Oab__group__add(X4092)
| c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(X4092),X4091,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4092))) = X4091 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J])]) ).
fof(i_0_2134,plain,
! [X4093,X4094] :
( ~ class_Groups_Ocomm__monoid__add(X4094)
| c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4094),X4093,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4094))) = X4093 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J])]) ).
fof(i_0_2135,plain,
! [X5230,X5231] :
( ~ class_Rings_Olinordered__idom(X5231)
| X5230 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5231))
| c_Polynomial_Opos__poly(X5231,X5230)
| c_Polynomial_Opos__poly(X5231,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X5231),X5230)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__poly__total])]) ).
fof(i_0_2136,plain,
! [X3549,X3550] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3550),X3549) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3550 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3550 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3550),X3549) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X3549 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3550),X3549) = 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,
! [X3031,X3032] :
( ~ class_RealVector_Oreal__algebra__1(X3032)
| c_RealVector_Oof__real(X3032,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X3031)) = c_Groups_Ouminus__class_Ouminus(X3032,c_RealVector_Oof__real(X3032,X3031)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__minus])]) ).
fof(i_0_2138,plain,
! [X5325,X5326] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5326)
| c_Groups_Osgn__class_Osgn(X5326,c_RealVector_Oof__real(X5326,X5325)) = c_RealVector_Oof__real(X5326,c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,X5325)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__of__real])]) ).
fof(i_0_2139,plain,
! [X3503] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3503,X3503),
inference(variable_rename,[status(thm)],[i_0_1329]) ).
fof(i_0_2140,plain,
! [X3498] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3498,X3498),
inference(variable_rename,[status(thm)],[i_0_1330]) ).
fof(i_0_2141,plain,
! [X3682,X3683] :
( X3683 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3683),X3682)
| X3682 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3683 = 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,
! [X4518,X4519] :
( ~ class_Groups_Ogroup__add(X4519)
| c_Groups_Ominus__class_Ominus(X4519,c_Groups_Ozero__class_Ozero(X4519),X4518) = c_Groups_Ouminus__class_Ouminus(X4519,X4518) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).
fof(i_0_2143,plain,
! [X3654,X3655] :
( ( X3655 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3655),X3654) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3654 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3655),X3654) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( X3655 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3654 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3655),X3654) = 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,
! [X3657,X3658] :
( ( X3658 = 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),X3658),X3657) )
& ( X3657 = 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),X3658),X3657) )
& ( X3658 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| X3657 != 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),X3658),X3657) ) ),
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,
! [X5182] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,X5182)),
inference(variable_rename,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(i_0_2146,plain,
! [X4773] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4773),X4773) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(i_0_2147,plain,
! [X4070,X4071] :
( ~ class_Groups_Ozero(X4071)
| c_Polynomial_Omonom(X4071,c_Groups_Ozero__class_Ozero(X4071),X4070) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4071)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_monom__eq__0])]) ).
fof(i_0_2148,plain,
! [X4195,X4196] :
( ~ class_Rings_Ocomm__semiring__0(X4196)
| c_Polynomial_Osmult(X4196,c_Groups_Ozero__class_Ozero(X4196),X4195) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4196)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__0__left])]) ).
fof(i_0_2149,plain,
! [X5121] :
( ~ class_Power_Opower(X5121)
| c_Power_Opower__class_Opower(X5121) = c_Power_Opower_Opower(X5121,c_Groups_Oone__class_Oone(X5121),c_Groups_Otimes__class_Otimes(X5121)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).
fof(i_0_2150,plain,
! [X4677,X4678] :
( ~ class_Rings_Ocomm__semiring__1(X4678)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4678),c_Groups_Ozero__class_Ozero(X4678)),X4677) = c_Groups_Ozero__class_Ozero(X4678) ),
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,
! [X3134,X3135] :
( ~ class_Rings_Omult__zero(X3135)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3135),c_Groups_Ozero__class_Ozero(X3135)),X3134) = c_Groups_Ozero__class_Ozero(X3135) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).
fof(i_0_2152,plain,
! [X2874,X2875] :
( ~ class_RealVector_Oreal__normed__algebra(X2875)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2875),c_Groups_Ozero__class_Ozero(X2875)),X2874) = c_Groups_Ozero__class_Ozero(X2875) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__left])]) ).
fof(i_0_2153,plain,
! [X2872,X2873] :
( ~ class_RealVector_Oreal__normed__algebra(X2873)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2873),c_Groups_Ozero__class_Ozero(X2873)),X2872) = c_Groups_Ozero__class_Ozero(X2873) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left_Ozero])]) ).
fof(i_0_2154,plain,
! [X2889,X2890] :
( ~ class_Groups_Omonoid__mult(X2890)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2890),c_Groups_Oone__class_Oone(X2890)),X2889) = c_Groups_Oone__class_Oone(X2890) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(i_0_2155,plain,
! [X3268] :
( ~ class_Rings_Olinordered__semidom(X3268)
| c_Orderings_Oord__class_Oless__eq(X3268,c_Groups_Ozero__class_Ozero(X3268),c_Groups_Oone__class_Oone(X3268)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).
fof(i_0_2156,plain,
! [X3270] :
( ~ class_Rings_Olinordered__semidom(X3270)
| c_Orderings_Oord__class_Oless(X3270,c_Groups_Ozero__class_Ozero(X3270),c_Groups_Oone__class_Oone(X3270)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).
fof(i_0_2157,plain,
! [X4710,X4711] :
( ~ class_Rings_Ocomm__semiring__1(X4711)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4711),c_Groups_Oone__class_Oone(X4711)),X4710) = X4710 ),
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,
! [X4372,X4373] :
( ~ class_Groups_Ocomm__monoid__mult(X4373)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4373),c_Groups_Oone__class_Oone(X4373)),X4372) = X4372 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).
fof(i_0_2159,plain,
! [X4370,X4371] :
( ~ class_Groups_Omonoid__mult(X4371)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4371),c_Groups_Oone__class_Oone(X4371)),X4370) = X4370 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).
fof(i_0_2160,plain,
! [X4679,X4680] :
( ~ class_Rings_Ocomm__semiring__1(X4680)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4680),X4679),c_Groups_Ozero__class_Ozero(X4680)) = c_Groups_Ozero__class_Ozero(X4680) ),
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,
! [X3136,X3137] :
( ~ class_Rings_Omult__zero(X3137)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3137),X3136),c_Groups_Ozero__class_Ozero(X3137)) = c_Groups_Ozero__class_Ozero(X3137) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).
fof(i_0_2162,plain,
! [X2870,X2871] :
( ~ class_RealVector_Oreal__normed__algebra(X2871)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2871),X2870),c_Groups_Ozero__class_Ozero(X2871)) = c_Groups_Ozero__class_Ozero(X2871) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ozero__right])]) ).
fof(i_0_2163,plain,
! [X2868,X2869] :
( ~ class_RealVector_Oreal__normed__algebra(X2869)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2869),X2868),c_Groups_Ozero__class_Ozero(X2869)) = c_Groups_Ozero__class_Ozero(X2869) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right_Ozero])]) ).
fof(i_0_2164,plain,
! [X4170,X4171] :
( ~ class_Rings_Ocomm__semiring__1(X4171)
| c_Polynomial_Osmult(X4171,c_Groups_Oone__class_Oone(X4171),X4170) = X4170 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smult__1__left])]) ).
fof(i_0_2165,plain,
! [X4282,X4283] :
( ~ class_Groups_Omonoid__add(X4283)
| c_Groups_Oplus__class_Oplus(X4283,c_Groups_Ozero__class_Ozero(X4283),X4282) = X4282 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).
fof(i_0_2166,plain,
! [X4681,X4682] :
( ~ class_Rings_Ocomm__semiring__1(X4682)
| c_Groups_Oplus__class_Oplus(X4682,c_Groups_Ozero__class_Ozero(X4682),X4681) = X4681 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(i_0_2167,plain,
! [X4284,X4285] :
( ~ class_Groups_Ocomm__monoid__add(X4285)
| c_Groups_Oplus__class_Oplus(X4285,c_Groups_Ozero__class_Ozero(X4285),X4284) = X4284 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
fof(i_0_2168,plain,
! [X4358,X4359] :
( ~ class_Groups_Ogroup__add(X4359)
| c_Groups_Ominus__class_Ominus(X4359,X4358,c_Groups_Ozero__class_Ozero(X4359)) = X4358 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).
fof(i_0_2169,plain,
! [X4288,X4289] :
( ~ class_Groups_Omonoid__add(X4289)
| c_Groups_Oplus__class_Oplus(X4289,X4288,c_Groups_Ozero__class_Ozero(X4289)) = X4288 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).
fof(i_0_2170,plain,
! [X4683,X4684] :
( ~ class_Rings_Ocomm__semiring__1(X4684)
| c_Groups_Oplus__class_Oplus(X4684,X4683,c_Groups_Ozero__class_Ozero(X4684)) = X4683 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).
fof(i_0_2171,plain,
! [X4290,X4291] :
( ~ class_Groups_Ocomm__monoid__add(X4291)
| c_Groups_Oplus__class_Oplus(X4291,X4290,c_Groups_Ozero__class_Ozero(X4291)) = X4290 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).
fof(i_0_2172,plain,
! [X5380,X5381] :
( ~ class_Rings_Ocomm__semiring__1(X5381)
| c_Rings_Odvd__class_Odvd(X5381,c_Groups_Oone__class_Oone(X5381),X5380) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).
fof(i_0_2173,plain,
! [X5349,X5350] :
( ~ class_Rings_Ocomm__semiring__1(X5350)
| c_Rings_Odvd__class_Odvd(X5350,X5349,c_Groups_Ozero__class_Ozero(X5350)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).
fof(i_0_2174,plain,
! [X4617,X4618] :
( ~ class_Rings_Ocomm__semiring__1(X4618)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4618),X4617),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X4618) ),
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,
! [X2843,X2844] :
( ~ class_Power_Opower(X2844)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2844),X2843),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X2844) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).
fof(i_0_2176,plain,
! [X4712,X4713] :
( ~ class_Rings_Ocomm__semiring__1(X4713)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4713),X4712),c_Groups_Oone__class_Oone(X4713)) = X4712 ),
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,
! [X4376,X4377] :
( ~ class_Groups_Ocomm__monoid__mult(X4377)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4377),X4376),c_Groups_Oone__class_Oone(X4377)) = X4376 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).
fof(i_0_2178,plain,
! [X4374,X4375] :
( ~ class_Groups_Omonoid__mult(X4375)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4375),X4374),c_Groups_Oone__class_Oone(X4375)) = X4374 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).
fof(i_0_2179,plain,
! [X4356,X4357] :
( ~ class_Groups_Ogroup__add(X4357)
| c_Groups_Ominus__class_Ominus(X4357,X4356,X4356) = c_Groups_Ozero__class_Ozero(X4357) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).
fof(i_0_2180,plain,
! [X4923,X4924,X4925] :
( ~ class_Orderings_Opreorder(X4925)
| X4924 != X4923
| c_Orderings_Oord__class_Oless__eq(X4925,X4924,X4923) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).
fof(i_0_2181,plain,
! [X3363,X3364,X3365] :
( ~ class_Rings_Odivision__ring(X3365)
| c_Rings_Oinverse__class_Oinverse(X3365,X3364) != c_Rings_Oinverse__class_Oinverse(X3365,X3363)
| X3364 = c_Groups_Ozero__class_Ozero(X3365)
| X3363 = c_Groups_Ozero__class_Ozero(X3365)
| X3364 = X3363 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__eq__imp__eq])]) ).
fof(i_0_2182,plain,
! [X4722,X4723] :
( ~ class_Rings_Ocomm__semiring__1(X4723)
| hAPP(hAPP(c_Power_Opower__class_Opower(X4723),X4722),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4722 ),
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,
! [X2831,X2832] :
( ~ class_Groups_Omonoid__mult(X2832)
| hAPP(hAPP(c_Power_Opower__class_Opower(X2832),X2831),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X2831 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).
fof(i_0_2184,plain,
! [X5152] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(X5152)),
inference(variable_rename,[status(thm)],[fact_zero__le__natfloor]) ).
fof(i_0_2185,plain,
! [X5116] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(X5116)),
inference(variable_rename,[status(thm)],[fact_zero__le__natceiling]) ).
fof(i_0_2186,plain,
! [X5399,X5400] :
( ~ class_Rings_Ocomm__semiring__1(X5400)
| c_Rings_Odvd__class_Odvd(X5400,X5399,X5399) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).
fof(i_0_2187,plain,
! [X4909,X4910] :
( ~ class_Orderings_Opreorder(X4910)
| c_Orderings_Oord__class_Oless__eq(X4910,X4909,X4909) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).
fof(i_0_2188,plain,
! [X5323,X5324] :
( ~ class_Rings_Olinordered__idom(X5324)
| c_Groups_Osgn__class_Osgn(X5324,c_Groups_Osgn__class_Osgn(X5324,X5323)) = c_Groups_Osgn__class_Osgn(X5324,X5323) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).
fof(i_0_2189,plain,
! [X4280,X4281] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4281)
| c_Groups_Oabs__class_Oabs(X4281,c_Groups_Oabs__class_Oabs(X4281,X4280)) = c_Groups_Oabs__class_Oabs(X4281,X4280) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).
fof(i_0_2190,plain,
! [X4443,X4444] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4444)
| c_Groups_Oabs__class_Oabs(X4444,c_Groups_Ouminus__class_Ouminus(X4444,X4443)) = c_Groups_Oabs__class_Oabs(X4444,X4443) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).
fof(i_0_2191,plain,
! [X3099,X3100] :
( ~ class_RealVector_Oreal__normed__vector(X3100)
| c_RealVector_Onorm__class_Onorm(X3100,c_Groups_Ouminus__class_Ouminus(X3100,X3099)) = c_RealVector_Onorm__class_Onorm(X3100,X3099) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel])]) ).
fof(i_0_2192,plain,
! [X4100,X4101,X4102] :
( ( c_Polynomial_Opoly(X4102,X4101) != c_Polynomial_Opoly(X4102,X4100)
| X4101 = X4100
| ~ class_Int_Oring__char__0(X4102)
| ~ class_Rings_Oidom(X4102) )
& ( X4101 != X4100
| c_Polynomial_Opoly(X4102,X4101) = c_Polynomial_Opoly(X4102,X4100)
| ~ class_Int_Oring__char__0(X4102)
| ~ class_Rings_Oidom(X4102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_poly__eq__iff])])]) ).
fof(i_0_2193,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_2194,plain,
! [X5285,X5286] :
( ~ class_Lattices_Oab__semigroup__idem__mult(X5286)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5286),X5285),X5285) = X5285 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).
fof(i_0_2195,plain,
! [X3538] :
( X3538 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3538) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).
fof(i_0_2196,plain,
! [X3713,X3714] :
( ~ class_RealVector_Oreal__normed__vector(X3714)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X3714,X3713)) = c_RealVector_Onorm__class_Onorm(X3714,X3713) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(i_0_2197,plain,
! [X3777,X3778] :
( ~ class_RealVector_Oreal__normed__algebra__1(X3778)
| c_RealVector_Onorm__class_Onorm(X3778,c_RealVector_Oof__real(X3778,X3777)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3777) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
fof(i_0_2198,plain,
! [X5195] :
( ~ class_Rings_Olinordered__idom(X5195)
| ~ c_Polynomial_Opos__poly(X5195,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X5195))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_1331])]) ).
fof(i_0_2199,plain,
! [X3719] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).
fof(i_0_2200,plain,
! [X5340,X5341] :
( ( X5340 != c_Groups_Ozero__class_Ozero(X5341)
| c_RealVector_Onorm__class_Onorm(X5341,c_Groups_Osgn__class_Osgn(X5341,X5340)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5341) )
& ( X5340 = c_Groups_Ozero__class_Ozero(X5341)
| c_RealVector_Onorm__class_Onorm(X5341,c_Groups_Osgn__class_Osgn(X5341,X5340)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X5341) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__sgn])])]) ).
fof(i_0_2201,plain,
! [X4833] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4833) = X4833,
inference(variable_rename,[status(thm)],[fact_zadd__0]) ).
fof(i_0_2202,plain,
! [X3539] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3539) = X3539,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(i_0_2203,plain,
! [X3718] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3718,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3718,
inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).
fof(i_0_2204,plain,
! [X4832] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4832,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X4832,
inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).
fof(i_0_2205,plain,
! [X3540] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3540,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3540,
inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).
fof(i_0_2206,plain,
! [X3521,X3522] :
( X3522 != X3521
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3522,X3521) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).
fof(i_0_2207,plain,
! [X3545] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3545),
inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).
fof(i_0_2208,plain,
! [X3311] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X3311),
inference(variable_rename,[status(thm)],[fact_le0]) ).
fof(i_0_2209,plain,
! [X4099] :
( ~ class_Groups_Oab__group__add(X4099)
| c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(X4099),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4099))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4099)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J])]) ).
fof(i_0_2210,plain,
! [X3717] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3717,X3717) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).
fof(i_0_2211,plain,
! [X3547] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3547) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[fact_mult__0]) ).
fof(i_0_2212,plain,
! [X3323,X3324,X3325] :
( ( c_Rings_Oinverse__class_Oinverse(X3325,X3324) != c_Rings_Oinverse__class_Oinverse(X3325,X3323)
| X3324 = X3323
| ~ class_Rings_Odivision__ring__inverse__zero(X3325) )
& ( X3324 != X3323
| c_Rings_Oinverse__class_Oinverse(X3325,X3324) = c_Rings_Oinverse__class_Oinverse(X3325,X3323)
| ~ class_Rings_Odivision__ring__inverse__zero(X3325) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__iff__eq])])]) ).
fof(i_0_2213,plain,
! [X3320,X3321,X3322] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3322)
| c_Rings_Oinverse__class_Oinverse(X3322,X3321) != c_Rings_Oinverse__class_Oinverse(X3322,X3320)
| X3321 = X3320 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__imp__eq])]) ).
fof(i_0_2214,plain,
! [X5289,X5290,X5291] :
( ( c_Groups_Ouminus__class_Ouminus(X5291,X5290) != c_Groups_Ouminus__class_Ouminus(X5291,X5289)
| X5290 = X5289
| ~ class_Lattices_Oboolean__algebra(X5291) )
& ( X5290 != X5289
| c_Groups_Ouminus__class_Ouminus(X5291,X5290) = c_Groups_Ouminus__class_Ouminus(X5291,X5289)
| ~ class_Lattices_Oboolean__algebra(X5291) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).
fof(i_0_2215,plain,
! [X4269,X4270,X4271] :
( ( c_Groups_Ouminus__class_Ouminus(X4271,X4270) != c_Groups_Ouminus__class_Ouminus(X4271,X4269)
| X4270 = X4269
| ~ class_Groups_Ogroup__add(X4271) )
& ( X4270 != X4269
| c_Groups_Ouminus__class_Ouminus(X4271,X4270) = c_Groups_Ouminus__class_Ouminus(X4271,X4269)
| ~ class_Groups_Ogroup__add(X4271) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).
fof(i_0_2216,plain,
! [X2865,X2866,X2867] :
( ( c_RealVector_Oof__real(X2867,X2866) != c_RealVector_Oof__real(X2867,X2865)
| X2866 = X2865
| ~ class_RealVector_Oreal__algebra__1(X2867) )
& ( X2866 != X2865
| c_RealVector_Oof__real(X2867,X2866) = c_RealVector_Oof__real(X2867,X2865)
| ~ class_RealVector_Oreal__algebra__1(X2867) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__eq__iff])])]) ).
fof(i_0_2217,plain,
! [X3368,X3369] :
( ~ class_Rings_Odivision__ring(X3369)
| X3368 = c_Groups_Ozero__class_Ozero(X3369)
| c_Rings_Oinverse__class_Oinverse(X3369,c_Rings_Oinverse__class_Oinverse(X3369,X3368)) = X3368 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__inverse__inverse__eq])]) ).
fof(i_0_2218,plain,
! [X4825] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X4825) = X4825,
inference(variable_rename,[status(thm)],[fact_zmult__1]) ).
fof(i_0_2219,plain,
! [X3659] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X3659) = X3659,
inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).
fof(i_0_2220,plain,
! [X2901] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X2901) = X2901,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(i_0_2221,plain,
! [X4852] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4852,X4852),
inference(variable_rename,[status(thm)],[fact_zle__refl]) ).
fof(i_0_2222,plain,
! [X3518] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3518,X3518),
inference(variable_rename,[status(thm)],[fact_le__refl]) ).
fof(i_0_2223,plain,
! [X2859] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2859,X2859),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
fof(i_0_2224,plain,
! [X3548] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3548),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,
! [X4824] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4824),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X4824,
inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).
fof(i_0_2226,plain,
! [X3656] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3656),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3656,
inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).
fof(i_0_2227,plain,
! [X3326,X3327] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3327)
| c_Rings_Oinverse__class_Oinverse(X3327,c_Rings_Oinverse__class_Oinverse(X3327,X3326)) = X3326 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__inverse__eq])]) ).
fof(i_0_2228,plain,
! [X5296,X5297] :
( ~ class_Lattices_Oboolean__algebra(X5297)
| c_Groups_Ouminus__class_Ouminus(X5297,c_Groups_Ouminus__class_Ouminus(X5297,X5296)) = X5296 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).
fof(i_0_2229,plain,
! [X4278,X4279] :
( ~ class_Groups_Ogroup__add(X4279)
| c_Groups_Ouminus__class_Ouminus(X4279,c_Groups_Ouminus__class_Ouminus(X4279,X4278)) = X4278 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
fof(i_0_2230,plain,
! [X5196] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X5196)) = c_RealDef_Oreal(tc_Nat_Onat,X5196),
inference(variable_rename,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(i_0_2231,plain,
! [X4272,X4273,X4274] :
( ( c_Groups_Ouminus__class_Ouminus(X4274,X4273) != X4272
| c_Groups_Ouminus__class_Ouminus(X4274,X4272) = X4273
| ~ class_Groups_Ogroup__add(X4274) )
& ( c_Groups_Ouminus__class_Ouminus(X4274,X4272) != X4273
| c_Groups_Ouminus__class_Ouminus(X4274,X4273) = X4272
| ~ class_Groups_Ogroup__add(X4274) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).
fof(i_0_2232,plain,
! [X4275,X4276,X4277] :
( ( X4276 != c_Groups_Ouminus__class_Ouminus(X4277,X4275)
| X4275 = c_Groups_Ouminus__class_Ouminus(X4277,X4276)
| ~ class_Groups_Ogroup__add(X4277) )
& ( X4275 != c_Groups_Ouminus__class_Ouminus(X4277,X4276)
| X4276 = c_Groups_Ouminus__class_Ouminus(X4277,X4275)
| ~ class_Groups_Ogroup__add(X4277) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).
fof(i_0_2233,plain,
! [X3445,X3446] :
( ( c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3446,X3445) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X3445 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3446))
| ~ class_Groups_Ozero(X3446) )
& ( X3445 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3446))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3446,X3445) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X3446) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psize__eq__0__iff])])]) ).
fof(i_0_2234,plain,
! [X5200,X5201] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5201) != c_RealDef_Oreal(tc_Nat_Onat,X5200)
| X5201 = X5200 )
& ( X5201 != X5200
| c_RealDef_Oreal(tc_Nat_Onat,X5201) = c_RealDef_Oreal(tc_Nat_Onat,X5200) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject])]) ).
fof(i_0_2235,plain,
! [X4379,X4380] :
( ( c_Groups_Ozero__class_Ozero(X4380) != c_Groups_Ouminus__class_Ouminus(X4380,X4379)
| c_Groups_Ozero__class_Ozero(X4380) = X4379
| ~ class_Groups_Ogroup__add(X4380) )
& ( c_Groups_Ozero__class_Ozero(X4380) != X4379
| c_Groups_Ozero__class_Ozero(X4380) = c_Groups_Ouminus__class_Ouminus(X4380,X4379)
| ~ class_Groups_Ogroup__add(X4380) ) ),
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,
! [X3940,X3941] :
( ( c_Rings_Oinverse__class_Oinverse(X3941,X3940) != c_Groups_Oone__class_Oone(X3941)
| X3940 = c_Groups_Oone__class_Oone(X3941)
| ~ class_Fields_Ofield__inverse__zero(X3941) )
& ( X3940 != c_Groups_Oone__class_Oone(X3941)
| c_Rings_Oinverse__class_Oinverse(X3941,X3940) = c_Groups_Oone__class_Oone(X3941)
| ~ class_Fields_Ofield__inverse__zero(X3941) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__eq__1__iff])])]) ).
fof(i_0_2237,plain,
! [X5314,X5315] :
( ( c_Groups_Osgn__class_Osgn(X5315,X5314) != c_Groups_Ozero__class_Ozero(X5315)
| X5314 = c_Groups_Ozero__class_Ozero(X5315)
| ~ class_Rings_Olinordered__idom(X5315) )
& ( X5314 != c_Groups_Ozero__class_Ozero(X5315)
| c_Groups_Osgn__class_Osgn(X5315,X5314) = c_Groups_Ozero__class_Ozero(X5315)
| ~ class_Rings_Olinordered__idom(X5315) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).
fof(i_0_2238,plain,
! [X5311,X5312] :
( ( c_Groups_Osgn__class_Osgn(X5312,X5311) != c_Groups_Ozero__class_Ozero(X5312)
| X5311 = c_Groups_Ozero__class_Ozero(X5312)
| ~ class_RealVector_Oreal__normed__vector(X5312) )
& ( X5311 != c_Groups_Ozero__class_Ozero(X5312)
| c_Groups_Osgn__class_Osgn(X5312,X5311) = c_Groups_Ozero__class_Ozero(X5312)
| ~ class_RealVector_Oreal__normed__vector(X5312) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff])])]) ).
fof(i_0_2239,plain,
! [X4429,X4430] :
( ( c_Groups_Oabs__class_Oabs(X4430,X4429) != c_Groups_Ozero__class_Ozero(X4430)
| X4429 = c_Groups_Ozero__class_Ozero(X4430)
| ~ class_Groups_Oordered__ab__group__add__abs(X4430) )
& ( X4429 != c_Groups_Ozero__class_Ozero(X4430)
| c_Groups_Oabs__class_Oabs(X4430,X4429) = c_Groups_Ozero__class_Ozero(X4430)
| ~ class_Groups_Oordered__ab__group__add__abs(X4430) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).
fof(i_0_2240,plain,
! [X3370,X3371] :
( ~ class_Rings_Odivision__ring(X3371)
| X3370 = c_Groups_Ozero__class_Ozero(X3371)
| c_Rings_Oinverse__class_Oinverse(X3371,X3370) != c_Groups_Ozero__class_Ozero(X3371) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__imp__inverse__nonzero])]) ).
fof(i_0_2241,plain,
! [X3366,X3367] :
( ~ class_Rings_Odivision__ring(X3367)
| c_Rings_Oinverse__class_Oinverse(X3367,X3366) != c_Groups_Ozero__class_Ozero(X3367)
| X3366 = c_Groups_Ozero__class_Ozero(X3367) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero__imp__zero])]) ).
fof(i_0_2242,plain,
! [X3372,X3373] :
( ( c_Rings_Oinverse__class_Oinverse(X3373,X3372) != c_Groups_Ozero__class_Ozero(X3373)
| X3372 = c_Groups_Ozero__class_Ozero(X3373)
| ~ class_Rings_Odivision__ring__inverse__zero(X3373) )
& ( X3372 != c_Groups_Ozero__class_Ozero(X3373)
| c_Rings_Oinverse__class_Oinverse(X3373,X3372) = c_Groups_Ozero__class_Ozero(X3373)
| ~ class_Rings_Odivision__ring__inverse__zero(X3373) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__nonzero__iff__nonzero])])]) ).
fof(i_0_2243,plain,
! [X4383,X4384] :
( ( c_Groups_Ouminus__class_Ouminus(X4384,X4383) != c_Groups_Ozero__class_Ozero(X4384)
| X4383 = c_Groups_Ozero__class_Ozero(X4384)
| ~ class_Groups_Ogroup__add(X4384) )
& ( X4383 != c_Groups_Ozero__class_Ozero(X4384)
| c_Groups_Ouminus__class_Ouminus(X4384,X4383) = c_Groups_Ozero__class_Ozero(X4384)
| ~ class_Groups_Ogroup__add(X4384) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).
fof(i_0_2244,plain,
! [X2943,X2944] :
( ( c_RealVector_Oof__real(X2944,X2943) != c_Groups_Ozero__class_Ozero(X2944)
| X2943 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X2944) )
& ( X2943 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X2944,X2943) = c_Groups_Ozero__class_Ozero(X2944)
| ~ class_RealVector_Oreal__algebra__1(X2944) ) ),
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,
! [X2938,X2939] :
( ( c_RealVector_Onorm__class_Onorm(X2939,X2938) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2938 = c_Groups_Ozero__class_Ozero(X2939)
| ~ class_RealVector_Oreal__normed__vector(X2939) )
& ( X2938 != c_Groups_Ozero__class_Ozero(X2939)
| c_RealVector_Onorm__class_Onorm(X2939,X2938) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X2939) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__eq__zero])])]) ).
fof(i_0_2246,plain,
! [X5431,X5432] :
( ~ class_Groups_Ouminus(X5432)
| class_Groups_Ouminus(tc_fun(X5431,X5432)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).
fof(i_0_2247,plain,
! [X5433,X5434] :
( ~ class_Groups_Ominus(X5434)
| class_Groups_Ominus(tc_fun(X5433,X5434)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).
fof(i_0_2248,plain,
! [X5423,X5424] :
( ~ class_Lattices_Oboolean__algebra(X5424)
| class_Lattices_Oboolean__algebra(tc_fun(X5423,X5424)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).
fof(i_0_2249,plain,
! [X5427,X5428] :
( ~ class_Orderings_Oorder(X5428)
| class_Orderings_Oorder(tc_fun(X5427,X5428)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).
fof(i_0_2250,plain,
! [X5429,X5430] :
( ~ class_Orderings_Oord(X5430)
| class_Orderings_Oord(tc_fun(X5429,X5430)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).
fof(i_0_2251,plain,
! [X5425,X5426] :
( ~ class_Orderings_Opreorder(X5426)
| class_Orderings_Opreorder(tc_fun(X5425,X5426)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).
fof(i_0_2252,plain,
! [X4860] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X4860)) = X4860,
inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).
fof(i_0_2253,plain,
! [X4385,X4386] :
( ( c_Groups_Ouminus__class_Ouminus(X4386,X4385) != X4385
| X4385 = c_Groups_Ozero__class_Ozero(X4386)
| ~ class_Groups_Olinordered__ab__group__add(X4386) )
& ( X4385 != c_Groups_Ozero__class_Ozero(X4386)
| c_Groups_Ouminus__class_Ouminus(X4386,X4385) = X4385
| ~ class_Groups_Olinordered__ab__group__add(X4386) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).
fof(i_0_2254,plain,
! [X4381,X4382] :
( ( X4381 != c_Groups_Ouminus__class_Ouminus(X4382,X4381)
| X4381 = c_Groups_Ozero__class_Ozero(X4382)
| ~ class_Groups_Olinordered__ab__group__add(X4382) )
& ( X4381 != c_Groups_Ozero__class_Ozero(X4382)
| X4381 = c_Groups_Ouminus__class_Ouminus(X4382,X4381)
| ~ class_Groups_Olinordered__ab__group__add(X4382) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).
fof(i_0_2255,plain,
! [X2945] :
( ~ class_RealVector_Oreal__algebra__1(X2945)
| ~ class_RealVector_Oreal__normed__vector(X2945)
| c_RealVector_Oof__real(X2945,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X2945) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real_Ozero])]) ).
fof(i_0_2256,plain,
! [X5327] :
( ~ class_RealVector_Oreal__normed__algebra__1(X5327)
| c_Groups_Osgn__class_Osgn(X5327,c_Groups_Oone__class_Oone(X5327)) = c_Groups_Oone__class_Oone(X5327) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__one])]) ).
fof(i_0_2257,plain,
! [X5322] :
( ~ class_Groups_Osgn__if(X5322)
| c_Groups_Osgn__class_Osgn(X5322,c_Groups_Ozero__class_Ozero(X5322)) = c_Groups_Ozero__class_Ozero(X5322) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).
fof(i_0_2258,plain,
! [X5313] :
( ~ class_RealVector_Oreal__normed__vector(X5313)
| c_Groups_Osgn__class_Osgn(X5313,c_Groups_Ozero__class_Ozero(X5313)) = c_Groups_Ozero__class_Ozero(X5313) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__zero])]) ).
fof(i_0_2259,plain,
! [X3709] :
( ~ class_Rings_Olinordered__idom(X3709)
| c_Groups_Oabs__class_Oabs(X3709,c_Groups_Oone__class_Oone(X3709)) = c_Groups_Oone__class_Oone(X3709) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).
fof(i_0_2260,plain,
! [X4431] :
( ~ class_Groups_Oordered__ab__group__add__abs(X4431)
| c_Groups_Oabs__class_Oabs(X4431,c_Groups_Ozero__class_Ozero(X4431)) = c_Groups_Ozero__class_Ozero(X4431) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).
fof(i_0_2261,plain,
! [X3375] :
( ~ class_Rings_Odivision__ring(X3375)
| c_Rings_Oinverse__class_Oinverse(X3375,c_Groups_Oone__class_Oone(X3375)) = c_Groups_Oone__class_Oone(X3375) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__1])]) ).
fof(i_0_2262,plain,
! [X3936] :
( ~ class_Fields_Ofield__inverse__zero(X3936)
| c_Rings_Oinverse__class_Oinverse(X3936,c_Groups_Ozero__class_Ozero(X3936)) = c_Groups_Ozero__class_Ozero(X3936) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__inverse__zero])]) ).
fof(i_0_2263,plain,
! [X3374] :
( ~ class_Rings_Odivision__ring__inverse__zero(X3374)
| c_Rings_Oinverse__class_Oinverse(X3374,c_Groups_Ozero__class_Ozero(X3374)) = c_Groups_Ozero__class_Ozero(X3374) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inverse__zero])]) ).
fof(i_0_2264,plain,
! [X4378] :
( ~ class_Groups_Ogroup__add(X4378)
| c_Groups_Ouminus__class_Ouminus(X4378,c_Groups_Ozero__class_Ozero(X4378)) = c_Groups_Ozero__class_Ozero(X4378) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).
fof(i_0_2265,plain,
! [X2959] :
( ~ class_RealVector_Oreal__normed__algebra__1(X2959)
| c_RealVector_Onorm__class_Onorm(X2959,c_Groups_Oone__class_Oone(X2959)) = 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,
! [X2937] :
( ~ class_RealVector_Oreal__normed__vector(X2937)
| c_RealVector_Onorm__class_Onorm(X2937,c_Groups_Ozero__class_Ozero(X2937)) = 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,
! [X2966] :
( ~ class_RealVector_Oreal__algebra__1(X2966)
| c_RealVector_Oof__real(X2966,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(X2966) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__1])]) ).
fof(i_0_2268,plain,
! [X2946] :
( ~ class_RealVector_Oreal__algebra__1(X2946)
| c_RealVector_Oof__real(X2946,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(X2946) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__real__0])]) ).
fof(i_0_2269,plain,
! [X5215] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X5215)) = X5215,
inference(variable_rename,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(i_0_2270,plain,
! [X5214] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X5214)) = X5214,
inference(variable_rename,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(i_0_2271,plain,
! [X5192] :
( ( c_RealDef_Oreal(tc_Nat_Onat,X5192) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X5192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( X5192 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,X5192) = 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,
! [X3703] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X3703) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3703),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(i_0_2273,plain,
! [X3148] :
( ~ class_Rings_Ozero__neq__one(X3148)
| c_Groups_Ozero__class_Ozero(X3148) != c_Groups_Oone__class_Oone(X3148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).
fof(i_0_2274,plain,
! [X3147] :
( ~ class_Rings_Ozero__neq__one(X3147)
| c_Groups_Oone__class_Oone(X3147) != c_Groups_Ozero__class_Ozero(X3147) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).
fof(i_0_2275,plain,
! [X5422] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5422)
| class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X5422)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add])]) ).
fof(i_0_2276,plain,
! [X5494] :
( ~ class_Rings_Ocomm__semiring__1(X5494)
| class_Rings_Odvd(tc_Polynomial_Opoly(X5494)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd])]) ).
fof(i_0_2277,plain,
! [X5485] :
( ~ class_Rings_Olinordered__idom(X5485)
| class_Groups_Osgn__if(tc_Polynomial_Opoly(X5485)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if])]) ).
fof(i_0_2278,plain,
! [X5484] :
( ~ class_Groups_Oab__group__add(X5484)
| class_Groups_Ouminus(tc_Polynomial_Opoly(X5484)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus])]) ).
fof(i_0_2279,plain,
! [X5488] :
( ~ class_Groups_Oab__group__add(X5488)
| class_Groups_Ominus(tc_Polynomial_Opoly(X5488)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus])]) ).
fof(i_0_2280,plain,
! [X5480] :
( ~ class_Rings_Olinordered__idom(X5480)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X5480)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder])]) ).
fof(i_0_2281,plain,
! [X5472] :
( ~ class_Rings_Olinordered__idom(X5472)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X5472)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder])]) ).
fof(i_0_2282,plain,
! [X5483] :
( ~ class_Rings_Olinordered__idom(X5483)
| class_Orderings_Oord(tc_Polynomial_Opoly(X5483)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord])]) ).
fof(i_0_2283,plain,
! [X5471] :
( ~ class_Rings_Olinordered__idom(X5471)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X5471)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder])]) ).
fof(i_0_2284,plain,
! [X5435] :
( ~ class_Rings_Oidom(X5435)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X5435)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct])]) ).
fof(i_0_2285,plain,
! [X5486] :
( ~ class_Rings_Olinordered__idom(X5486)
| class_Groups_Oabs__if(tc_Polynomial_Opoly(X5486)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if])]) ).
fof(i_0_2286,plain,
! [X5443] :
( ~ class_Rings_Olinordered__idom(X5443)
| class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X5443)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add])]) ).
fof(i_0_2287,plain,
! [X5452] :
( ~ class_Rings_Olinordered__idom(X5452)
| class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X5452)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add])]) ).
fof(i_0_2288,plain,
! [X5436] :
( ~ class_Rings_Olinordered__idom(X5436)
| class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X5436)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add])]) ).
fof(i_0_2289,plain,
! [X5441] :
( ~ class_Rings_Olinordered__idom(X5441)
| class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X5441)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add])]) ).
fof(i_0_2290,plain,
! [X5437] :
( ~ class_Rings_Olinordered__idom(X5437)
| class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X5437)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le])]) ).
fof(i_0_2291,plain,
! [X5444] :
( ~ class_Rings_Olinordered__idom(X5444)
| class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X5444)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add])]) ).
fof(i_0_2292,plain,
! [X5475] :
( ~ class_Groups_Ocomm__monoid__add(X5475)
| class_Groups_Omonoid__add(tc_Polynomial_Opoly(X5475)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add])]) ).
fof(i_0_2293,plain,
! [X5493] :
( ~ class_Rings_Ocomm__semiring__1(X5493)
| class_Groups_Oone(tc_Polynomial_Opoly(X5493)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone])]) ).
fof(i_0_2294,plain,
! [X5458] :
( ~ class_Groups_Ocomm__monoid__add(X5458)
| class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X5458)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add])]) ).
fof(i_0_2295,plain,
! [X5445] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5445)
| class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X5445)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add])]) ).
fof(i_0_2296,plain,
! [X5453] :
( ~ class_Groups_Ocancel__comm__monoid__add(X5453)
| class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X5453)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add])]) ).
fof(i_0_2297,plain,
! [X5456] :
( ~ class_Rings_Ocomm__semiring__0(X5456)
| class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X5456)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult])]) ).
fof(i_0_2298,plain,
! [X5442] :
( ~ class_Rings_Olinordered__idom(X5442)
| class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X5442)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs])]) ).
fof(i_0_2299,plain,
! [X5474] :
( ~ class_Rings_Ocomm__ring__1(X5474)
| class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X5474)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1])]) ).
fof(i_0_2300,plain,
! [X5479] :
( ~ class_Rings_Ocomm__ring(X5479)
| class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X5479)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring])]) ).
fof(i_0_2301,plain,
! [X5481] :
( ~ class_Rings_Olinordered__idom(X5481)
| class_Int_Oring__char__0(tc_Polynomial_Opoly(X5481)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0])]) ).
fof(i_0_2302,plain,
! [X5465] :
( ~ class_Rings_Ocomm__semiring__1(X5465)
| class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X5465)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1])]) ).
fof(i_0_2303,plain,
! [X5462] :
( ~ class_Groups_Ocomm__monoid__add(X5462)
| class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X5462)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add])]) ).
fof(i_0_2304,plain,
! [X5466] :
( ~ class_Rings_Ocomm__semiring__0(X5466)
| class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X5466)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0])]) ).
fof(i_0_2305,plain,
! [X5468] :
( ~ class_Groups_Oab__group__add(X5468)
| class_Groups_Oab__group__add(tc_Polynomial_Opoly(X5468)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add])]) ).
fof(i_0_2306,plain,
! [X5460] :
( ~ class_Rings_Olinordered__idom(X5460)
| class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X5460)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs])]) ).
fof(i_0_2307,plain,
! [X5490] :
( ~ class_Groups_Ozero(X5490)
| class_Groups_Ozero(tc_Polynomial_Opoly(X5490)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero])]) ).
fof(i_0_2308,plain,
! [X5438] :
( ~ class_Rings_Olinordered__idom(X5438)
| class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X5438)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict])]) ).
fof(i_0_2309,plain,
! [X5450] :
( ~ class_Rings_Olinordered__idom(X5450)
| class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X5450)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring])]) ).
fof(i_0_2310,plain,
! [X5459] :
( ~ class_Rings_Olinordered__idom(X5459)
| class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X5459)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring])]) ).
fof(i_0_2311,plain,
! [X5470] :
( ~ class_Rings_Olinordered__idom(X5470)
| class_Rings_Oordered__ring(tc_Polynomial_Opoly(X5470)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring])]) ).
fof(i_0_2312,plain,
! [X5447] :
( ~ class_Rings_Olinordered__idom(X5447)
| class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X5447)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring])]) ).
fof(i_0_2313,plain,
! [X5448] :
( ~ class_Rings_Olinordered__idom(X5448)
| class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X5448)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict])]) ).
fof(i_0_2314,plain,
! [X5463] :
( ~ class_Rings_Olinordered__idom(X5463)
| class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X5463)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring])]) ).
fof(i_0_2315,plain,
! [X5449] :
( ~ class_Rings_Oidom(X5449)
| class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X5449)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors])]) ).
fof(i_0_2316,plain,
! [X5439] :
( ~ class_Rings_Olinordered__idom(X5439)
| class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X5439)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict])]) ).
fof(i_0_2317,plain,
! [X5487] :
( ~ class_Rings_Ocomm__ring__1(X5487)
| class_Rings_Oring__1(tc_Polynomial_Opoly(X5487)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1])]) ).
fof(i_0_2318,plain,
! [X5451] :
( ~ class_Rings_Olinordered__idom(X5451)
| class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X5451)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1])]) ).
fof(i_0_2319,plain,
! [X5482] :
( ~ class_Rings_Ocomm__semiring__0(X5482)
| class_Rings_Osemiring(tc_Polynomial_Opoly(X5482)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring])]) ).
fof(i_0_2320,plain,
! [X5467] :
( ~ class_Rings_Ocomm__semiring__0(X5467)
| class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X5467)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring])]) ).
fof(i_0_2321,plain,
! [X5492] :
( ~ class_Rings_Oidom(X5492)
| class_Rings_Oidom(tc_Polynomial_Opoly(X5492)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom])]) ).
fof(i_0_2322,plain,
! [X5491] :
( ~ class_Rings_Ocomm__ring(X5491)
| class_Rings_Oring(tc_Polynomial_Opoly(X5491)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring])]) ).
fof(i_0_2323,plain,
! [X5477] :
( ~ class_Groups_Oab__group__add(X5477)
| class_Groups_Ogroup__add(tc_Polynomial_Opoly(X5477)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add])]) ).
fof(i_0_2324,plain,
! [X5454] :
( ~ class_Rings_Olinordered__idom(X5454)
| class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X5454)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring])]) ).
fof(i_0_2325,plain,
! [X5440] :
( ~ class_Rings_Olinordered__idom(X5440)
| class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X5440)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict])]) ).
fof(i_0_2326,plain,
! [X5464] :
( ~ class_Rings_Olinordered__idom(X5464)
| class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X5464)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom])]) ).
fof(i_0_2327,plain,
! [X5476] :
( ~ class_Rings_Ocomm__semiring__0(X5476)
| class_Rings_Osemiring__0(tc_Polynomial_Opoly(X5476)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0])]) ).
fof(i_0_2328,plain,
! [X5457] :
( ~ class_Rings_Ocomm__semiring__1(X5457)
| class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X5457)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult])]) ).
fof(i_0_2329,plain,
! [X5469] :
( ~ class_Rings_Ocomm__semiring__1(X5469)
| class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X5469)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one])]) ).
fof(i_0_2330,plain,
! [X5461] :
( ~ class_Rings_Oidom(X5461)
| class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X5461)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors])]) ).
fof(i_0_2331,plain,
! [X5478] :
( ~ class_Rings_Ocomm__semiring__0(X5478)
| class_Rings_Omult__zero(tc_Polynomial_Opoly(X5478)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero])]) ).
fof(i_0_2332,plain,
! [X5446] :
( ~ class_Rings_Oidom(X5446)
| class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X5446)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors])]) ).
fof(i_0_2333,plain,
! [X5489] :
( ~ class_Rings_Ocomm__semiring__1(X5489)
| class_Power_Opower(tc_Polynomial_Opoly(X5489)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower])]) ).
fof(i_0_2334,plain,
! [X5473] :
( ~ class_Rings_Ocomm__semiring__1(X5473)
| class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X5473)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult])]) ).
fof(i_0_2335,plain,
! [X5455] :
( ~ class_Rings_Olinordered__idom(X5455)
| class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X5455)) ),
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,hypothesis,
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____)))) = 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_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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)],[conj_0]),
[final] ).
cnf(i_0_2343,plain,
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____)))) = 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)))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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_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_A_061t_A_094_Ak_A_K_A_It_A_K_A_Icmod_Aw_A_094_A_Ik_A_L_A1_J_A_K_Acmod_A_Ipoly_As_A_Icomplex__of__real_At_A_K_Aw_J_J_J_J_096]),
[final] ).
cnf(i_0_2344,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(split_conjunct,[status(thm)],[i_0_1332]),
[final] ).
cnf(i_0_2345,plain,
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)],[fact_th30]),
[final] ).
cnf(i_0_2346,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_1333]),
[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,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_1334]),
[final] ).
cnf(i_0_2348,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_1335]),
[final] ).
cnf(i_0_2349,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_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____)),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_1334]),
[final] ).
cnf(i_0_2351,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_1337]),
[final] ).
cnf(i_0_2352,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_1338]),
[final] ).
cnf(i_0_2353,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____)),esk15_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_1339]),
[final] ).
cnf(i_0_2354,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_2355,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_1340]),
[final] ).
cnf(i_0_2356,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_2357,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_1341]),
[final] ).
cnf(i_0_2358,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_2359,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk9_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_1342]),
[final] ).
cnf(i_0_2360,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_2361,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_1343]),
[final] ).
cnf(i_0_2362,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_1344]),
[final] ).
cnf(i_0_2363,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____)),esk16_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____)),esk17_0),
inference(split_conjunct,[status(thm)],[i_0_1345]),
[final] ).
cnf(i_0_2364,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_1346]),
[final] ).
cnf(i_0_2365,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_1347]),
[final] ).
cnf(i_0_2366,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_1348]),
[final] ).
cnf(i_0_2367,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_1349]),
[final] ).
cnf(i_0_2368,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_1350]),
[final] ).
cnf(i_0_2369,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_1351]),
[final] ).
cnf(i_0_2370,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_1352]),
[final] ).
cnf(i_0_2371,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_1353]),
[final] ).
cnf(i_0_2372,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_1354]),
[final] ).
cnf(i_0_2373,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_1355]),
[final] ).
cnf(i_0_2374,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_1356]),
[final] ).
cnf(i_0_2375,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_1347]),
[final] ).
cnf(i_0_2376,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_1348]),
[final] ).
cnf(i_0_2377,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_1349]),
[final] ).
cnf(i_0_2378,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_1350]),
[final] ).
cnf(i_0_2379,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_1351]),
[final] ).
cnf(i_0_2380,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_1352]),
[final] ).
cnf(i_0_2381,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_1353]),
[final] ).
cnf(i_0_2382,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_1354]),
[final] ).
cnf(i_0_2383,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_1357]),
[final] ).
cnf(i_0_2384,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),esk19_2(X2,X1)),X2)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[i_0_1358]),
[final] ).
cnf(i_0_2385,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_1359]),
[final] ).
cnf(i_0_2386,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)),esk35_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_1360]),
[final] ).
cnf(i_0_2387,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_1361]),
[final] ).
cnf(i_0_2388,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_1362]),
[final] ).
cnf(i_0_2389,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_1363]),
[final] ).
cnf(i_0_2390,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_1364]),
[final] ).
cnf(i_0_2391,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))))),esk18_0) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1365]),
[final] ).
cnf(i_0_2392,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_1366]),
[final] ).
cnf(i_0_2393,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_1367]),
[final] ).
cnf(i_0_2394,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_1368]),
[final] ).
cnf(i_0_2395,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_1369]),
[final] ).
cnf(i_0_2396,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_1370]),
[final] ).
cnf(i_0_2397,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))),esk28_1(X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_2398,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_1372]),
[final] ).
cnf(i_0_2399,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_1373]),
[final] ).
cnf(i_0_2400,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_1374]),
[final] ).
cnf(i_0_2401,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_1375]),
[final] ).
cnf(i_0_2402,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_1376]),
[final] ).
cnf(i_0_2403,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_1377]),
[final] ).
cnf(i_0_2404,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_1378]),
[final] ).
cnf(i_0_2405,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_1379]),
[final] ).
cnf(i_0_2406,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_1380]),
[final] ).
cnf(i_0_2407,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_1381]),
[final] ).
cnf(i_0_2408,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_1366]),
[final] ).
cnf(i_0_2409,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_1367]),
[final] ).
cnf(i_0_2410,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_1375]),
[final] ).
cnf(i_0_2411,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_1376]),
[final] ).
cnf(i_0_2412,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_1377]),
[final] ).
cnf(i_0_2413,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_1378]),
[final] ).
cnf(i_0_2414,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_1382]),
[final] ).
cnf(i_0_2415,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_2416,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_1333]),
[final] ).
cnf(i_0_2417,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_1383]),
[final] ).
cnf(i_0_2418,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_1384]),
[final] ).
cnf(i_0_2419,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_1385]),
[final] ).
cnf(i_0_2420,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_1386]),
[final] ).
cnf(i_0_2421,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_1387]),
[final] ).
cnf(i_0_2422,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_1388]),
[final] ).
cnf(i_0_2423,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_1389]),
[final] ).
cnf(i_0_2424,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_1390]),
[final] ).
cnf(i_0_2425,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_1391]),
[final] ).
cnf(i_0_2426,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_1392]),
[final] ).
cnf(i_0_2427,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_1392]),
[final] ).
cnf(i_0_2428,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_1393]),
[final] ).
cnf(i_0_2429,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_2430,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_1394]),
[final] ).
cnf(i_0_2431,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_1395]),
[final] ).
cnf(i_0_2432,hypothesis,
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____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_RealVector_Oof__real(tc_Complex_Ocomplex,v_t____)),v_w____))),v_m____),
inference(split_conjunct,[status(thm)],[conj_1]),
[final] ).
cnf(i_0_2433,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_1396]),
[final] ).
cnf(i_0_2434,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_1397]),
[final] ).
cnf(i_0_2435,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_1398]),
[final] ).
cnf(i_0_2436,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_1399]),
[final] ).
cnf(i_0_2437,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_1400]),
[final] ).
cnf(i_0_2438,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_1401]),
[final] ).
cnf(i_0_2439,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_2440,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_1402]),
[final] ).
cnf(i_0_2441,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_1403]),
[final] ).
cnf(i_0_2442,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_1387]),
[final] ).
cnf(i_0_2443,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_1404]),
[final] ).
cnf(i_0_2444,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_1405]),
[final] ).
cnf(i_0_2445,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_1406]),
[final] ).
cnf(i_0_2446,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_1407]),
[final] ).
cnf(i_0_2447,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_1408]),
[final] ).
cnf(i_0_2448,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_1409]),
[final] ).
cnf(i_0_2449,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_1410]),
[final] ).
cnf(i_0_2450,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_1411]),
[final] ).
cnf(i_0_2451,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_1412]),
[final] ).
cnf(i_0_2452,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_1413]),
[final] ).
cnf(i_0_2453,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2454,plain,
( hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk13_3(X2,X3,X1)))
| ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
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),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_1416]),
[final] ).
cnf(i_0_2456,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| hBOOL(hAPP(X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)))
| ~ hBOOL(hAPP(X1,esk14_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2457,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,esk13_3(X2,X3,X1))) ),
inference(split_conjunct,[status(thm)],[i_0_1415]),
[final] ).
cnf(i_0_2458,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_1417]),
[final] ).
cnf(i_0_2459,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_1418]),
[final] ).
cnf(i_0_2460,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_1419]),
[final] ).
cnf(i_0_2461,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_1420]),
[final] ).
cnf(i_0_2462,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_1337]),
[final] ).
cnf(i_0_2463,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_2464,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_1421]),
[final] ).
cnf(i_0_2465,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_1422]),
[final] ).
cnf(i_0_2466,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_1401]),
[final] ).
cnf(i_0_2467,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_1401]),
[final] ).
cnf(i_0_2468,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_1423]),
[final] ).
cnf(i_0_2469,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_1424]),
[final] ).
cnf(i_0_2470,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_1425]),
[final] ).
cnf(i_0_2471,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_1426]),
[final] ).
cnf(i_0_2472,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_1427]),
[final] ).
cnf(i_0_2473,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_1428]),
[final] ).
cnf(i_0_2474,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_1429]),
[final] ).
cnf(i_0_2475,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_1430]),
[final] ).
cnf(i_0_2476,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_1431]),
[final] ).
cnf(i_0_2477,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_1387]),
[final] ).
cnf(i_0_2478,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_1432]),
[final] ).
cnf(i_0_2479,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_1433]),
[final] ).
cnf(i_0_2480,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_1434]),
[final] ).
cnf(i_0_2481,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_1392]),
[final] ).
cnf(i_0_2482,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_1390]),
[final] ).
cnf(i_0_2483,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_1390]),
[final] ).
cnf(i_0_2484,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_1435]),
[final] ).
cnf(i_0_2485,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_1436]),
[final] ).
cnf(i_0_2486,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_1437]),
[final] ).
cnf(i_0_2487,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_1438]),
[final] ).
cnf(i_0_2488,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_1439]),
[final] ).
cnf(i_0_2489,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_1440]),
[final] ).
cnf(i_0_2490,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_1441]),
[final] ).
cnf(i_0_2491,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_1442]),
[final] ).
cnf(i_0_2492,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_1443]),
[final] ).
cnf(i_0_2493,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_1444]),
[final] ).
cnf(i_0_2494,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_2495,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_1446]),
[final] ).
cnf(i_0_2496,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_1447]),
[final] ).
cnf(i_0_2497,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_1448]),
[final] ).
cnf(i_0_2498,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_1449]),
[final] ).
cnf(i_0_2499,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_1450]),
[final] ).
cnf(i_0_2500,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_1451]),
[final] ).
cnf(i_0_2501,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_1452]),
[final] ).
cnf(i_0_2502,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_1453]),
[final] ).
cnf(i_0_2503,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_1454]),
[final] ).
cnf(i_0_2504,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_1455]),
[final] ).
cnf(i_0_2505,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_1456]),
[final] ).
cnf(i_0_2506,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_1457]),
[final] ).
cnf(i_0_2507,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_1458]),
[final] ).
cnf(i_0_2508,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_1459]),
[final] ).
cnf(i_0_2509,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_1460]),
[final] ).
cnf(i_0_2510,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_1461]),
[final] ).
cnf(i_0_2511,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_1462]),
[final] ).
cnf(i_0_2512,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_1463]),
[final] ).
cnf(i_0_2513,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_1464]),
[final] ).
cnf(i_0_2514,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)),esk29_2(X3,X1)))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_2515,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_1466]),
[final] ).
cnf(i_0_2516,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_1467]),
[final] ).
cnf(i_0_2517,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_1468]),
[final] ).
cnf(i_0_2518,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_1469]),
[final] ).
cnf(i_0_2519,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_1470]),
[final] ).
cnf(i_0_2520,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_1471]),
[final] ).
cnf(i_0_2521,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_1472]),
[final] ).
cnf(i_0_2522,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_1473]),
[final] ).
cnf(i_0_2523,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_1474]),
[final] ).
cnf(i_0_2524,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_1464]),
[final] ).
cnf(i_0_2525,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_1463]),
[final] ).
cnf(i_0_2526,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_1463]),
[final] ).
cnf(i_0_2527,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_1464]),
[final] ).
cnf(i_0_2528,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_1400]),
[final] ).
cnf(i_0_2529,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_1399]),
[final] ).
cnf(i_0_2530,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_1464]),
[final] ).
cnf(i_0_2531,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_1463]),
[final] ).
cnf(i_0_2532,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_1475]),
[final] ).
cnf(i_0_2533,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_1476]),
[final] ).
cnf(i_0_2534,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_1477]),
[final] ).
cnf(i_0_2535,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_1423]),
[final] ).
cnf(i_0_2536,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_1424]),
[final] ).
cnf(i_0_2537,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_1478]),
[final] ).
cnf(i_0_2538,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_1479]),
[final] ).
cnf(i_0_2539,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_1480]),
[final] ).
cnf(i_0_2540,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_1481]),
[final] ).
cnf(i_0_2541,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_1482]),
[final] ).
cnf(i_0_2542,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_1483]),
[final] ).
cnf(i_0_2543,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_1484]),
[final] ).
cnf(i_0_2544,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_1485]),
[final] ).
cnf(i_0_2545,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_1486]),
[final] ).
cnf(i_0_2546,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_1487]),
[final] ).
cnf(i_0_2547,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_1488]),
[final] ).
cnf(i_0_2548,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_1489]),
[final] ).
cnf(i_0_2549,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_1490]),
[final] ).
cnf(i_0_2550,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_1491]),
[final] ).
cnf(i_0_2551,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_1492]),
[final] ).
cnf(i_0_2552,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_1493]),
[final] ).
cnf(i_0_2553,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_1494]),
[final] ).
cnf(i_0_2554,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_1495]),
[final] ).
cnf(i_0_2555,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_1496]),
[final] ).
cnf(i_0_2556,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_1497]),
[final] ).
cnf(i_0_2557,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_1498]),
[final] ).
cnf(i_0_2558,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_1414]),
[final] ).
cnf(i_0_2559,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_1415]),
[final] ).
cnf(i_0_2560,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_1414]),
[final] ).
cnf(i_0_2561,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_1415]),
[final] ).
cnf(i_0_2562,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_1499]),
[final] ).
cnf(i_0_2563,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_1499]),
[final] ).
cnf(i_0_2564,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_1500]),
[final] ).
cnf(i_0_2565,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_1501]),
[final] ).
cnf(i_0_2566,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_1502]),
[final] ).
cnf(i_0_2567,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_1503]),
[final] ).
cnf(i_0_2568,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_1504]),
[final] ).
cnf(i_0_2569,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_1505]),
[final] ).
cnf(i_0_2570,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_1506]),
[final] ).
cnf(i_0_2571,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_1507]),
[final] ).
cnf(i_0_2572,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_1508]),
[final] ).
cnf(i_0_2573,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_1509]),
[final] ).
cnf(i_0_2574,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_1510]),
[final] ).
cnf(i_0_2575,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_1511]),
[final] ).
cnf(i_0_2576,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_1512]),
[final] ).
cnf(i_0_2577,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_1513]),
[final] ).
cnf(i_0_2578,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_1514]),
[final] ).
cnf(i_0_2579,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_2580,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),esk7_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_2581,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_2582,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_1419]),
[final] ).
cnf(i_0_2583,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_2584,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_2585,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_2586,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_2587,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_2588,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_2589,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)))
| ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2590,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_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_1415]),
[final] ).
cnf(i_0_2591,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_2592,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_2593,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_2594,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_2595,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_2596,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_2597,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_2598,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk14_3(X2,X1,X3))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| hBOOL(hAPP(X3,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2))) ),
inference(split_conjunct,[status(thm)],[i_0_1414]),
[final] ).
cnf(i_0_2599,plain,
( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,esk13_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_1415]),
[final] ).
cnf(i_0_2600,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_2601,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_2602,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_2603,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_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))
| ~ 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_2605,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_2606,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_1440]),
[final] ).
cnf(i_0_2607,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_2608,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_1463]),
[final] ).
cnf(i_0_2609,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_2610,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_1464]),
[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))
| ~ 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_2612,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_2613,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_2614,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_2615,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_2616,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_1448]),
[final] ).
cnf(i_0_2617,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_1463]),
[final] ).
cnf(i_0_2618,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_2619,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_1464]),
[final] ).
cnf(i_0_2620,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_2621,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_1449]),
[final] ).
cnf(i_0_2622,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_2623,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_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__eq(X1,X4,X5) ),
inference(split_conjunct,[status(thm)],[i_0_1545]),
[final] ).
cnf(i_0_2625,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_2626,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_2627,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_2628,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_1450]),
[final] ).
cnf(i_0_2629,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_2630,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_1452]),
[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,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_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,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_2633,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_2634,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_2635,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_2636,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_2637,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_2638,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_2639,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_2640,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_2641,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_2642,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_2643,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_2644,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_2645,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_2646,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_2647,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_2648,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_2649,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_2650,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_2651,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_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_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1566]),
[final] ).
cnf(i_0_2653,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_2654,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_2655,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_2656,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_2657,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_2658,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_2659,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_2660,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_2661,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Groups_Oab__semigroup__mult(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1573]),
[final] ).
cnf(i_0_2662,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1574]),
[final] ).
cnf(i_0_2663,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_2664,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_2665,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_2666,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_2667,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_2668,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_2669,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_2670,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_2671,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_2672,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_2673,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_1485]),
[final] ).
cnf(i_0_2674,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_1486]),
[final] ).
cnf(i_0_2675,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_1487]),
[final] ).
cnf(i_0_2676,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_2677,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_2678,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_2679,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_2680,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_2681,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_1488]),
[final] ).
cnf(i_0_2682,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_2683,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_1490]),
[final] ).
cnf(i_0_2684,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_2685,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_2686,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_2687,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_2688,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_2689,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_2690,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1593]),
[final] ).
cnf(i_0_2691,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3),X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1594]),
[final] ).
cnf(i_0_2692,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_2693,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_2694,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_2695,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_2696,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_2697,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_2698,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_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,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_2700,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_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),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_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),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_2703,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_2704,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_2705,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_2706,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_2707,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_2708,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_2709,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_2710,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_2711,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_2712,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_2713,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_2714,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_2715,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_2716,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_2717,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_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__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1613]),
[final] ).
cnf(i_0_2719,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_2720,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_2721,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_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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X3) ),
inference(split_conjunct,[status(thm)],[i_0_1617]),
[final] ).
cnf(i_0_2723,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_2724,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_2725,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_2726,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_2727,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_2728,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_2729,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_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))
| ~ 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_1625]),
[final] ).
cnf(i_0_2731,plain,
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),c_Groups_Ozero__class_Ozero(X1))
| ~ 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_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,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_1625]),
[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))
| ~ 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_2734,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_2735,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_2736,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_2737,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_2738,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_2739,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_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_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2741,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_2742,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_2743,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_2744,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_2745,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Oordered__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1632]),
[final] ).
cnf(i_0_2746,plain,
( c_Orderings_Oord__class_Oless__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_2747,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_2748,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_2749,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_2750,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_1507]),
[final] ).
cnf(i_0_2751,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_2752,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_1509]),
[final] ).
cnf(i_0_2753,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_2754,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_1511]),
[final] ).
cnf(i_0_2755,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_2756,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_1513]),
[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)),esk21_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_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_s____),X1)),esk2_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_2759,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_2760,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_2761,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_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,esk34_2(X2,X1)),hAPP(X2,esk33_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)),esk20_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 = 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_1671]),
[final] ).
cnf(i_0_2789,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1672]),
[final] ).
cnf(i_0_2790,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1673]),
[final] ).
cnf(i_0_2791,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,c_RealDef_Oreal(tc_Nat_Onat,X1))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1674]),
[final] ).
cnf(i_0_2792,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),c_Polynomial_Osmult(X1,X2,X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_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_Groups_Oab__semigroup__add(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_Rings_Ocomm__semiring__1(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_1483]),
[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_1484]),
[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_Rings_Odvd__class_Odvd(X1,X3,X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4) ),
inference(split_conjunct,[status(thm)],[i_0_1722]),
[final] ).
cnf(i_0_2847,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_1723]),
[final] ).
cnf(i_0_2848,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_1724]),
[final] ).
cnf(i_0_2849,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_1725]),
[final] ).
cnf(i_0_2850,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_1726]),
[final] ).
cnf(i_0_2851,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_1727]),
[final] ).
cnf(i_0_2852,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_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__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_1730]),
[final] ).
cnf(i_0_2855,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_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,X1,X3),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2857,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X2) ),
inference(split_conjunct,[status(thm)],[i_0_1732]),
[final] ).
cnf(i_0_2858,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_1733]),
[final] ).
cnf(i_0_2859,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_1734]),
[final] ).
cnf(i_0_2860,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_1735]),
[final] ).
cnf(i_0_2861,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_1736]),
[final] ).
cnf(i_0_2862,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_1737]),
[final] ).
cnf(i_0_2863,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_1737]),
[final] ).
cnf(i_0_2864,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_1738]),
[final] ).
cnf(i_0_2865,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_1739]),
[final] ).
cnf(i_0_2866,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_1740]),
[final] ).
cnf(i_0_2867,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_1741]),
[final] ).
cnf(i_0_2868,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_1742]),
[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_1743]),
[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_1744]),
[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_1484]),
[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_1483]),
[final] ).
cnf(i_0_2873,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_2874,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_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),X2),X1)) ),
inference(split_conjunct,[status(thm)],[i_0_1701]),
[final] ).
cnf(i_0_2876,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_1745]),
[final] ).
cnf(i_0_2877,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_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_1747]),
[final] ).
cnf(i_0_2879,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_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_1749]),
[final] ).
cnf(i_0_2881,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_1750]),
[final] ).
cnf(i_0_2882,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_2883,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_2884,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_2885,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_2886,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_1751]),
[final] ).
cnf(i_0_2887,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_1752]),
[final] ).
cnf(i_0_2888,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_1737]),
[final] ).
cnf(i_0_2889,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_1753]),
[final] ).
cnf(i_0_2890,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_1754]),
[final] ).
cnf(i_0_2891,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),esk10_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_1755]),
[final] ).
cnf(i_0_2892,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,c_Polynomial_Osmult(X1,X4,X3))
| ~ class_Rings_Ocomm__semiring__1(X1)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(X1),X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_1756]),
[final] ).
cnf(i_0_2893,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_2894,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_2895,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_2896,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_2897,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_2898,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_1757]),
[final] ).
cnf(i_0_2899,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_1758]),
[final] ).
cnf(i_0_2900,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_1759]),
[final] ).
cnf(i_0_2901,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_1760]),
[final] ).
cnf(i_0_2902,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_1761]),
[final] ).
cnf(i_0_2903,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_1762]),
[final] ).
cnf(i_0_2904,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_1763]),
[final] ).
cnf(i_0_2905,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_1764]),
[final] ).
cnf(i_0_2906,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(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_1765]),
[final] ).
cnf(i_0_2907,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_1766]),
[final] ).
cnf(i_0_2908,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_1767]),
[final] ).
cnf(i_0_2909,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_1768]),
[final] ).
cnf(i_0_2910,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_1769]),
[final] ).
cnf(i_0_2911,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_1742]),
[final] ).
cnf(i_0_2912,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_2913,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_2914,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_1770]),
[final] ).
cnf(i_0_2915,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_1771]),
[final] ).
cnf(i_0_2916,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_1760]),
[final] ).
cnf(i_0_2917,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_1758]),
[final] ).
cnf(i_0_2918,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_1772]),
[final] ).
cnf(i_0_2919,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_1773]),
[final] ).
cnf(i_0_2920,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_1774]),
[final] ).
cnf(i_0_2921,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_1775]),
[final] ).
cnf(i_0_2922,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_1776]),
[final] ).
cnf(i_0_2923,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_1777]),
[final] ).
cnf(i_0_2924,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_1778]),
[final] ).
cnf(i_0_2925,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_1779]),
[final] ).
cnf(i_0_2926,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_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_1360]),
[final] ).
cnf(i_0_2927,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_1780]),
[final] ).
cnf(i_0_2928,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_1781]),
[final] ).
cnf(i_0_2929,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_2930,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_2931,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_2932,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_1782]),
[final] ).
cnf(i_0_2933,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_2934,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_1783]),
[final] ).
cnf(i_0_2935,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_2936,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_2937,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_2938,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_1784]),
[final] ).
cnf(i_0_2939,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_1785]),
[final] ).
cnf(i_0_2940,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_1723]),
[final] ).
cnf(i_0_2941,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_1724]),
[final] ).
cnf(i_0_2942,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_1725]),
[final] ).
cnf(i_0_2943,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_2944,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_1754]),
[final] ).
cnf(i_0_2945,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_1786]),
[final] ).
cnf(i_0_2946,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_1787]),
[final] ).
cnf(i_0_2947,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_1788]),
[final] ).
cnf(i_0_2948,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_2949,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_1789]),
[final] ).
cnf(i_0_2950,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_1790]),
[final] ).
cnf(i_0_2951,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_1791]),
[final] ).
cnf(i_0_2952,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_1341]),
[final] ).
cnf(i_0_2953,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_1792]),
[final] ).
cnf(i_0_2954,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_1793]),
[final] ).
cnf(i_0_2955,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_1794]),
[final] ).
cnf(i_0_2956,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_1795]),
[final] ).
cnf(i_0_2957,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_1796]),
[final] ).
cnf(i_0_2958,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_1797]),
[final] ).
cnf(i_0_2959,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_1798]),
[final] ).
cnf(i_0_2960,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_1799]),
[final] ).
cnf(i_0_2961,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_1800]),
[final] ).
cnf(i_0_2962,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_1751]),
[final] ).
cnf(i_0_2963,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_1801]),
[final] ).
cnf(i_0_2964,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_1802]),
[final] ).
cnf(i_0_2965,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_1803]),
[final] ).
cnf(i_0_2966,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_1752]),
[final] ).
cnf(i_0_2967,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_1804]),
[final] ).
cnf(i_0_2968,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_1805]),
[final] ).
cnf(i_0_2969,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_1806]),
[final] ).
cnf(i_0_2970,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_2971,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_1744]),
[final] ).
cnf(i_0_2972,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_1807]),
[final] ).
cnf(i_0_2973,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_1808]),
[final] ).
cnf(i_0_2974,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_1809]),
[final] ).
cnf(i_0_2975,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_1810]),
[final] ).
cnf(i_0_2976,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_1811]),
[final] ).
cnf(i_0_2977,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_1812]),
[final] ).
cnf(i_0_2978,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_1813]),
[final] ).
cnf(i_0_2979,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_1814]),
[final] ).
cnf(i_0_2980,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_1815]),
[final] ).
cnf(i_0_2981,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_1816]),
[final] ).
cnf(i_0_2982,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_1817]),
[final] ).
cnf(i_0_2983,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_1818]),
[final] ).
cnf(i_0_2984,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_1819]),
[final] ).
cnf(i_0_2985,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_1820]),
[final] ).
cnf(i_0_2986,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_1821]),
[final] ).
cnf(i_0_2987,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_1822]),
[final] ).
cnf(i_0_2988,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_1823]),
[final] ).
cnf(i_0_2989,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_1824]),
[final] ).
cnf(i_0_2990,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_1825]),
[final] ).
cnf(i_0_2991,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_1826]),
[final] ).
cnf(i_0_2992,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_1827]),
[final] ).
cnf(i_0_2993,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_1828]),
[final] ).
cnf(i_0_2994,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_1829]),
[final] ).
cnf(i_0_2995,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_1830]),
[final] ).
cnf(i_0_2996,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_1831]),
[final] ).
cnf(i_0_2997,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_1754]),
[final] ).
cnf(i_0_2998,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_1832]),
[final] ).
cnf(i_0_2999,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_1832]),
[final] ).
cnf(i_0_3000,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_3001,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_1833]),
[final] ).
cnf(i_0_3002,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_1834]),
[final] ).
cnf(i_0_3003,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_1835]),
[final] ).
cnf(i_0_3004,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_1836]),
[final] ).
cnf(i_0_3005,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_1837]),
[final] ).
cnf(i_0_3006,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_3007,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_1838]),
[final] ).
cnf(i_0_3008,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_1839]),
[final] ).
cnf(i_0_3009,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_1840]),
[final] ).
cnf(i_0_3010,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_1841]),
[final] ).
cnf(i_0_3011,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_1742]),
[final] ).
cnf(i_0_3012,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_3013,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_1842]),
[final] ).
cnf(i_0_3014,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_1843]),
[final] ).
cnf(i_0_3015,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_1843]),
[final] ).
cnf(i_0_3016,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_1731]),
[final] ).
cnf(i_0_3017,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_1844]),
[final] ).
cnf(i_0_3018,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_1844]),
[final] ).
cnf(i_0_3019,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_1845]),
[final] ).
cnf(i_0_3020,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_1845]),
[final] ).
cnf(i_0_3021,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_1846]),
[final] ).
cnf(i_0_3022,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_1846]),
[final] ).
cnf(i_0_3023,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_1847]),
[final] ).
cnf(i_0_3024,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_1848]),
[final] ).
cnf(i_0_3025,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_1849]),
[final] ).
cnf(i_0_3026,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_1850]),
[final] ).
cnf(i_0_3027,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_1851]),
[final] ).
cnf(i_0_3028,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_1852]),
[final] ).
cnf(i_0_3029,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_1853]),
[final] ).
cnf(i_0_3030,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_1854]),
[final] ).
cnf(i_0_3031,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_1855]),
[final] ).
cnf(i_0_3032,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_1856]),
[final] ).
cnf(i_0_3033,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_1857]),
[final] ).
cnf(i_0_3034,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_1858]),
[final] ).
cnf(i_0_3035,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_1859]),
[final] ).
cnf(i_0_3036,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_1860]),
[final] ).
cnf(i_0_3037,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_1747]),
[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_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_1749]),
[final] ).
cnf(i_0_3039,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_1861]),
[final] ).
cnf(i_0_3040,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_1862]),
[final] ).
cnf(i_0_3041,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_1863]),
[final] ).
cnf(i_0_3042,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_1864]),
[final] ).
cnf(i_0_3043,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_1865]),
[final] ).
cnf(i_0_3044,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_1747]),
[final] ).
cnf(i_0_3045,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_1866]),
[final] ).
cnf(i_0_3046,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_1749]),
[final] ).
cnf(i_0_3047,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_1867]),
[final] ).
cnf(i_0_3048,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_1868]),
[final] ).
cnf(i_0_3049,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_1869]),
[final] ).
cnf(i_0_3050,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_1870]),
[final] ).
cnf(i_0_3051,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_1871]),
[final] ).
cnf(i_0_3052,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_1823]),
[final] ).
cnf(i_0_3053,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_1872]),
[final] ).
cnf(i_0_3054,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_1873]),
[final] ).
cnf(i_0_3055,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_1824]),
[final] ).
cnf(i_0_3056,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_1825]),
[final] ).
cnf(i_0_3057,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_1874]),
[final] ).
cnf(i_0_3058,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_1875]),
[final] ).
cnf(i_0_3059,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_1750]),
[final] ).
cnf(i_0_3060,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_1876]),
[final] ).
cnf(i_0_3061,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_1877]),
[final] ).
cnf(i_0_3062,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_1878]),
[final] ).
cnf(i_0_3063,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_1879]),
[final] ).
cnf(i_0_3064,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_1880]),
[final] ).
cnf(i_0_3065,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_1881]),
[final] ).
cnf(i_0_3066,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_1882]),
[final] ).
cnf(i_0_3067,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_1883]),
[final] ).
cnf(i_0_3068,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_1884]),
[final] ).
cnf(i_0_3069,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_1885]),
[final] ).
cnf(i_0_3070,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_1764]),
[final] ).
cnf(i_0_3071,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_1858]),
[final] ).
cnf(i_0_3072,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_1765]),
[final] ).
cnf(i_0_3073,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_1859]),
[final] ).
cnf(i_0_3074,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_1764]),
[final] ).
cnf(i_0_3075,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_1863]),
[final] ).
cnf(i_0_3076,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_1865]),
[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__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1765]),
[final] ).
cnf(i_0_3078,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_1886]),
[final] ).
cnf(i_0_3079,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_1864]),
[final] ).
cnf(i_0_3080,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_1860]),
[final] ).
cnf(i_0_3081,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_1862]),
[final] ).
cnf(i_0_3082,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_1887]),
[final] ).
cnf(i_0_3083,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_1861]),
[final] ).
cnf(i_0_3084,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_1866]),
[final] ).
cnf(i_0_3085,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_1867]),
[final] ).
cnf(i_0_3086,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_1888]),
[final] ).
cnf(i_0_3087,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_1889]),
[final] ).
cnf(i_0_3088,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_1890]),
[final] ).
cnf(i_0_3089,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_1891]),
[final] ).
cnf(i_0_3090,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_1892]),
[final] ).
cnf(i_0_3091,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_1893]),
[final] ).
cnf(i_0_3092,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_3093,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_1894]),
[final] ).
cnf(i_0_3094,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_1731]),
[final] ).
cnf(i_0_3095,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_1895]),
[final] ).
cnf(i_0_3096,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_1896]),
[final] ).
cnf(i_0_3097,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_1897]),
[final] ).
cnf(i_0_3098,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_1898]),
[final] ).
cnf(i_0_3099,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_1899]),
[final] ).
cnf(i_0_3100,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_1899]),
[final] ).
cnf(i_0_3101,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_1877]),
[final] ).
cnf(i_0_3102,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_1878]),
[final] ).
cnf(i_0_3103,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_1879]),
[final] ).
cnf(i_0_3104,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_1880]),
[final] ).
cnf(i_0_3105,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_1900]),
[final] ).
cnf(i_0_3106,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_1901]),
[final] ).
cnf(i_0_3107,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_1856]),
[final] ).
cnf(i_0_3108,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_1857]),
[final] ).
cnf(i_0_3109,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_1902]),
[final] ).
cnf(i_0_3110,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_1903]),
[final] ).
cnf(i_0_3111,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_1904]),
[final] ).
cnf(i_0_3112,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_1905]),
[final] ).
cnf(i_0_3113,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_1906]),
[final] ).
cnf(i_0_3114,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_1907]),
[final] ).
cnf(i_0_3115,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_1908]),
[final] ).
cnf(i_0_3116,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_1909]),
[final] ).
cnf(i_0_3117,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_1909]),
[final] ).
cnf(i_0_3118,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_1910]),
[final] ).
cnf(i_0_3119,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_1911]),
[final] ).
cnf(i_0_3120,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_1912]),
[final] ).
cnf(i_0_3121,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_1913]),
[final] ).
cnf(i_0_3122,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_1914]),
[final] ).
cnf(i_0_3123,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_1915]),
[final] ).
cnf(i_0_3124,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_1916]),
[final] ).
cnf(i_0_3125,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_3126,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_1917]),
[final] ).
cnf(i_0_3127,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_1918]),
[final] ).
cnf(i_0_3128,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_1919]),
[final] ).
cnf(i_0_3129,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3130,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_1921]),
[final] ).
cnf(i_0_3131,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_1868]),
[final] ).
cnf(i_0_3132,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_3133,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_3134,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1924]),
[final] ).
cnf(i_0_3135,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1925]),
[final] ).
cnf(i_0_3136,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_1926]),
[final] ).
cnf(i_0_3137,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_1927]),
[final] ).
cnf(i_0_3138,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_1928]),
[final] ).
cnf(i_0_3139,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_1929]),
[final] ).
cnf(i_0_3140,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_1930]),
[final] ).
cnf(i_0_3141,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_3142,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_1893]),
[final] ).
cnf(i_0_3143,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_1892]),
[final] ).
cnf(i_0_3144,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_1896]),
[final] ).
cnf(i_0_3145,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_1895]),
[final] ).
cnf(i_0_3146,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_1931]),
[final] ).
cnf(i_0_3147,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_1750]),
[final] ).
cnf(i_0_3148,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_1932]),
[final] ).
cnf(i_0_3149,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_1933]),
[final] ).
cnf(i_0_3150,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_1934]),
[final] ).
cnf(i_0_3151,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_1935]),
[final] ).
cnf(i_0_3152,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_1936]),
[final] ).
cnf(i_0_3153,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_1937]),
[final] ).
cnf(i_0_3154,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_1938]),
[final] ).
cnf(i_0_3155,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_1939]),
[final] ).
cnf(i_0_3156,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_1939]),
[final] ).
cnf(i_0_3157,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_1940]),
[final] ).
cnf(i_0_3158,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_1941]),
[final] ).
cnf(i_0_3159,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_1942]),
[final] ).
cnf(i_0_3160,plain,
hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,esk11_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_1943]),
[final] ).
cnf(i_0_3161,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_1944]),
[final] ).
cnf(i_0_3162,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_1907]),
[final] ).
cnf(i_0_3163,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_3164,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk8_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1945]),
[final] ).
cnf(i_0_3165,plain,
( X2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk6_2(X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1946]),
[final] ).
cnf(i_0_3166,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_1947]),
[final] ).
cnf(i_0_3167,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_1948]),
[final] ).
cnf(i_0_3168,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_1949]),
[final] ).
cnf(i_0_3169,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_1950]),
[final] ).
cnf(i_0_3170,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_1951]),
[final] ).
cnf(i_0_3171,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_1952]),
[final] ).
cnf(i_0_3172,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_1931]),
[final] ).
cnf(i_0_3173,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_1953]),
[final] ).
cnf(i_0_3174,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_1954]),
[final] ).
cnf(i_0_3175,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_3176,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_1744]),
[final] ).
cnf(i_0_3177,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_1955]),
[final] ).
cnf(i_0_3178,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_1754]),
[final] ).
cnf(i_0_3179,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_1953]),
[final] ).
cnf(i_0_3180,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X1))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3181,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3182,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_1954]),
[final] ).
cnf(i_0_3183,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_1957]),
[final] ).
cnf(i_0_3184,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_1958]),
[final] ).
cnf(i_0_3185,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_3186,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_1960]),
[final] ).
cnf(i_0_3187,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_1961]),
[final] ).
cnf(i_0_3188,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_3189,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_1963]),
[final] ).
cnf(i_0_3190,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_1964]),
[final] ).
cnf(i_0_3191,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_3192,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_3193,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_3194,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_1968]),
[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_1969]),
[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_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1901]),
[final] ).
cnf(i_0_3197,plain,
( X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1970]),
[final] ).
cnf(i_0_3198,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_1971]),
[final] ).
cnf(i_0_3199,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_1804]),
[final] ).
cnf(i_0_3200,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_1972]),
[final] ).
cnf(i_0_3201,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_1939]),
[final] ).
cnf(i_0_3202,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_1973]),
[final] ).
cnf(i_0_3203,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_1974]),
[final] ).
cnf(i_0_3204,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_1975]),
[final] ).
cnf(i_0_3205,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3206,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3207,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_1976]),
[final] ).
cnf(i_0_3208,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_1868]),
[final] ).
cnf(i_0_3209,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),X1)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ),
inference(split_conjunct,[status(thm)],[i_0_1956]),
[final] ).
cnf(i_0_3210,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_1977]),
[final] ).
cnf(i_0_3211,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_1978]),
[final] ).
cnf(i_0_3212,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_1978]),
[final] ).
cnf(i_0_3213,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_1979]),
[final] ).
cnf(i_0_3214,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_1980]),
[final] ).
cnf(i_0_3215,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_1981]),
[final] ).
cnf(i_0_3216,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_1982]),
[final] ).
cnf(i_0_3217,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_1983]),
[final] ).
cnf(i_0_3218,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_1984]),
[final] ).
cnf(i_0_3219,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_1985]),
[final] ).
cnf(i_0_3220,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_1986]),
[final] ).
cnf(i_0_3221,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_1987]),
[final] ).
cnf(i_0_3222,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_1988]),
[final] ).
cnf(i_0_3223,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_1989]),
[final] ).
cnf(i_0_3224,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_1990]),
[final] ).
cnf(i_0_3225,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_1991]),
[final] ).
cnf(i_0_3226,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_1992]),
[final] ).
cnf(i_0_3227,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_3228,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_1994]),
[final] ).
cnf(i_0_3229,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_1995]),
[final] ).
cnf(i_0_3230,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_1988]),
[final] ).
cnf(i_0_3231,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_1996]),
[final] ).
cnf(i_0_3232,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_1997]),
[final] ).
cnf(i_0_3233,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_3234,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_1946]),
[final] ).
cnf(i_0_3235,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_1998]),
[final] ).
cnf(i_0_3236,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_1999]),
[final] ).
cnf(i_0_3237,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_3238,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_2001]),
[final] ).
cnf(i_0_3239,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_1989]),
[final] ).
cnf(i_0_3240,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_3241,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_3242,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_1991]),
[final] ).
cnf(i_0_3243,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_3244,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_2004]),
[final] ).
cnf(i_0_3245,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_3246,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_1994]),
[final] ).
cnf(i_0_3247,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_3248,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_2005]),
[final] ).
cnf(i_0_3249,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_1897]),
[final] ).
cnf(i_0_3250,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_2006]),
[final] ).
cnf(i_0_3251,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_2007]),
[final] ).
cnf(i_0_3252,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_2008]),
[final] ).
cnf(i_0_3253,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_2009]),
[final] ).
cnf(i_0_3254,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_2010]),
[final] ).
cnf(i_0_3255,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_2011]),
[final] ).
cnf(i_0_3256,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_2012]),
[final] ).
cnf(i_0_3257,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_3258,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_2014]),
[final] ).
cnf(i_0_3259,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_2015]),
[final] ).
cnf(i_0_3260,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_2016]),
[final] ).
cnf(i_0_3261,plain,
( X1 = X2
| hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2017]),
[final] ).
cnf(i_0_3262,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,esk33_2(X1,X2),esk34_2(X1,X2))
| c_SEQ_Odecseq(X2,X1)
| ~ class_Orderings_Oorder(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1648]),
[final] ).
cnf(i_0_3263,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_2018]),
[final] ).
cnf(i_0_3264,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_2019]),
[final] ).
cnf(i_0_3265,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_2020]),
[final] ).
cnf(i_0_3266,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_2021]),
[final] ).
cnf(i_0_3267,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_2022]),
[final] ).
cnf(i_0_3268,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_2022]),
[final] ).
cnf(i_0_3269,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_2023]),
[final] ).
cnf(i_0_3270,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_3271,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_3272,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_2025]),
[final] ).
cnf(i_0_3273,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_2026]),
[final] ).
cnf(i_0_3274,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_2027]),
[final] ).
cnf(i_0_3275,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_1970]),
[final] ).
cnf(i_0_3276,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_2028]),
[final] ).
cnf(i_0_3277,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_2029]),
[final] ).
cnf(i_0_3278,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_2030]),
[final] ).
cnf(i_0_3279,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_3280,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_3281,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_3282,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_2034]),
[final] ).
cnf(i_0_3283,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_1921]),
[final] ).
cnf(i_0_3284,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_2035]),
[final] ).
cnf(i_0_3285,plain,
( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1)
| hAPP(X1,esk4_1(X1)) != hAPP(X1,esk5_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3286,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_2037]),
[final] ).
cnf(i_0_3287,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_2038]),
[final] ).
cnf(i_0_3288,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_3289,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_2040]),
[final] ).
cnf(i_0_3290,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_2041]),
[final] ).
cnf(i_0_3291,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1920]),
[final] ).
cnf(i_0_3292,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_3293,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_2043]),
[final] ).
cnf(i_0_3294,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_1918]),
[final] ).
cnf(i_0_3295,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_2044]),
[final] ).
cnf(i_0_3296,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_2045]),
[final] ).
cnf(i_0_3297,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_2046]),
[final] ).
cnf(i_0_3298,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_2047]),
[final] ).
cnf(i_0_3299,plain,
( hAPP(X3,X4) = hAPP(X3,X5)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2036]),
[final] ).
cnf(i_0_3300,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_2028]),
[final] ).
cnf(i_0_3301,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_2048]),
[final] ).
cnf(i_0_3302,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_2049]),
[final] ).
cnf(i_0_3303,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_2050]),
[final] ).
cnf(i_0_3304,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_3305,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_2052]),
[final] ).
cnf(i_0_3306,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_2053]),
[final] ).
cnf(i_0_3307,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_2054]),
[final] ).
cnf(i_0_3308,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_3309,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_2056]),
[final] ).
cnf(i_0_3310,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_2057]),
[final] ).
cnf(i_0_3311,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_2058]),
[final] ).
cnf(i_0_3312,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_2059]),
[final] ).
cnf(i_0_3313,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_2060]),
[final] ).
cnf(i_0_3314,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_2061]),
[final] ).
cnf(i_0_3315,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_2062]),
[final] ).
cnf(i_0_3316,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_3317,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_2064]),
[final] ).
cnf(i_0_3318,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_1928]),
[final] ).
cnf(i_0_3319,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_2018]),
[final] ).
cnf(i_0_3320,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_1932]),
[final] ).
cnf(i_0_3321,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_3322,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_3323,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_3324,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_3325,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_3326,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_3327,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_3328,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_3329,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_3330,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_3331,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_3332,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_3333,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_3334,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_1975]),
[final] ).
cnf(i_0_3335,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_3336,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_3337,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_3338,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_3339,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_3340,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_1955]),
[final] ).
cnf(i_0_3341,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_3342,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_3343,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_2028]),
[final] ).
cnf(i_0_3344,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_3345,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_3346,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_1960]),
[final] ).
cnf(i_0_3347,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_1957]),
[final] ).
cnf(i_0_3348,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_1987]),
[final] ).
cnf(i_0_3349,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_2022]),
[final] ).
cnf(i_0_3350,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_2023]),
[final] ).
cnf(i_0_3351,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1969]),
[final] ).
cnf(i_0_3352,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2)
| ~ class_Orderings_Olinorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1921]),
[final] ).
cnf(i_0_3353,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2085]),
[final] ).
cnf(i_0_3354,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_3355,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[i_0_2087]),
[final] ).
cnf(i_0_3356,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3357,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2030]),
[final] ).
cnf(i_0_3358,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_3359,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_3360,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_3361,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_3362,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_3363,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_3364,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_1979]),
[final] ).
cnf(i_0_3365,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_3366,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_3367,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_3368,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_3369,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_3370,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_3371,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_3372,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_3373,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_3374,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_3375,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_3376,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_3377,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_3378,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_2106]),
[final] ).
cnf(i_0_3379,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_2107]),
[final] ).
cnf(i_0_3380,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_3381,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_3382,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_3383,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_3384,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_3385,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_3386,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_3387,plain,
( hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_pa____),esk12_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_3388,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_2029]),
[final] ).
cnf(i_0_3389,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_2019]),
[final] ).
cnf(i_0_3390,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_3391,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_2046]),
[final] ).
cnf(i_0_3392,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_2047]),
[final] ).
cnf(i_0_3393,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_3394,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_1467]),
[final] ).
cnf(i_0_3395,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk29_2(X1,X2))
| ~ class_RealVector_Oreal__normed__algebra(X2) ),
inference(split_conjunct,[status(thm)],[i_0_1465]),
[final] ).
cnf(i_0_3396,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_3397,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_3398,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_3399,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_3400,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_3401,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_3402,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_3403,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_3404,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_3405,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_3406,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1989]),
[final] ).
cnf(i_0_3407,plain,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_1990]),
[final] ).
cnf(i_0_3408,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3409,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(split_conjunct,[status(thm)],[i_0_2063]),
[final] ).
cnf(i_0_3410,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_3411,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_3412,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_3413,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_3414,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_3415,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_3416,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_3417,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_3418,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_3419,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_3420,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_3421,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_2016]),
[final] ).
cnf(i_0_3422,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_2015]),
[final] ).
cnf(i_0_3423,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_3424,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_3425,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_3426,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2139]),
[final] ).
cnf(i_0_3427,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2140]),
[final] ).
cnf(i_0_3428,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_2006]),
[final] ).
cnf(i_0_3429,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_2020]),
[final] ).
cnf(i_0_3430,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_3431,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_3432,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_3433,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_3434,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_3435,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_3436,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_2048]),
[final] ).
cnf(i_0_3437,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_2019]),
[final] ).
cnf(i_0_3438,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_3439,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_3440,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_3441,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_3442,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_3443,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_3444,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_3445,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk20_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_3446,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_3447,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_3448,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_3449,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_3450,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_3451,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_3452,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_3453,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_3454,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_3455,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_3456,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_3457,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_3458,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_2023]),
[final] ).
cnf(i_0_3459,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_3460,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_3461,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_1751]),
[final] ).
cnf(i_0_3462,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_3463,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_2050]),
[final] ).
cnf(i_0_3464,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_3465,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_2052]),
[final] ).
cnf(i_0_3466,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_1963]),
[final] ).
cnf(i_0_3467,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_3468,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_3469,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_3470,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_3471,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk28_1(X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1371]),
[final] ).
cnf(i_0_3472,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_3473,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_3474,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_3475,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_1928]),
[final] ).
cnf(i_0_3476,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_3477,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_3478,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_2165]),
[final] ).
cnf(i_0_3479,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_2166]),
[final] ).
cnf(i_0_3480,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_3481,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_3482,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_2169]),
[final] ).
cnf(i_0_3483,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_2170]),
[final] ).
cnf(i_0_3484,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_3485,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_3486,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_3487,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_3488,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_3489,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_3490,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_3491,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_3492,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_3493,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_3494,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3495,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| X3 != X2
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_1906]),
[final] ).
cnf(i_0_3496,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_3497,plain,
( c_Orderings_Oord__class_Oless__eq(X3,X1,X2)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(split_conjunct,[status(thm)],[i_0_1968]),
[final] ).
cnf(i_0_3498,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_3499,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_3500,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_3501,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_3502,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_3503,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_3504,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_3505,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_3506,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_3507,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_3508,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_3509,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_3510,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_3511,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_3512,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_3513,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_3514,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_3515,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_3516,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_3517,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_3518,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_3519,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_3520,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_3521,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_3522,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_3523,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_3524,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_3525,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_3526,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_3527,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_3528,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_3529,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_3530,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_3531,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_3532,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_3533,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1991]),
[final] ).
cnf(i_0_3534,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2004]),
[final] ).
cnf(i_0_3535,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_2206]),
[final] ).
cnf(i_0_3536,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[i_0_1994]),
[final] ).
cnf(i_0_3537,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_3538,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_3539,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_3540,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_1931]),
[final] ).
cnf(i_0_3541,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_3542,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_3543,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_3544,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_3545,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk21_0),
inference(split_conjunct,[status(thm)],[i_0_1642]),
[final] ).
cnf(i_0_3546,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk9_0),
inference(split_conjunct,[status(thm)],[i_0_1342]),
[final] ).
cnf(i_0_3547,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0),
inference(split_conjunct,[status(thm)],[i_0_1643]),
[final] ).
cnf(i_0_3548,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_3549,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_3550,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk9_0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[i_0_1342]),
[final] ).
cnf(i_0_3551,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_3552,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_1422]),
[final] ).
cnf(i_0_3553,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_3554,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_3555,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_3556,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_2212]),
[final] ).
cnf(i_0_3557,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_2213]),
[final] ).
cnf(i_0_3558,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_2214]),
[final] ).
cnf(i_0_3559,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_2215]),
[final] ).
cnf(i_0_3560,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_2216]),
[final] ).
cnf(i_0_3561,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_3562,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_3563,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_3564,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_3565,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2221]),
[final] ).
cnf(i_0_3566,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2222]),
[final] ).
cnf(i_0_3567,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[i_0_2223]),
[final] ).
cnf(i_0_3568,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_3569,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_3570,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_3571,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_2227]),
[final] ).
cnf(i_0_3572,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_2228]),
[final] ).
cnf(i_0_3573,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_2229]),
[final] ).
cnf(i_0_3574,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_3575,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_3576,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_3577,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_3578,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_3579,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_3580,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_3581,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_3582,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_3583,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_3584,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_3585,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_3586,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_3587,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2240]),
[final] ).
cnf(i_0_3588,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_3589,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3590,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_2243]),
[final] ).
cnf(i_0_3591,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_3592,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_3593,plain,
( class_Groups_Ouminus(tc_fun(X2,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2246]),
[final] ).
cnf(i_0_3594,plain,
( class_Groups_Ominus(tc_fun(X2,X1))
| ~ class_Groups_Ominus(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2247]),
[final] ).
cnf(i_0_3595,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_3596,plain,
( class_Orderings_Oorder(tc_fun(X2,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2249]),
[final] ).
cnf(i_0_3597,plain,
( class_Orderings_Oord(tc_fun(X2,X1))
| ~ class_Orderings_Oord(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2250]),
[final] ).
cnf(i_0_3598,plain,
( class_Orderings_Opreorder(tc_fun(X2,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2251]),
[final] ).
cnf(i_0_3599,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_3600,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_3601,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_3602,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_3603,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_2018]),
[final] ).
cnf(i_0_3604,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_3605,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_3606,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_3607,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_3608,plain,
( c_Rings_Oinverse__class_Oinverse(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2242]),
[final] ).
cnf(i_0_3609,plain,
( c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(split_conjunct,[status(thm)],[i_0_2243]),
[final] ).
cnf(i_0_3610,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_3611,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_3612,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_3613,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_3614,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_3615,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_3616,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_3617,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_2261]),
[final] ).
cnf(i_0_3618,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2262]),
[final] ).
cnf(i_0_3619,plain,
( c_Rings_Oinverse__class_Oinverse(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2263]),
[final] ).
cnf(i_0_3620,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_2264]),
[final] ).
cnf(i_0_3621,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_3622,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_3623,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_3624,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_3625,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_3626,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_3627,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_3628,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2269]),
[final] ).
cnf(i_0_3629,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(split_conjunct,[status(thm)],[i_0_2270]),
[final] ).
cnf(i_0_3630,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_3631,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_3632,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_3633,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_1942]),
[final] ).
cnf(i_0_3634,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,esk11_0) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),
inference(split_conjunct,[status(thm)],[i_0_1943]),
[final] ).
cnf(i_0_3635,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_3636,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_3637,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oone__class_Oone(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2273]),
[final] ).
cnf(i_0_3638,plain,
( ~ class_Rings_Ozero__neq__one(X1)
| c_Groups_Oone__class_Oone(X1) != c_Groups_Ozero__class_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2274]),
[final] ).
cnf(i_0_3639,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_3640,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_3641,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_3642,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_3643,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_3644,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_3645,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_3646,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_3647,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_3648,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_3649,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_3650,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_3651,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_3652,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2284]),
[final] ).
cnf(i_0_3653,plain,
( class_Groups_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2285]),
[final] ).
cnf(i_0_3654,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2286]),
[final] ).
cnf(i_0_3655,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2287]),
[final] ).
cnf(i_0_3656,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2288]),
[final] ).
cnf(i_0_3657,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2289]),
[final] ).
cnf(i_0_3658,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_2290]),
[final] ).
cnf(i_0_3659,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2291]),
[final] ).
cnf(i_0_3660,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2292]),
[final] ).
cnf(i_0_3661,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2293]),
[final] ).
cnf(i_0_3662,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2294]),
[final] ).
cnf(i_0_3663,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_2295]),
[final] ).
cnf(i_0_3664,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ocancel__comm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2296]),
[final] ).
cnf(i_0_3665,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2297]),
[final] ).
cnf(i_0_3666,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2298]),
[final] ).
cnf(i_0_3667,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2299]),
[final] ).
cnf(i_0_3668,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2300]),
[final] ).
cnf(i_0_3669,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2301]),
[final] ).
cnf(i_0_3670,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2302]),
[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_2303]),
[final] ).
cnf(i_0_3672,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2304]),
[final] ).
cnf(i_0_3673,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2305]),
[final] ).
cnf(i_0_3674,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2306]),
[final] ).
cnf(i_0_3675,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Ozero(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2307]),
[final] ).
cnf(i_0_3676,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2308]),
[final] ).
cnf(i_0_3677,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2309]),
[final] ).
cnf(i_0_3678,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2310]),
[final] ).
cnf(i_0_3679,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2311]),
[final] ).
cnf(i_0_3680,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2312]),
[final] ).
cnf(i_0_3681,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2313]),
[final] ).
cnf(i_0_3682,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2314]),
[final] ).
cnf(i_0_3683,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2315]),
[final] ).
cnf(i_0_3684,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2316]),
[final] ).
cnf(i_0_3685,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2317]),
[final] ).
cnf(i_0_3686,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2318]),
[final] ).
cnf(i_0_3687,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2319]),
[final] ).
cnf(i_0_3688,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2320]),
[final] ).
cnf(i_0_3689,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2321]),
[final] ).
cnf(i_0_3690,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__ring(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2322]),
[final] ).
cnf(i_0_3691,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Groups_Oab__group__add(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2323]),
[final] ).
cnf(i_0_3692,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2324]),
[final] ).
cnf(i_0_3693,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2325]),
[final] ).
cnf(i_0_3694,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2326]),
[final] ).
cnf(i_0_3695,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2327]),
[final] ).
cnf(i_0_3696,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2328]),
[final] ).
cnf(i_0_3697,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2329]),
[final] ).
cnf(i_0_3698,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2330]),
[final] ).
cnf(i_0_3699,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2331]),
[final] ).
cnf(i_0_3700,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Oidom(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2332]),
[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_2333]),
[final] ).
cnf(i_0_3702,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[i_0_2334]),
[final] ).
cnf(i_0_3703,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_3704,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_3705,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_3706,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_3707,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_3708,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_3709,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_3710,plain,
esk24_0 != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[i_0_1337]),
[final] ).
cnf(i_0_3711,plain,
esk23_0 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[i_0_1337]),
[final] ).
cnf(i_0_3712,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_3713,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_3714,plain,
v_k____ != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[fact_kas_I2_J]),
[final] ).
cnf(i_0_3715,plain,
v_a____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_kas_I1_J]),
[final] ).
cnf(i_0_3716,plain,
v_w____ != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[fact_w0]),
[final] ).
cnf(i_0_3717,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_3718,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_3719,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_3720,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_3721,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
[final] ).
cnf(i_0_3722,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
[final] ).
cnf(i_0_3723,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]),
[final] ).
cnf(i_0_3724,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]),
[final] ).
cnf(i_0_3725,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
[final] ).
cnf(i_0_3726,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]),
[final] ).
cnf(i_0_3727,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
[final] ).
cnf(i_0_3728,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
[final] ).
cnf(i_0_3729,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]),
[final] ).
cnf(i_0_3730,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]),
[final] ).
cnf(i_0_3731,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
[final] ).
cnf(i_0_3732,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
[final] ).
cnf(i_0_3733,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
[final] ).
cnf(i_0_3734,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]),
[final] ).
cnf(i_0_3735,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]),
[final] ).
cnf(i_0_3736,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
[final] ).
cnf(i_0_3737,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
[final] ).
cnf(i_0_3738,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
[final] ).
cnf(i_0_3739,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
[final] ).
cnf(i_0_3740,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]),
[final] ).
cnf(i_0_3741,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
[final] ).
cnf(i_0_3742,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
[final] ).
cnf(i_0_3743,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]),
[final] ).
cnf(i_0_3744,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
[final] ).
cnf(i_0_3745,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
[final] ).
cnf(i_0_3746,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
[final] ).
cnf(i_0_3747,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]),
[final] ).
cnf(i_0_3748,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
[final] ).
cnf(i_0_3749,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
[final] ).
cnf(i_0_3750,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
[final] ).
cnf(i_0_3751,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]),
[final] ).
cnf(i_0_3752,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_3753,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_3754,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_3755,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_3756,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
[final] ).
cnf(i_0_3757,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]),
[final] ).
cnf(i_0_3758,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_3759,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_3760,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_3761,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_3762,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_3763,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_3764,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_3765,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_3766,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_3767,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_3768,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_3769,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_3770,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_3771,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_3772,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_3773,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_3774,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3775,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3776,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3777,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]),
[final] ).
cnf(i_0_3778,plain,
class_Groups_Oone(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
[final] ).
cnf(i_0_3779,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
[final] ).
cnf(i_0_3780,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]),
[final] ).
cnf(i_0_3781,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]),
[final] ).
cnf(i_0_3782,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_3783,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_3784,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_3785,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_3786,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_3787,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_3788,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_3789,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_3790,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_3791,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_3792,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_3793,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_3794,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_3795,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_3796,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_3797,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_3798,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_3799,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_3800,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_3801,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_3802,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_3803,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3804,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3805,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]),
[final] ).
cnf(i_0_3806,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_3807,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_3808,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_3809,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_3810,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_3811,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_3812,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_3813,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_3814,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_3815,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_3816,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_3817,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_3818,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_3819,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_3820,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_3821,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]),
[final] ).
cnf(i_0_3822,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]),
[final] ).
cnf(i_0_3823,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]),
[final] ).
cnf(i_0_3824,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_3825,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_3826,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_3827,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_3828,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_3829,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_3830,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_3831,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_3832,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
[final] ).
cnf(i_0_3833,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
[final] ).
cnf(i_0_3834,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]),
[final] ).
cnf(i_0_3835,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]),
[final] ).
cnf(i_0_3836,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3837,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]),
[final] ).
cnf(i_0_3838,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_3839,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_3840,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_3841,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_3842,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_3843,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_3844,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_3845,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_3846,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_3847,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_3848,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3849,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3850,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]),
[final] ).
cnf(i_0_3851,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3852,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]),
[final] ).
cnf(i_0_3853,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_3854,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_3855,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_3856,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_3857,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_3858,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3859,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]),
[final] ).
cnf(i_0_3860,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_3861,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_3862,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_3863,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_3864,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_3865,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
[final] ).
cnf(i_0_3866,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]),
[final] ).
cnf(i_0_3867,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]),
[final] ).
cnf(i_0_3868,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_3869,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_3870,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring]),
[final] ).
cnf(i_0_3871,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]),
[final] ).
cnf(i_0_3872,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]),
[final] ).
cnf(i_0_3873,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]),
[final] ).
cnf(i_0_3874,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3875,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3876,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3877,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]),
[final] ).
cnf(i_0_3878,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
[final] ).
cnf(i_0_3879,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]),
[final] ).
cnf(i_0_3880,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]),
[final] ).
cnf(i_0_3881,plain,
class_Rings_Oring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
[final] ).
cnf(i_0_3882,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]),
[final] ).
cnf(i_0_3883,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]),
[final] ).
cnf(i_0_3884,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3885,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3886,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]),
[final] ).
cnf(i_0_3887,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3888,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3889,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]),
[final] ).
cnf(i_0_3890,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_3891,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_3892,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_3893,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3894,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]),
[final] ).
cnf(i_0_3895,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_3896,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_3897,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3898,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3899,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3900,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]),
[final] ).
cnf(i_0_3901,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_3902,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_3903,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_3904,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_3905,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_3906,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_3907,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_3908,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_3909,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_3910,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_3911,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_3912,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_3913,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
[final] ).
cnf(i_0_3914,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
[final] ).
cnf(i_0_3915,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]),
[final] ).
cnf(i_0_3916,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]),
[final] ).
cnf(i_0_3917,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_3918,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_3919,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_3920,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_3921,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_3922,plain,
class_Power_Opower(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
[final] ).
cnf(i_0_3923,plain,
class_Power_Opower(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
[final] ).
cnf(i_0_3924,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]),
[final] ).
cnf(i_0_3925,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Power_Opower]),
[final] ).
cnf(i_0_3926,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3927,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3928,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3929,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]),
[final] ).
cnf(i_0_3930,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]),
[final] ).
cnf(i_0_3931,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_3932,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_3933,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]),
[final] ).
cnf(i_0_3934,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3935,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3936,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]),
[final] ).
cnf(i_0_3937,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_3938,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_3939,axiom,
X1 = X1 ).
cnf(i_0_3940,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3941,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3942,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3943,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3944,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3945,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3946,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3947,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3948,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3949,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3950,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3951,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3952,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3953,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3954,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3955,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3956,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3957,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3958,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3959,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3960,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3961,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3962,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3963,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3964,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3965,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3966,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3967,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3968,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3969,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3970,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3971,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3972,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3973,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_3974,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_3975,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_3976,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3977,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3978,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3979,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3980,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3981,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3982,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3983,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3984,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3985,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3986,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3987,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3988,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3989,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3990,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3991,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3992,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3993,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_3994,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_3995,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_3996,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_3997,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_3998,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_3999,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| c_Orderings_Oord__class_Oless__eq(X2,X3,X4) ) ).
cnf(i_0_4000,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X4)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X4) ) ).
cnf(i_0_4001,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X4,X1)
| c_Orderings_Oord__class_Oless__eq(X3,X4,X2) ) ).
cnf(i_0_4002,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4003,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4004,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4005,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4006,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4007,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4008,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4009,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4010,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4011,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4012,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4013,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4014,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4015,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4016,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4017,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4018,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4019,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4020,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4021,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4022,axiom,
( X1 != X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).
cnf(i_0_4023,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4024,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4025,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4026,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4027,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4028,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4029,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4030,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4031,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4032,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4033,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4034,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4035,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
| class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_4036,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4037,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4038,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4039,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4040,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4041,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4042,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4043,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4044,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4045,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4046,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4047,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4048,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4049,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4050,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4051,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4052,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4053,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4054,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4055,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4056,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4057,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4058,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4059,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4060,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4061,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4062,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4063,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4064,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4065,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4066,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4067,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4068,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4069,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4070,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4071,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4072,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4073,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4074,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4075,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4076,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4077,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4078,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4079,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4080,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4081,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4082,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X3,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X4) ) ).
cnf(i_0_4083,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X1,X4)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X2,X4) ) ).
cnf(i_0_4084,axiom,
( X1 != X2
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X1)
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X3,X4,X2) ) ).
cnf(i_0_4085,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4086,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4087,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4088,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4089,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4090,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_3939_001,axiom,
X1 = X1 ).
cnf(i_0_3940_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_3941_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_3942_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_3943_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_3944_006,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X1,X3) = c_Groups_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_3945_007,axiom,
( X1 != X2
| c_Groups_Oabs__class_Oabs(X3,X1) = c_Groups_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_3946_008,axiom,
( X1 != X2
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).
cnf(i_0_3947_009,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_3948_010,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_3949_011,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_3950_012,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X1,X3) = c_Rings_Oinverse__class_Oinverse(X2,X3) ) ).
cnf(i_0_3951_013,axiom,
( X1 != X2
| c_Rings_Oinverse__class_Oinverse(X3,X1) = c_Rings_Oinverse__class_Oinverse(X3,X2) ) ).
cnf(i_0_3952_014,axiom,
( X1 != X2
| c_Polynomial_OpCons(X1,X3,X4) = c_Polynomial_OpCons(X2,X3,X4) ) ).
cnf(i_0_3953_015,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X1,X4) = c_Polynomial_OpCons(X3,X2,X4) ) ).
cnf(i_0_3954_016,axiom,
( X1 != X2
| c_Polynomial_OpCons(X3,X4,X1) = c_Polynomial_OpCons(X3,X4,X2) ) ).
cnf(i_0_3955_017,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X3) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X3) ) ).
cnf(i_0_3956_018,axiom,
( X1 != X2
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X1) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X3,X2) ) ).
cnf(i_0_3957_019,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X1,X3) = c_Groups_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_3958_020,axiom,
( X1 != X2
| c_Groups_Ouminus__class_Ouminus(X3,X1) = c_Groups_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_3959_021,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X1,X3,X4) = c_Groups_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_3960_022,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X1,X4) = c_Groups_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_3961_023,axiom,
( X1 != X2
| c_Groups_Oplus__class_Oplus(X3,X4,X1) = c_Groups_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_3962_024,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X1,X3,X4) = c_Polynomial_Osynthetic__div(X2,X3,X4) ) ).
cnf(i_0_3963_025,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X1,X4) = c_Polynomial_Osynthetic__div(X3,X2,X4) ) ).
cnf(i_0_3964_026,axiom,
( X1 != X2
| c_Polynomial_Osynthetic__div(X3,X4,X1) = c_Polynomial_Osynthetic__div(X3,X4,X2) ) ).
cnf(i_0_3965_027,axiom,
( X1 != X2
| c_Polynomial_Omonom(X1,X3,X4) = c_Polynomial_Omonom(X2,X3,X4) ) ).
cnf(i_0_3966_028,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X1,X4) = c_Polynomial_Omonom(X3,X2,X4) ) ).
cnf(i_0_3967_029,axiom,
( X1 != X2
| c_Polynomial_Omonom(X3,X4,X1) = c_Polynomial_Omonom(X3,X4,X2) ) ).
cnf(i_0_3968_030,axiom,
( X1 != X2
| c_Polynomial_Oorder(X1,X3,X4) = c_Polynomial_Oorder(X2,X3,X4) ) ).
cnf(i_0_3969_031,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X1,X4) = c_Polynomial_Oorder(X3,X2,X4) ) ).
cnf(i_0_3970_032,axiom,
( X1 != X2
| c_Polynomial_Oorder(X3,X4,X1) = c_Polynomial_Oorder(X3,X4,X2) ) ).
cnf(i_0_3971_033,axiom,
( X1 != X2
| c_RealDef_Oreal(X1,X3) = c_RealDef_Oreal(X2,X3) ) ).
cnf(i_0_3972_034,axiom,
( X1 != X2
| c_RealDef_Oreal(X3,X1) = c_RealDef_Oreal(X3,X2) ) ).
cnf(i_0_3973_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_3974_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_3975_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_3976_038,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_3977_039,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_3978_040,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X1,X3,X4) = c_Polynomial_Opcompose(X2,X3,X4) ) ).
cnf(i_0_3979_041,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X1,X4) = c_Polynomial_Opcompose(X3,X2,X4) ) ).
cnf(i_0_3980_042,axiom,
( X1 != X2
| c_Polynomial_Opcompose(X3,X4,X1) = c_Polynomial_Opcompose(X3,X4,X2) ) ).
cnf(i_0_3981_043,axiom,
( X1 != X2
| c_RComplete_Onatfloor(X1) = c_RComplete_Onatfloor(X2) ) ).
cnf(i_0_3982_044,axiom,
( X1 != X2
| c_RComplete_Onatceiling(X1) = c_RComplete_Onatceiling(X2) ) ).
cnf(i_0_3983_045,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X1,X3,X4) = c_Groups_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_3984_046,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X1,X4) = c_Groups_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_3985_047,axiom,
( X1 != X2
| c_Groups_Ominus__class_Ominus(X3,X4,X1) = c_Groups_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_3986_048,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).
cnf(i_0_3987_049,axiom,
( X1 != X2
| c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).
cnf(i_0_3988_050,axiom,
( X1 != X2
| c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).
cnf(i_0_3989_051,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).
cnf(i_0_3990_052,axiom,
( X1 != X2
| c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).
cnf(i_0_3991_053,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).
cnf(i_0_3992_054,axiom,
( X1 != X2
| c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).
cnf(i_0_3993_055,axiom,
( X1 != X2
| c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).
cnf(i_0_3994_056,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_3995_057,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_3996_058,axiom,
( X1 != X2
| c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).
cnf(i_0_3997_059,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3) = c_Polynomial_Opoly(X2,X3) ) ).
cnf(i_0_3998_060,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1) = c_Polynomial_Opoly(X3,X2) ) ).
cnf(i_0_3999_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_4000_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_4001_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_4002_064,axiom,
( X1 != X2
| ~ class_Rings_Oidom(X1)
| class_Rings_Oidom(X2) ) ).
cnf(i_0_4003_065,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| class_Groups_Oordered__ab__group__add__abs(X2) ) ).
cnf(i_0_4004_066,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring(X1)
| class_Rings_Odivision__ring(X2) ) ).
cnf(i_0_4005_067,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring(X1)
| class_Rings_Ocomm__ring(X2) ) ).
cnf(i_0_4006_068,axiom,
( X1 != X2
| ~ class_Rings_Odvd(X1)
| class_Rings_Odvd(X2) ) ).
cnf(i_0_4007_069,axiom,
( X1 != X2
| ~ class_Fields_Ofield(X1)
| class_Fields_Ofield(X2) ) ).
cnf(i_0_4008_070,axiom,
( X1 != X2
| ~ class_Rings_Oring(X1)
| class_Rings_Oring(X2) ) ).
cnf(i_0_4009_071,axiom,
( X1 != X2
| ~ class_Rings_Osemiring(X1)
| class_Rings_Osemiring(X2) ) ).
cnf(i_0_4010_072,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1(X1)
| class_Rings_Olinordered__semiring__1(X2) ) ).
cnf(i_0_4011_073,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__1__strict(X1)
| class_Rings_Olinordered__semiring__1__strict(X2) ) ).
cnf(i_0_4012_074,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| c_Orderings_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_4013_075,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X1,X4)
| c_Orderings_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_4014_076,axiom,
( X1 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X4,X1)
| c_Orderings_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_4015_077,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_4016_078,axiom,
( X1 != X2
| ~ class_Rings_Osemiring__0(X1)
| class_Rings_Osemiring__0(X2) ) ).
cnf(i_0_4017_079,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring__strict(X1)
| class_Rings_Olinordered__ring__strict(X2) ) ).
cnf(i_0_4018_080,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__1(X1)
| class_Rings_Ocomm__semiring__1(X2) ) ).
cnf(i_0_4019_081,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__ring(X1)
| class_Rings_Olinordered__ring(X2) ) ).
cnf(i_0_4020_082,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring__0(X1)
| class_Rings_Ocomm__semiring__0(X2) ) ).
cnf(i_0_4021_083,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__mult(X1)
| class_Groups_Omonoid__mult(X2) ) ).
cnf(i_0_4022_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_4023_085,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__idom(X1)
| class_Rings_Olinordered__idom(X2) ) ).
cnf(i_0_4024_086,axiom,
( X1 != X2
| ~ class_Rings_Oring__1(X1)
| class_Rings_Oring__1(X2) ) ).
cnf(i_0_4025_087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_4026_088,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semidom(X1)
| class_Rings_Olinordered__semidom(X2) ) ).
cnf(i_0_4027_089,axiom,
( X1 != X2
| ~ class_Rings_Oordered__semiring(X1)
| class_Rings_Oordered__semiring(X2) ) ).
cnf(i_0_4028_090,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring__strict(X1)
| class_Rings_Olinordered__semiring__strict(X2) ) ).
cnf(i_0_4029_091,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__mult(X1)
| class_Groups_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_4030_092,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__semiring(X1)
| class_Rings_Olinordered__semiring(X2) ) ).
cnf(i_0_4031_093,axiom,
( X1 != X2
| ~ class_Groups_Oab__group__add(X1)
| class_Groups_Oab__group__add(X2) ) ).
cnf(i_0_4032_094,axiom,
( X1 != X2
| ~ class_Groups_Ocomm__monoid__add(X1)
| class_Groups_Ocomm__monoid__add(X2) ) ).
cnf(i_0_4033_095,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__semiring(X1)
| class_Rings_Ocomm__semiring(X2) ) ).
cnf(i_0_4034_096,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_4035_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_4036_098,axiom,
( X1 != X2
| ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(X2) ) ).
cnf(i_0_4037_099,axiom,
( X1 != X2
| ~ class_Rings_Oordered__comm__semiring(X1)
| class_Rings_Oordered__comm__semiring(X2) ) ).
cnf(i_0_4038_100,axiom,
( X1 != X2
| ~ class_Rings_Olinordered__comm__semiring__strict(X1)
| class_Rings_Olinordered__comm__semiring__strict(X2) ) ).
cnf(i_0_4039_101,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| class_Groups_Oordered__ab__semigroup__add(X2) ) ).
cnf(i_0_4040_102,axiom,
( X1 != X2
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4041_103,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring__abs(X1)
| class_Rings_Oordered__ring__abs(X2) ) ).
cnf(i_0_4042_104,axiom,
( X1 != X2
| ~ class_Power_Opower(X1)
| class_Power_Opower(X2) ) ).
cnf(i_0_4043_105,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__mult(X1)
| class_Groups_Oab__semigroup__mult(X2) ) ).
cnf(i_0_4044_106,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_4045_107,axiom,
( X1 != X2
| ~ class_Groups_Oordered__comm__monoid__add(X1)
| class_Groups_Oordered__comm__monoid__add(X2) ) ).
cnf(i_0_4046_108,axiom,
( X1 != X2
| ~ class_Rings_Oordered__cancel__semiring(X1)
| class_Rings_Oordered__cancel__semiring(X2) ) ).
cnf(i_0_4047_109,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_4048_110,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1,X3)
| c_SEQ_Odecseq(X2,X3) ) ).
cnf(i_0_4049_111,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X3,X1)
| c_SEQ_Odecseq(X3,X2) ) ).
cnf(i_0_4050_112,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_4051_113,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_4052_114,axiom,
( X1 != X2
| ~ class_Groups_Olinordered__ab__group__add(X1)
| class_Groups_Olinordered__ab__group__add(X2) ) ).
cnf(i_0_4053_115,axiom,
( X1 != X2
| ~ class_Groups_Oab__semigroup__add(X1)
| class_Groups_Oab__semigroup__add(X2) ) ).
cnf(i_0_4054_116,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field(X1)
| class_Fields_Olinordered__field(X2) ) ).
cnf(i_0_4055_117,axiom,
( X1 != X2
| ~ class_Groups_Oordered__ab__group__add(X1)
| class_Groups_Oordered__ab__group__add(X2) ) ).
cnf(i_0_4056_118,axiom,
( X1 != X2
| ~ class_Groups_Ominus(X1)
| class_Groups_Ominus(X2) ) ).
cnf(i_0_4057_119,axiom,
( X1 != X2
| ~ class_Fields_Olinordered__field__inverse__zero(X1)
| class_Fields_Olinordered__field__inverse__zero(X2) ) ).
cnf(i_0_4058_120,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X1,X3)
| c_Polynomial_Opos__poly(X2,X3) ) ).
cnf(i_0_4059_121,axiom,
( X1 != X2
| ~ c_Polynomial_Opos__poly(X3,X1)
| c_Polynomial_Opos__poly(X3,X2) ) ).
cnf(i_0_4060_122,axiom,
( X1 != X2
| ~ class_Rings_Ocomm__ring__1(X1)
| class_Rings_Ocomm__ring__1(X2) ) ).
cnf(i_0_4061_123,axiom,
( X1 != X2
| ~ class_Fields_Ofield__inverse__zero(X1)
| class_Fields_Ofield__inverse__zero(X2) ) ).
cnf(i_0_4062_124,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_4063_125,axiom,
( X1 != X2
| ~ class_Groups_Ogroup__add(X1)
| class_Groups_Ogroup__add(X2) ) ).
cnf(i_0_4064_126,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_4065_127,axiom,
( X1 != X2
| ~ class_Rings_Odivision__ring__inverse__zero(X1)
| class_Rings_Odivision__ring__inverse__zero(X2) ) ).
cnf(i_0_4066_128,axiom,
( X1 != X2
| ~ class_Lattices_Oab__semigroup__idem__mult(X1)
| class_Lattices_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_4067_129,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_4068_130,axiom,
( X1 != X2
| ~ class_Groups_Ozero(X1)
| class_Groups_Ozero(X2) ) ).
cnf(i_0_4069_131,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__semigroup__add(X1)
| class_Groups_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_4070_132,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__ab__semigroup__add(X1)
| class_Groups_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_4071_133,axiom,
( X1 != X2
| ~ class_Rings_Oordered__ring(X1)
| class_Rings_Oordered__ring(X2) ) ).
cnf(i_0_4072_134,axiom,
( X1 != X2
| ~ class_Groups_Ouminus(X1)
| class_Groups_Ouminus(X2) ) ).
cnf(i_0_4073_135,axiom,
( X1 != X2
| ~ class_Groups_Oabs__if(X1)
| class_Groups_Oabs__if(X2) ) ).
cnf(i_0_4074_136,axiom,
( X1 != X2
| ~ class_Groups_Osgn__if(X1)
| class_Groups_Osgn__if(X2) ) ).
cnf(i_0_4075_137,axiom,
( X1 != X2
| ~ class_Rings_Omult__zero(X1)
| class_Rings_Omult__zero(X2) ) ).
cnf(i_0_4076_138,axiom,
( X1 != X2
| ~ class_Rings_Ono__zero__divisors(X1)
| class_Rings_Ono__zero__divisors(X2) ) ).
cnf(i_0_4077_139,axiom,
( X1 != X2
| ~ class_Rings_Ozero__neq__one(X1)
| class_Rings_Ozero__neq__one(X2) ) ).
cnf(i_0_4078_140,axiom,
( X1 != X2
| ~ class_Rings_Oring__1__no__zero__divisors(X1)
| class_Rings_Oring__1__no__zero__divisors(X2) ) ).
cnf(i_0_4079_141,axiom,
( X1 != X2
| ~ class_Rings_Oring__no__zero__divisors(X1)
| class_Rings_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_4080_142,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_4081_143,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__div__algebra(X1)
| class_RealVector_Oreal__div__algebra(X2) ) ).
cnf(i_0_4082_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_4083_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_4084_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_4085_147,axiom,
( X1 != X2
| ~ class_Groups_Omonoid__add(X1)
| class_Groups_Omonoid__add(X2) ) ).
cnf(i_0_4086_148,axiom,
( X1 != X2
| ~ class_Groups_Ocancel__comm__monoid__add(X1)
| class_Groups_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_4087_149,axiom,
( X1 != X2
| ~ class_Groups_Oone(X1)
| class_Groups_Oone(X2) ) ).
cnf(i_0_4088_150,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X1,X3,X4)
| c_Rings_Odvd__class_Odvd(X2,X3,X4) ) ).
cnf(i_0_4089_151,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X1,X4)
| c_Rings_Odvd__class_Odvd(X3,X2,X4) ) ).
cnf(i_0_4090_152,axiom,
( X1 != X2
| ~ c_Rings_Odvd__class_Odvd(X3,X4,X1)
| c_Rings_Odvd__class_Odvd(X3,X4,X2) ) ).
cnf(i_0_4091,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,[],[2395]) ).
cnf(i_0_4092,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,[],[2396]) ).
cnf(i_0_4093,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,[],[2401]) ).
cnf(i_0_4094,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,[],[2402]) ).
cnf(i_0_4095,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,[],[2403]) ).
cnf(i_0_4096,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,[],[2404]) ).
cnf(i_0_4097,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,[],[2410]) ).
cnf(i_0_4098,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,[],[2411]) ).
cnf(i_0_4099,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,[],[2412]) ).
cnf(i_0_4100,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,[],[2413]) ).
cnf(i_0_4101,plain,
( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X2 = X3
| X4 = X4 ),
inference(equality_inference,[],[2437]) ).
cnf(i_0_4102,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,[],[2529]) ).
cnf(i_0_4103,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,[],[2561]) ).
cnf(i_0_4104,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,[],[2594]) ).
cnf(i_0_4105,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,[],[2706]) ).
cnf(i_0_4106,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(equality_inference,[],[2788]) ).
cnf(i_0_4107,plain,
( ~ class_Rings_Olinordered__semidom(X1)
| X2 = X2
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),X3) ),
inference(equality_inference,[],[2898]) ).
cnf(i_0_4108,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,[],[2943]) ).
cnf(i_0_4109,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,[],[2944]) ).
cnf(i_0_4110,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,[],[2967]) ).
cnf(i_0_4111,plain,
( X1 = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(equality_inference,[],[2968]) ).
cnf(i_0_4112,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,[],[2998]) ).
cnf(i_0_4113,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,[],[2999]) ).
cnf(i_0_4114,plain,
( ~ class_Rings_Oidom(X1)
| X2 = X2
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[3097]) ).
cnf(i_0_4115,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3116]) ).
cnf(i_0_4116,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3117]) ).
cnf(i_0_4117,plain,
( ~ class_Groups_Ozero(X1)
| X2 = X2 ),
inference(equality_inference,[],[3118]) ).
cnf(i_0_4118,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3120]) ).
cnf(i_0_4119,plain,
( X1 = X1
| ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[3121]) ).
cnf(i_0_4120,plain,
( X1 = X1
| ~ class_Groups_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[3123]) ).
cnf(i_0_4121,plain,
X1 = X1,
inference(equality_inference,[],[3157]) ).
cnf(i_0_4122,plain,
X1 = X1,
inference(equality_inference,[],[3158]) ).
cnf(i_0_4123,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,[],[3163]) ).
cnf(i_0_4124,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,[],[3176]) ).
cnf(i_0_4125,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,[],[3177]) ).
cnf(i_0_4126,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3183]) ).
cnf(i_0_4127,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3184]) ).
cnf(i_0_4128,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(equality_inference,[],[3186]) ).
cnf(i_0_4129,plain,
( X1 = X1
| X2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[3187]) ).
cnf(i_0_4130,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,[],[3213]) ).
cnf(i_0_4131,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(equality_inference,[],[3234]) ).
cnf(i_0_4132,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,[],[3249]) ).
cnf(i_0_4133,plain,
X1 = X1,
inference(equality_inference,[],[3261]) ).
cnf(i_0_4134,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,[],[3275]) ).
cnf(i_0_4135,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(equality_inference,[],[3327]) ).
cnf(i_0_4136,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,[],[3334]) ).
cnf(i_0_4137,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,[],[3346]) ).
cnf(i_0_4138,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,[],[3347]) ).
cnf(i_0_4139,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,[],[3348]) ).
cnf(i_0_4140,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,[],[3349]) ).
cnf(i_0_4141,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,[],[3350]) ).
cnf(i_0_4142,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3353]) ).
cnf(i_0_4143,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3355]) ).
cnf(i_0_4144,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3356]) ).
cnf(i_0_4145,plain,
( ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X2) ),
inference(equality_inference,[],[3357]) ).
cnf(i_0_4146,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,[],[3388]) ).
cnf(i_0_4147,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,[],[3389]) ).
cnf(i_0_4148,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_inference,[],[3390]) ).
cnf(i_0_4149,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,[],[3391]) ).
cnf(i_0_4150,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,[],[3392]) ).
cnf(i_0_4151,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(equality_inference,[],[3406]) ).
cnf(i_0_4152,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3410]) ).
cnf(i_0_4153,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3411]) ).
cnf(i_0_4154,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3412]) ).
cnf(i_0_4155,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,[],[3421]) ).
cnf(i_0_4156,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,[],[3422]) ).
cnf(i_0_4157,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,[],[3429]) ).
cnf(i_0_4158,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,[],[3436]) ).
cnf(i_0_4159,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,[],[3437]) ).
cnf(i_0_4160,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,[],[3443]) ).
cnf(i_0_4161,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,[],[3451]) ).
cnf(i_0_4162,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,[],[3452]) ).
cnf(i_0_4163,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,[],[3458]) ).
cnf(i_0_4164,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,[],[3459]) ).
cnf(i_0_4165,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,[],[3460]) ).
cnf(i_0_4166,plain,
( ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(X1),X2,X2) ),
inference(equality_inference,[],[3461]) ).
cnf(i_0_4167,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,[],[3462]) ).
cnf(i_0_4168,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,[],[3472]) ).
cnf(i_0_4169,plain,
( ~ class_Groups_Oab__group__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3473]) ).
cnf(i_0_4170,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ominus__class_Ominus(X1,X2,X2) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3474]) ).
cnf(i_0_4171,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,[],[3475]) ).
cnf(i_0_4172,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3495]) ).
cnf(i_0_4173,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3496]) ).
cnf(i_0_4174,plain,
( ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(equality_inference,[],[3497]) ).
cnf(i_0_4175,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,[],[3498]) ).
cnf(i_0_4176,plain,
( ~ class_Int_Oring__char__0(X1)
| ~ class_Rings_Oidom(X1)
| X2 = X2 ),
inference(equality_inference,[],[3511]) ).
cnf(i_0_4177,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,[],[3525]) ).
cnf(i_0_4178,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(equality_inference,[],[3535]) ).
cnf(i_0_4179,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(equality_inference,[],[3536]) ).
cnf(i_0_4180,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,[],[3540]) ).
cnf(i_0_4181,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,[],[3553]) ).
cnf(i_0_4182,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,[],[3554]) ).
cnf(i_0_4183,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,[],[3555]) ).
cnf(i_0_4184,plain,
( X1 = X1
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(equality_inference,[],[3557]) ).
cnf(i_0_4185,plain,
( ~ class_Lattices_Oboolean__algebra(X1)
| X2 = X2 ),
inference(equality_inference,[],[3558]) ).
cnf(i_0_4186,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = X2 ),
inference(equality_inference,[],[3559]) ).
cnf(i_0_4187,plain,
( ~ class_RealVector_Oreal__algebra__1(X1)
| X2 = X2 ),
inference(equality_inference,[],[3560]) ).
cnf(i_0_4188,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2 ),
inference(equality_inference,[],[3576]) ).
cnf(i_0_4189,plain,
( ~ class_Groups_Ogroup__add(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) ),
inference(equality_inference,[],[3578]) ).
cnf(i_0_4190,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,[],[3580]) ).
cnf(i_0_4191,plain,
X1 = X1,
inference(equality_inference,[],[3581]) ).
cnf(i_0_4192,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,[],[3603]) ).
cnf(i_0_4193,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,[],[3604]) ).
cnf(i_0_4194,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,[],[3605]) ).
cnf(i_0_4195,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,[],[3606]) ).
cnf(i_0_4196,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,[],[3607]) ).
cnf(i_0_4197,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,[],[3608]) ).
cnf(i_0_4198,plain,
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ozero__class_Ozero(X1)) = c_Groups_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[3609]) ).
cnf(i_0_4199,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,[],[3610]) ).
cnf(i_0_4200,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,[],[3611]) ).
cnf(i_0_4201,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,[],[3621]) ).
cnf(i_0_4202,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,[],[3622]) ).
cnf(i_0_4203,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,[],[3623]) ).
cnf(i_0_4204,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,[],[3636]) ).
cnf(i_0_4205,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_3567,i_0_3147]) ).
cnf(i_0_4206,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4207,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3147]) ).
cnf(i_0_4208,plain,
c_Orderings_Oord__class_Oless__eq(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(scs_inference,[],[i_0_3567,i_0_2984,i_0_3147,i_0_3246]) ).
cnf(i_0_4209,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3246]) ).
cnf(i_0_4210,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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(scs_inference,[],[i_0_2344,i_0_3567,i_0_2984,i_0_3147,i_0_3246,i_0_3323]) ).
cnf(i_0_4211,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(rename_variables,[],[i_0_3323]) ).
cnf(i_0_4212,plain,
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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))) != 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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____),
inference(scs_inference,[],[i_0_2344,i_0_3567,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536]) ).
cnf(i_0_4213,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3536]) ).
cnf(i_0_4214,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_3567,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665]) ).
cnf(i_0_4215,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_4216,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(rename_variables,[],[i_0_2665]) ).
cnf(i_0_4217,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(scs_inference,[],[i_0_2344,i_0_3567,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666]) ).
cnf(i_0_4218,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4219,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(rename_variables,[],[i_0_2666]) ).
cnf(i_0_4220,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),X1),
inference(scs_inference,[],[i_0_2344,i_0_3566,i_0_3567,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685]) ).
cnf(i_0_4221,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4222,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(rename_variables,[],[i_0_2685]) ).
cnf(i_0_4223,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X2)),
inference(scs_inference,[],[i_0_2344,i_0_3566,i_0_4221,i_0_3567,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687]) ).
cnf(i_0_4224,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4225,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2687]) ).
cnf(i_0_4226,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_3566,i_0_4221,i_0_3567,i_0_3125,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688]) ).
cnf(i_0_4227,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2688]) ).
cnf(i_0_4228,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2344,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3125,i_0_3401,i_0_2984,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764]) ).
cnf(i_0_4229,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4230,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(rename_variables,[],[i_0_2764]) ).
cnf(i_0_4231,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3125,i_0_3401,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805]) ).
cnf(i_0_4232,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4233,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(rename_variables,[],[i_0_2805]) ).
cnf(i_0_4234,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3125,i_0_3401,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845]) ).
cnf(i_0_4235,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4236,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(rename_variables,[],[i_0_2845]) ).
cnf(i_0_4237,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_3125,i_0_3401,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858]) ).
cnf(i_0_4238,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_3170]) ).
cnf(i_0_4239,plain,
( ~ 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,X1,X3) ),
inference(rename_variables,[],[i_0_2858]) ).
cnf(i_0_4240,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3)),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859]) ).
cnf(i_0_4241,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_3170]) ).
cnf(i_0_4242,plain,
( ~ 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(rename_variables,[],[i_0_2859]) ).
cnf(i_0_4243,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,v_k____,c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_pa____)),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860]) ).
cnf(i_0_4244,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2860]) ).
cnf(i_0_4245,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883]) ).
cnf(i_0_4246,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(rename_variables,[],[i_0_2803]) ).
cnf(i_0_4247,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rename_variables,[],[i_0_2883]) ).
cnf(i_0_4248,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_3(X1,X2,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926]) ).
cnf(i_0_4249,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4250,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_3(X2,X3,X1)) ),
inference(rename_variables,[],[i_0_2926]) ).
cnf(i_0_4251,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)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936]) ).
cnf(i_0_4252,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4253,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(rename_variables,[],[i_0_2936]) ).
cnf(i_0_4254,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937]) ).
cnf(i_0_4255,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4256,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(rename_variables,[],[i_0_2937]) ).
cnf(i_0_4257,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953]) ).
cnf(i_0_4258,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3427]) ).
cnf(i_0_4259,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2953]) ).
cnf(i_0_4260,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_2938,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959]) ).
cnf(i_0_4261,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_2938]) ).
cnf(i_0_4262,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(rename_variables,[],[i_0_2959]) ).
cnf(i_0_4263,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X2),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961]) ).
cnf(i_0_4264,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_2938]) ).
cnf(i_0_4265,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,X3) ),
inference(rename_variables,[],[i_0_2961]) ).
cnf(i_0_4266,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032]) ).
cnf(i_0_4267,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_4268,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(rename_variables,[],[i_0_3032]) ).
cnf(i_0_4269,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033]) ).
cnf(i_0_4270,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(rename_variables,[],[i_0_3033]) ).
cnf(i_0_4271,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059]) ).
cnf(i_0_4272,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4273,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1) ),
inference(rename_variables,[],[i_0_3059]) ).
cnf(i_0_4274,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136]) ).
cnf(i_0_4275,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4276,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) ),
inference(rename_variables,[],[i_0_3136]) ).
cnf(i_0_4277,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137]) ).
cnf(i_0_4278,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(X1))),
inference(rename_variables,[],[i_0_3401]) ).
cnf(i_0_4279,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)) ),
inference(rename_variables,[],[i_0_3137]) ).
cnf(i_0_4280,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) != X1,
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163]) ).
cnf(i_0_4281,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4282,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(rename_variables,[],[i_0_3163]) ).
cnf(i_0_4283,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173]) ).
cnf(i_0_4284,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(rename_variables,[],[i_0_3173]) ).
cnf(i_0_4285,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174]) ).
cnf(i_0_4286,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(rename_variables,[],[i_0_3174]) ).
cnf(i_0_4287,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179]) ).
cnf(i_0_4288,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4289,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(rename_variables,[],[i_0_3179]) ).
cnf(i_0_4290,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180]) ).
cnf(i_0_4291,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4292,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X1)) ),
inference(rename_variables,[],[i_0_3180]) ).
cnf(i_0_4293,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181]) ).
cnf(i_0_4294,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4295,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rename_variables,[],[i_0_3181]) ).
cnf(i_0_4296,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182]) ).
cnf(i_0_4297,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4298,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(rename_variables,[],[i_0_3182]) ).
cnf(i_0_4299,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209]) ).
cnf(i_0_4300,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4301,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),X1) ),
inference(rename_variables,[],[i_0_3209]) ).
cnf(i_0_4302,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211]) ).
cnf(i_0_4303,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4304,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(rename_variables,[],[i_0_3211]) ).
cnf(i_0_4305,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222]) ).
cnf(i_0_4306,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(rename_variables,[],[i_0_3167]) ).
cnf(i_0_4307,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(rename_variables,[],[i_0_3222]) ).
cnf(i_0_4308,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234]) ).
cnf(i_0_4309,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4310,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3234]) ).
cnf(i_0_4311,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239]) ).
cnf(i_0_4312,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3239]) ).
cnf(i_0_4313,plain,
c_Orderings_Oord__class_Oless__eq(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(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244]) ).
cnf(i_0_4314,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3244]) ).
cnf(i_0_4315,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,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(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299]) ).
cnf(i_0_4316,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1) ),
inference(rename_variables,[],[i_0_3299]) ).
cnf(i_0_4317,plain,
c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303]) ).
cnf(i_0_4318,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) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) ),
inference(rename_variables,[],[i_0_3303]) ).
cnf(i_0_4319,plain,
c_RComplete_Onatfloor(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361]) ).
cnf(i_0_4320,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3361]) ).
cnf(i_0_4321,plain,
c_RComplete_Onatceiling(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362]) ).
cnf(i_0_4322,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3362]) ).
cnf(i_0_4323,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390]) ).
cnf(i_0_4324,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3390]) ).
cnf(i_0_4325,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,esk23_0) != X1,
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397]) ).
cnf(i_0_4326,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_3397]) ).
cnf(i_0_4327,plain,
X1 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406]) ).
cnf(i_0_4328,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3406]) ).
cnf(i_0_4329,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410]) ).
cnf(i_0_4330,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_3410]) ).
cnf(i_0_4331,plain,
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(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411]) ).
cnf(i_0_4332,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3411]) ).
cnf(i_0_4333,plain,
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(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412]) ).
cnf(i_0_4334,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3412]) ).
cnf(i_0_4335,plain,
c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463]) ).
cnf(i_0_4336,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4337,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(rename_variables,[],[i_0_3463]) ).
cnf(i_0_4338,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465]) ).
cnf(i_0_4339,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4154]) ).
cnf(i_0_4340,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(rename_variables,[],[i_0_3465]) ).
cnf(i_0_4341,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506]) ).
cnf(i_0_4342,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3506]) ).
cnf(i_0_4343,plain,
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),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)),X2),X3)),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093]) ).
cnf(i_0_4344,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(rename_variables,[],[i_0_4093]) ).
cnf(i_0_4345,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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2),X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094]) ).
cnf(i_0_4346,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(rename_variables,[],[i_0_4094]) ).
cnf(i_0_4347,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,X1)),X2),X3) = X3,
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097]) ).
cnf(i_0_4348,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(rename_variables,[],[i_0_4097]) ).
cnf(i_0_4349,plain,
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,X2)),X3),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098]) ).
cnf(i_0_4350,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(rename_variables,[],[i_0_4098]) ).
cnf(i_0_4351,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113]) ).
cnf(i_0_4352,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(rename_variables,[],[i_0_4113]) ).
cnf(i_0_4353,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940]) ).
cnf(i_0_4354,plain,
X1 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960]) ).
cnf(i_0_4355,plain,
X1 != c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972]) ).
cnf(i_0_4356,plain,
esk16_0 != esk17_0,
inference(scs_inference,[],[i_0_2344,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995]) ).
cnf(i_0_4357,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285]) ).
cnf(i_0_4358,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(rename_variables,[],[i_0_4137]) ).
cnf(i_0_4359,plain,
( hAPP(X1,esk4_1(X1)) != hAPP(X1,esk5_1(X1))
| c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X2,X3,X1) ),
inference(rename_variables,[],[i_0_3285]) ).
cnf(i_0_4360,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505]) ).
cnf(i_0_4361,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3505]) ).
cnf(i_0_4362,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3770,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571]) ).
cnf(i_0_4363,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_2571]) ).
cnf(i_0_4364,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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3770,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675]) ).
cnf(i_0_4365,plain,
( 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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X3) ),
inference(rename_variables,[],[i_0_2675]) ).
cnf(i_0_4366,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3748,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093]) ).
cnf(i_0_4367,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4368,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) ),
inference(rename_variables,[],[i_0_3093]) ).
cnf(i_0_4369,plain,
c_Orderings_Oord__class_Oless__eq(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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3738,i_0_3748,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206]) ).
cnf(i_0_4370,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3206]) ).
cnf(i_0_4371,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk21_0),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3738,i_0_3748,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208]) ).
cnf(i_0_4372,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3208]) ).
cnf(i_0_4373,plain,
c_Orderings_Oord__class_Oless__eq(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)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3738,i_0_3743,i_0_3748,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294]) ).
cnf(i_0_4374,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3294]) ).
cnf(i_0_4375,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495]) ).
cnf(i_0_4376,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3495]) ).
cnf(i_0_4377,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496]) ).
cnf(i_0_4378,plain,
( ~ class_Orderings_Opreorder(X1)
| X2 != X3
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3496]) ).
cnf(i_0_4379,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497]) ).
cnf(i_0_4380,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3497]) ).
cnf(i_0_4381,plain,
~ c_Orderings_Oord__class_Oless__eq(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,tc_RealDef_Oreal)),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_4309,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999]) ).
cnf(i_0_4382,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4383,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____)))))),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(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),v_m____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000]) ).
cnf(i_0_4384,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4385,plain,
~ 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_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001]) ).
cnf(i_0_4386,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_Int_Oint),X2,X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_4367,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357]) ).
cnf(i_0_4387,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4388,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk22_4(X3,X2,X4,X1)),hAPP(X3,esk22_4(X3,X2,X4,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_2357]) ).
cnf(i_0_4389,plain,
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),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X4)),X2),X3))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365]) ).
cnf(i_0_4390,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4391,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,X3)),X4),X5),X6)
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2365]) ).
cnf(i_0_4392,plain,
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),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X1)),X2),X4)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),X4)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367]) ).
cnf(i_0_4393,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4394,plain,
( ~ 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))
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2367]) ).
cnf(i_0_4395,plain,
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X1)),X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368]) ).
cnf(i_0_4396,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4397,plain,
( ~ 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))
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2368]) ).
cnf(i_0_4398,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,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)),X3),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370]) ).
cnf(i_0_4399,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_2939]) ).
cnf(i_0_4400,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),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(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,X4,X1) ),
inference(rename_variables,[],[i_0_2370]) ).
cnf(i_0_4401,plain,
~ 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,X2)),X3),X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372]) ).
cnf(i_0_4402,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3427]) ).
cnf(i_0_4403,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),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(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,X1,X4) ),
inference(rename_variables,[],[i_0_2372]) ).
cnf(i_0_4404,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),X3),X3),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375]) ).
cnf(i_0_4405,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4406,plain,
( ~ 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))
| 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)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2375]) ).
cnf(i_0_4407,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376]) ).
cnf(i_0_4408,plain,
( ~ 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))
| 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)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2376]) ).
cnf(i_0_4409,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3),X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377]) ).
cnf(i_0_4410,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4411,plain,
( ~ 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))
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2377]) ).
cnf(i_0_4412,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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1),X2),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379]) ).
cnf(i_0_4413,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4414,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4415,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),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,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,X4,X1) ),
inference(rename_variables,[],[i_0_2379]) ).
cnf(i_0_4416,plain,
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,X2)),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381]) ).
cnf(i_0_4417,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_3171]) ).
cnf(i_0_4418,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),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,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,X1,X4) ),
inference(rename_variables,[],[i_0_2381]) ).
cnf(i_0_4419,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X3)),X2))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403]) ).
cnf(i_0_4420,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(rename_variables,[],[i_0_4157]) ).
cnf(i_0_4421,plain,
( 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
| 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)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2403]) ).
cnf(i_0_4422,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X1)),X2))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),X3),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404]) ).
cnf(i_0_4423,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3329]) ).
cnf(i_0_4424,plain,
( 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)
| 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)
| ~ class_Rings_Oring(X2) ),
inference(rename_variables,[],[i_0_2404]) ).
cnf(i_0_4425,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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X3)) = X3,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410]) ).
cnf(i_0_4426,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(rename_variables,[],[i_0_2422]) ).
cnf(i_0_4427,plain,
( 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_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,X4,X1) ),
inference(rename_variables,[],[i_0_2410]) ).
cnf(i_0_4428,plain,
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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X4,X1),X4)),X2),X3),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411]) ).
cnf(i_0_4429,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(rename_variables,[],[i_0_2422]) ).
cnf(i_0_4430,plain,
( 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)
| 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,X1,X4) ),
inference(rename_variables,[],[i_0_2411]) ).
cnf(i_0_4431,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412]) ).
cnf(i_0_4432,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3329]) ).
cnf(i_0_4433,plain,
( 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)
| 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
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2412]) ).
cnf(i_0_4434,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413]) ).
cnf(i_0_4435,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3329]) ).
cnf(i_0_4436,plain,
( 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)
| 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)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2413]) ).
cnf(i_0_4437,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,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,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466]) ).
cnf(i_0_4438,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4439,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X2)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_2466]) ).
cnf(i_0_4440,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467]) ).
cnf(i_0_4441,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4442,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_4443,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562]) ).
cnf(i_0_4444,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4445,plain,
( ~ 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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_2562]) ).
cnf(i_0_4446,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563]) ).
cnf(i_0_4447,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_3170]) ).
cnf(i_0_4448,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_3171]) ).
cnf(i_0_4449,plain,
( ~ 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,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2563]) ).
cnf(i_0_4450,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575]) ).
cnf(i_0_4451,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4452,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_2575]) ).
cnf(i_0_4453,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577]) ).
cnf(i_0_4454,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2577]) ).
cnf(i_0_4455,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643]) ).
cnf(i_0_4456,plain,
( 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(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_2643]) ).
cnf(i_0_4457,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645]) ).
cnf(i_0_4458,plain,
( 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,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_2645]) ).
cnf(i_0_4459,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753]) ).
cnf(i_0_4460,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(rename_variables,[],[i_0_2803]) ).
cnf(i_0_4461,plain,
( 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__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4) ),
inference(rename_variables,[],[i_0_2753]) ).
cnf(i_0_4462,plain,
c_SEQ_Odecseq(tc_HOL_Obool,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763]) ).
cnf(i_0_4463,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk34_2(X2,X1)),hAPP(X2,esk33_2(X2,X1)))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Odecseq(X1,X2) ),
inference(rename_variables,[],[i_0_2763]) ).
cnf(i_0_4464,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),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))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789]) ).
cnf(i_0_4465,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_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2) ),
inference(rename_variables,[],[i_0_2789]) ).
cnf(i_0_4466,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813]) ).
cnf(i_0_4467,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(rename_variables,[],[i_0_2813]) ).
cnf(i_0_4468,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850]) ).
cnf(i_0_4469,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(rename_variables,[],[i_0_3529]) ).
cnf(i_0_4470,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3427]) ).
cnf(i_0_4471,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X4)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X4)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2) ),
inference(rename_variables,[],[i_0_2850]) ).
cnf(i_0_4472,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881]) ).
cnf(i_0_4473,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4474,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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(rename_variables,[],[i_0_2881]) ).
cnf(i_0_4475,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893]) ).
cnf(i_0_4476,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4477,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(rename_variables,[],[i_0_2893]) ).
cnf(i_0_4478,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894]) ).
cnf(i_0_4479,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(rename_variables,[],[i_0_2894]) ).
cnf(i_0_4480,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895]) ).
cnf(i_0_4481,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(rename_variables,[],[i_0_2895]) ).
cnf(i_0_4482,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896]) ).
cnf(i_0_4483,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4484,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(rename_variables,[],[i_0_2896]) ).
cnf(i_0_4485,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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897]) ).
cnf(i_0_4486,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4487,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(rename_variables,[],[i_0_2897]) ).
cnf(i_0_4488,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900]) ).
cnf(i_0_4489,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4490,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3427]) ).
cnf(i_0_4491,plain,
( ~ 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))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(X1),X2) ),
inference(rename_variables,[],[i_0_2900]) ).
cnf(i_0_4492,plain,
~ class_Groups_Oordered__ab__group__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913]) ).
cnf(i_0_4493,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3400]) ).
cnf(i_0_4494,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(rename_variables,[],[i_0_2913]) ).
cnf(i_0_4495,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915]) ).
cnf(i_0_4496,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4497,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X2)) ),
inference(rename_variables,[],[i_0_2915]) ).
cnf(i_0_4498,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916]) ).
cnf(i_0_4499,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4500,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4501,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X2),X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,c_RComplete_Onatfloor(X1)) ),
inference(rename_variables,[],[i_0_2916]) ).
cnf(i_0_4502,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998]) ).
cnf(i_0_4503,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4504,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4505,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3) = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_2998]) ).
cnf(i_0_4506,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999]) ).
cnf(i_0_4507,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(rename_variables,[],[i_0_3541]) ).
cnf(i_0_4508,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4509,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2) != X3
| X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_2999]) ).
cnf(i_0_4510,plain,
~ 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_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003]) ).
cnf(i_0_4511,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X3,X1) ),
inference(rename_variables,[],[i_0_3003]) ).
cnf(i_0_4512,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004]) ).
cnf(i_0_4513,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_3169]) ).
cnf(i_0_4514,plain,
( ~ 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(rename_variables,[],[i_0_3004]) ).
cnf(i_0_4515,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013]) ).
cnf(i_0_4516,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4517,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(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(rename_variables,[],[i_0_3013]) ).
cnf(i_0_4518,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015]) ).
cnf(i_0_4519,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4520,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_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3015]) ).
cnf(i_0_4521,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016]) ).
cnf(i_0_4522,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4523,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_3016]) ).
cnf(i_0_4524,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018]) ).
cnf(i_0_4525,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4526,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ouminus__class_Ouminus(X1,X3),X2)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3018]) ).
cnf(i_0_4527,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020]) ).
cnf(i_0_4528,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4529,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3020]) ).
cnf(i_0_4530,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022]) ).
cnf(i_0_4531,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ouminus__class_Ouminus(X1,X2))
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(rename_variables,[],[i_0_3022]) ).
cnf(i_0_4532,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034]) ).
cnf(i_0_4533,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(rename_variables,[],[i_0_3034]) ).
cnf(i_0_4534,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),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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039]) ).
cnf(i_0_4535,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(rename_variables,[],[i_0_3039]) ).
cnf(i_0_4536,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045]) ).
cnf(i_0_4537,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(rename_variables,[],[i_0_3045]) ).
cnf(i_0_4538,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047]) ).
cnf(i_0_4539,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(rename_variables,[],[i_0_3047]) ).
cnf(i_0_4540,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061]) ).
cnf(i_0_4541,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(rename_variables,[],[i_0_3061]) ).
cnf(i_0_4542,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070]) ).
cnf(i_0_4543,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4544,plain,
( ~ 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(rename_variables,[],[i_0_3070]) ).
cnf(i_0_4545,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071]) ).
cnf(i_0_4546,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4547,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(rename_variables,[],[i_0_3071]) ).
cnf(i_0_4548,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072]) ).
cnf(i_0_4549,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4550,plain,
( ~ 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(rename_variables,[],[i_0_3072]) ).
cnf(i_0_4551,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073]) ).
cnf(i_0_4552,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4553,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(rename_variables,[],[i_0_3073]) ).
cnf(i_0_4554,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074]) ).
cnf(i_0_4555,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4556,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_Oone__class_Oone(X1))
| ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
inference(rename_variables,[],[i_0_3074]) ).
cnf(i_0_4557,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075]) ).
cnf(i_0_4558,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4559,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(rename_variables,[],[i_0_3075]) ).
cnf(i_0_4560,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076]) ).
cnf(i_0_4561,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(rename_variables,[],[i_0_3076]) ).
cnf(i_0_4562,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077]) ).
cnf(i_0_4563,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4564,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| 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(rename_variables,[],[i_0_3077]) ).
cnf(i_0_4565,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080]) ).
cnf(i_0_4566,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4567,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(rename_variables,[],[i_0_3080]) ).
cnf(i_0_4568,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081]) ).
cnf(i_0_4569,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4570,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(rename_variables,[],[i_0_3081]) ).
cnf(i_0_4571,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,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082]) ).
cnf(i_0_4572,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4573,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(X1) ),
inference(rename_variables,[],[i_0_3082]) ).
cnf(i_0_4574,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,esk21_0)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083]) ).
cnf(i_0_4575,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(rename_variables,[],[i_0_3083]) ).
cnf(i_0_4576,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084]) ).
cnf(i_0_4577,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4578,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(rename_variables,[],[i_0_3084]) ).
cnf(i_0_4579,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085]) ).
cnf(i_0_4580,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(rename_variables,[],[i_0_3085]) ).
cnf(i_0_4581,plain,
c_Polynomial_Osmult(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) != c_Polynomial_OpCons(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086]) ).
cnf(i_0_4582,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) != c_Polynomial_OpCons(X2,X4,X1)
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(rename_variables,[],[i_0_3086]) ).
cnf(i_0_4583,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094]) ).
cnf(i_0_4584,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4585,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1)
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3094]) ).
cnf(i_0_4586,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)),c_RealDef_Oreal(tc_Nat_Onat,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101]) ).
cnf(i_0_4587,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(rename_variables,[],[i_0_3101]) ).
cnf(i_0_4588,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102]) ).
cnf(i_0_4589,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4590,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(rename_variables,[],[i_0_3102]) ).
cnf(i_0_4591,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_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103]) ).
cnf(i_0_4592,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(rename_variables,[],[i_0_3103]) ).
cnf(i_0_4593,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104]) ).
cnf(i_0_4594,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(rename_variables,[],[i_0_3104]) ).
cnf(i_0_4595,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),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____))) = 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____))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120]) ).
cnf(i_0_4596,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X4,X3)
| X2 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3120]) ).
cnf(i_0_4597,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1)),X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121]) ).
cnf(i_0_4598,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| X3 = X4
| ~ class_Groups_Ocancel__ab__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3121]) ).
cnf(i_0_4599,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3)) = X1,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123]) ).
cnf(i_0_4600,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Oplus__class_Oplus(X1,X2,X4)
| X3 = X4
| ~ class_Groups_Ocancel__semigroup__add(X1) ),
inference(rename_variables,[],[i_0_3123]) ).
cnf(i_0_4601,plain,
~ c_Orderings_Oord__class_Oless(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)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126]) ).
cnf(i_0_4602,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3126]) ).
cnf(i_0_4603,plain,
~ c_Orderings_Oord__class_Oless__eq(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)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129]) ).
cnf(i_0_4604,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3129]) ).
cnf(i_0_4605,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130]) ).
cnf(i_0_4606,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3130]) ).
cnf(i_0_4607,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131]) ).
cnf(i_0_4608,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3131]) ).
cnf(i_0_4609,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_3529,i_0_3214,i_0_3545,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135]) ).
cnf(i_0_4610,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3135]) ).
cnf(i_0_4611,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139]) ).
cnf(i_0_4612,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(rename_variables,[],[i_0_3166]) ).
cnf(i_0_4613,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(rename_variables,[],[i_0_3167]) ).
cnf(i_0_4614,plain,
( 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)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3139]) ).
cnf(i_0_4615,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150]) ).
cnf(i_0_4616,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3150]) ).
cnf(i_0_4617,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151]) ).
cnf(i_0_4618,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3151]) ).
cnf(i_0_4619,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152]) ).
cnf(i_0_4620,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(rename_variables,[],[i_0_3438]) ).
cnf(i_0_4621,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3152]) ).
cnf(i_0_4622,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177]) ).
cnf(i_0_4623,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(rename_variables,[],[i_0_3177]) ).
cnf(i_0_4624,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204]) ).
cnf(i_0_4625,plain,
( X1 = c_Groups_Ozero__class_Ozero(X2)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(rename_variables,[],[i_0_3204]) ).
cnf(i_0_4626,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226]) ).
cnf(i_0_4627,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4628,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3226]) ).
cnf(i_0_4629,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228]) ).
cnf(i_0_4630,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(rename_variables,[],[i_0_3438]) ).
cnf(i_0_4631,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3228]) ).
cnf(i_0_4632,plain,
c_Groups_Ouminus__class_Ouminus(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____),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3885,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296]) ).
cnf(i_0_4633,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Ouminus__class_Ouminus(X1,X2) = X3
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3296]) ).
cnf(i_0_4634,plain,
X1 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297]) ).
cnf(i_0_4635,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ouminus__class_Ouminus(X1,X3)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3297]) ).
cnf(i_0_4636,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298]) ).
cnf(i_0_4637,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) = X1,
inference(rename_variables,[],[i_0_3528]) ).
cnf(i_0_4638,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ouminus__class_Ouminus(X1,X2)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3298]) ).
cnf(i_0_4639,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314]) ).
cnf(i_0_4640,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1) = X1,
inference(rename_variables,[],[i_0_3564]) ).
cnf(i_0_4641,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Oone__class_Oone(X1)
| c_Rings_Oinverse__class_Oinverse(X1,X2) = X3
| ~ class_Rings_Odivision__ring(X1) ),
inference(rename_variables,[],[i_0_3314]) ).
cnf(i_0_4642,plain,
c_Polynomial_Oorder(tc_Complex_Ocomplex,c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_q____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318]) ).
cnf(i_0_4643,plain,
( 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(rename_variables,[],[i_0_3318]) ).
cnf(i_0_4644,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,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334]) ).
cnf(i_0_4645,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(rename_variables,[],[i_0_3334]) ).
cnf(i_0_4646,plain,
~ class_Groups_Oab__group__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335]) ).
cnf(i_0_4647,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(rename_variables,[],[i_0_3524]) ).
cnf(i_0_4648,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Oab__group__add(X1)
| X2 = X3 ),
inference(rename_variables,[],[i_0_3335]) ).
cnf(i_0_4649,plain,
~ class_Groups_Ogroup__add(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2339,i_0_2581,i_0_3745,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336]) ).
cnf(i_0_4650,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(rename_variables,[],[i_0_3524]) ).
cnf(i_0_4651,plain,
( c_Groups_Ominus__class_Ominus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1)
| X2 = X3 ),
inference(rename_variables,[],[i_0_3336]) ).
cnf(i_0_4652,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),v_k____)),hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_a____,v_s____)),c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339]) ).
cnf(i_0_4653,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(rename_variables,[],[i_0_2352]) ).
cnf(i_0_4654,plain,
( X1 != c_Groups_Oplus__class_Oplus(X2,X1,X3)
| X3 = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_3339]) ).
cnf(i_0_4655,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340]) ).
cnf(i_0_4656,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(rename_variables,[],[i_0_3340]) ).
cnf(i_0_4657,plain,
~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk33_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353]) ).
cnf(i_0_4658,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(rename_variables,[],[i_0_4137]) ).
cnf(i_0_4659,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3353]) ).
cnf(i_0_4660,plain,
~ c_Orderings_Oord__class_Oless(tc_HOL_Obool,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355]) ).
cnf(i_0_4661,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3355]) ).
cnf(i_0_4662,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356]) ).
cnf(i_0_4663,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X2) ),
inference(rename_variables,[],[i_0_3356]) ).
cnf(i_0_4664,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357]) ).
cnf(i_0_4665,plain,
( X1 != X2
| ~ class_Orderings_Olinorder(X3)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3357]) ).
cnf(i_0_4666,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Int_Oint,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388]) ).
cnf(i_0_4667,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4668,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,X1,X3) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Ocomm__semiring__0(X2) ),
inference(rename_variables,[],[i_0_3388]) ).
cnf(i_0_4669,plain,
c_Polynomial_Osmult(tc_Int_Oint,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389]) ).
cnf(i_0_4670,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4671,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Osmult(X2,X3,X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Oidom(X2) ),
inference(rename_variables,[],[i_0_3389]) ).
cnf(i_0_4672,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii),c_Complex_Oii) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391]) ).
cnf(i_0_4673,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| c_Groups_Oplus__class_Oplus(X2,X1,X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3391]) ).
cnf(i_0_4674,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Oii,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii)) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392]) ).
cnf(i_0_4675,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| c_Groups_Oplus__class_Oplus(X2,X3,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3392]) ).
cnf(i_0_4676,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451]) ).
cnf(i_0_4677,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oplus__class_Oplus(X2,X1,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_3451]) ).
cnf(i_0_4678,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462]) ).
cnf(i_0_4679,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(rename_variables,[],[i_0_3462]) ).
cnf(i_0_4680,plain,
hAPP(c_Polynomial_Opoly(tc_Int_Oint,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))),X1) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475]) ).
cnf(i_0_4681,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4682,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| hAPP(c_Polynomial_Opoly(X2,X1),X3) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oidom(X2) ),
inference(rename_variables,[],[i_0_3475]) ).
cnf(i_0_4683,plain,
c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(tc_Int_Oint),c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540]) ).
cnf(i_0_4684,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4685,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(X2),X1) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rename_variables,[],[i_0_3540]) ).
cnf(i_0_4686,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,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))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576]) ).
cnf(i_0_4687,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != X3
| c_Groups_Ouminus__class_Ouminus(X1,X3) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3576]) ).
cnf(i_0_4688,plain,
c_Complex_Oii = c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_Complex_Oii)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578]) ).
cnf(i_0_4689,plain,
( X1 != c_Groups_Ouminus__class_Ouminus(X2,X3)
| X3 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3578]) ).
cnf(i_0_4690,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579]) ).
cnf(i_0_4691,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3579]) ).
cnf(i_0_4692,plain,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Int_Oint,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580]) ).
cnf(i_0_4693,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4694,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X2,X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3580]) ).
cnf(i_0_4695,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582]) ).
cnf(i_0_4696,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(rename_variables,[],[i_0_3582]) ).
cnf(i_0_4697,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1)),X2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590]) ).
cnf(i_0_4698,plain,
( c_Groups_Ouminus__class_Ouminus(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Groups_Ogroup__add(X1) ),
inference(rename_variables,[],[i_0_3590]) ).
cnf(i_0_4699,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk23_0)) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591]) ).
cnf(i_0_4700,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X2,X1) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(rename_variables,[],[i_0_3591]) ).
cnf(i_0_4701,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603]) ).
cnf(i_0_4702,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(rename_variables,[],[i_0_4157]) ).
cnf(i_0_4703,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Osgn__if(X2) ),
inference(rename_variables,[],[i_0_3603]) ).
cnf(i_0_4704,plain,
c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604]) ).
cnf(i_0_4705,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rename_variables,[],[i_0_3604]) ).
cnf(i_0_4706,plain,
c_Groups_Osgn__class_Osgn(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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605]) ).
cnf(i_0_4707,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Osgn__class_Osgn(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__normed__vector(X2) ),
inference(rename_variables,[],[i_0_3605]) ).
cnf(i_0_4708,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,X1))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606]) ).
cnf(i_0_4709,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Oabs__class_Oabs(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(rename_variables,[],[i_0_3606]) ).
cnf(i_0_4710,plain,
c_Rings_Oinverse__class_Oinverse(tc_Complex_Ocomplex,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607]) ).
cnf(i_0_4711,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4712,plain,
( X1 != c_Groups_Oone__class_Oone(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) = c_Groups_Oone__class_Oone(X2)
| ~ class_Fields_Ofield__inverse__zero(X2) ),
inference(rename_variables,[],[i_0_3607]) ).
cnf(i_0_4713,plain,
c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608]) ).
cnf(i_0_4714,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Rings_Oinverse__class_Oinverse(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Odivision__ring__inverse__zero(X2) ),
inference(rename_variables,[],[i_0_3608]) ).
cnf(i_0_4715,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609]) ).
cnf(i_0_4716,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(rename_variables,[],[i_0_3609]) ).
cnf(i_0_4717,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610]) ).
cnf(i_0_4718,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(rename_variables,[],[i_0_3610]) ).
cnf(i_0_4719,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621]) ).
cnf(i_0_4720,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_RealVector_Oof__real(X2,X1) = c_Groups_Ozero__class_Ozero(X2)
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(rename_variables,[],[i_0_3621]) ).
cnf(i_0_4721,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622]) ).
cnf(i_0_4722,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ouminus__class_Ouminus(X2,X1) = X1
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_3622]) ).
cnf(i_0_4723,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623]) ).
cnf(i_0_4724,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X1 = c_Groups_Ouminus__class_Ouminus(X2,X1)
| ~ class_Groups_Olinordered__ab__group__add(X2) ),
inference(rename_variables,[],[i_0_3623]) ).
cnf(i_0_4725,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941]) ).
cnf(i_0_4726,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4727,plain,
class_Groups_Oordered__ab__group__add__abs(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003]) ).
cnf(i_0_4728,plain,
~ c_Orderings_Oord__class_Oless(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,tc_Int_Oint)),X1,X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012]) ).
cnf(i_0_4729,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4730,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013]) ).
cnf(i_0_4731,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4154]) ).
cnf(i_0_4732,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014]) ).
cnf(i_0_4733,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3427]) ).
cnf(i_0_4734,plain,
class_Rings_Olinordered__ring__strict(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3851,i_0_3856,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017]) ).
cnf(i_0_4735,plain,
class_Rings_Oordered__semiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3848,i_0_3851,i_0_3856,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027]) ).
cnf(i_0_4736,plain,
class_Rings_Olinordered__semiring__strict(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028]) ).
cnf(i_0_4737,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035]) ).
cnf(i_0_4738,plain,
class_Rings_Oordered__comm__semiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037]) ).
cnf(i_0_4739,plain,
class_Orderings_Oorder(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050]) ).
cnf(i_0_4740,plain,
tc_Int_Oint != tc_Nat_Onat,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055]) ).
cnf(i_0_4741,plain,
class_Orderings_Opreorder(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062]) ).
cnf(i_0_4742,plain,
class_Lattices_Oboolean__algebra(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064]) ).
cnf(i_0_4743,plain,
class_Orderings_Olinorder(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067]) ).
cnf(i_0_4744,plain,
class_Rings_Oordered__ring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071]) ).
cnf(i_0_4745,plain,
class_Rings_Oidom(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002]) ).
cnf(i_0_4746,plain,
class_Rings_Ocomm__ring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005]) ).
cnf(i_0_4747,plain,
class_Rings_Odvd(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006]) ).
cnf(i_0_4748,plain,
class_Orderings_Oord(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036]) ).
cnf(i_0_4749,plain,
class_Rings_Ocomm__ring__1(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060]) ).
cnf(i_0_4750,plain,
tc_Complex_Ocomplex != tc_Nat_Onat,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063]) ).
cnf(i_0_4751,plain,
class_Groups_Ozero(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068]) ).
cnf(i_0_4752,plain,
class_Groups_Ocancel__semigroup__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069]) ).
cnf(i_0_4753,plain,
class_Groups_Ocancel__ab__semigroup__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070]) ).
cnf(i_0_4754,plain,
class_Groups_Ouminus(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072]) ).
cnf(i_0_4755,plain,
class_Groups_Oabs__if(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073]) ).
cnf(i_0_4756,plain,
class_Groups_Osgn__if(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074]) ).
cnf(i_0_4757,plain,
class_Rings_Omult__zero(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3913,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075]) ).
cnf(i_0_4758,plain,
class_Rings_Ono__zero__divisors(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3909,i_0_3913,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076]) ).
cnf(i_0_4759,plain,
class_Rings_Ozero__neq__one(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077]) ).
cnf(i_0_4760,plain,
class_Rings_Oring__1__no__zero__divisors(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078]) ).
cnf(i_0_4761,plain,
class_Rings_Oring__no__zero__divisors(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079]) ).
cnf(i_0_4762,plain,
class_Int_Oring__char__0(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080]) ).
cnf(i_0_4763,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,tc_Complex_Ocomplex)),tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082]) ).
cnf(i_0_4764,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4765,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,tc_Complex_Ocomplex)),c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083]) ).
cnf(i_0_4766,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4767,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(tc_Complex_Ocomplex,tc_Complex_Ocomplex,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Polynomial_Opoly(tc_Complex_Ocomplex,v_q____)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084]) ).
cnf(i_0_4768,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4769,plain,
class_Groups_Omonoid__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085]) ).
cnf(i_0_4770,plain,
class_Groups_Ocancel__comm__monoid__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086]) ).
cnf(i_0_4771,plain,
class_Groups_Oone(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087]) ).
cnf(i_0_4772,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X1)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846]) ).
cnf(i_0_4773,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3),X4)
| ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2846]) ).
cnf(i_0_4774,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090]) ).
cnf(i_0_4775,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Ouminus__class_Ouminus(X1,X2),X3)
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3090]) ).
cnf(i_0_4776,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091]) ).
cnf(i_0_4777,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,c_Groups_Oabs__class_Oabs(X1,X2),X3)
| ~ class_Rings_Olinordered__idom(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3091]) ).
cnf(i_0_4778,plain,
c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327]) ).
cnf(i_0_4779,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) != c_Groups_Oabs__class_Oabs(X1,X3)
| ~ class_Rings_Olinordered__idom(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3327]) ).
cnf(i_0_4780,plain,
class_Rings_Oring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008]) ).
cnf(i_0_4781,plain,
class_Rings_Osemiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009]) ).
cnf(i_0_4782,plain,
class_Rings_Olinordered__semiring__1(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010]) ).
cnf(i_0_4783,plain,
class_Rings_Olinordered__semiring__1__strict(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011]) ).
cnf(i_0_4784,plain,
class_Rings_Osemiring__0(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016]) ).
cnf(i_0_4785,plain,
class_Rings_Ocomm__semiring__1(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018]) ).
cnf(i_0_4786,plain,
class_Rings_Olinordered__ring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019]) ).
cnf(i_0_4787,plain,
class_Rings_Ocomm__semiring__0(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020]) ).
cnf(i_0_4788,plain,
class_Groups_Omonoid__mult(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021]) ).
cnf(i_0_4789,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022]) ).
cnf(i_0_4790,plain,
class_Rings_Olinordered__idom(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023]) ).
cnf(i_0_4791,plain,
class_Rings_Oring__1(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024]) ).
cnf(i_0_4792,plain,
class_Rings_Olinordered__semidom(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026]) ).
cnf(i_0_4793,plain,
class_Groups_Ocomm__monoid__mult(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029]) ).
cnf(i_0_4794,plain,
class_Rings_Olinordered__semiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030]) ).
cnf(i_0_4795,plain,
tc_RealDef_Oreal != tc_Nat_Onat,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031]) ).
cnf(i_0_4796,plain,
class_Groups_Ocomm__monoid__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032]) ).
cnf(i_0_4797,plain,
class_Rings_Ocomm__semiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033]) ).
cnf(i_0_4798,plain,
class_Rings_Olinordered__comm__semiring__strict(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038]) ).
cnf(i_0_4799,plain,
class_Groups_Oordered__ab__semigroup__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039]) ).
cnf(i_0_4800,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040]) ).
cnf(i_0_4801,plain,
class_Rings_Oordered__ring__abs(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041]) ).
cnf(i_0_4802,plain,
class_Power_Opower(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042]) ).
cnf(i_0_4803,plain,
class_Groups_Oab__semigroup__mult(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043]) ).
cnf(i_0_4804,plain,
class_Groups_Oordered__comm__monoid__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045]) ).
cnf(i_0_4805,plain,
class_Rings_Oordered__cancel__semiring(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046]) ).
cnf(i_0_4806,plain,
class_Groups_Olinordered__ab__group__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052]) ).
cnf(i_0_4807,plain,
class_Groups_Oab__semigroup__add(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,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),X2))),X3),tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053]) ).
cnf(i_0_4808,plain,
class_Groups_Ominus(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056]) ).
cnf(i_0_4809,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604]) ).
cnf(i_0_4810,plain,
( 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__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Oordered__comm__semiring(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2604]) ).
cnf(i_0_4811,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275]) ).
cnf(i_0_4812,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_2939]) ).
cnf(i_0_4813,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| X2 != X3
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3275]) ).
cnf(i_0_4814,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438]) ).
cnf(i_0_4815,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4154]) ).
cnf(i_0_4816,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(rename_variables,[],[i_0_3028]) ).
cnf(i_0_4817,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ominus__class_Ominus(X1,X3,X4),X2)
| ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_2438]) ).
cnf(i_0_4818,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1),X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468]) ).
cnf(i_0_4819,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4820,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_3171]) ).
cnf(i_0_4821,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2468]) ).
cnf(i_0_4822,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624]) ).
cnf(i_0_4823,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(rename_variables,[],[i_0_2939]) ).
cnf(i_0_4824,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_2624]) ).
cnf(i_0_4825,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625]) ).
cnf(i_0_4826,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(rename_variables,[],[i_0_2803]) ).
cnf(i_0_4827,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_2625]) ).
cnf(i_0_4828,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626]) ).
cnf(i_0_4829,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(rename_variables,[],[i_0_2803]) ).
cnf(i_0_4830,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(rename_variables,[],[i_0_2984]) ).
cnf(i_0_4831,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X5) ),
inference(rename_variables,[],[i_0_2626]) ).
cnf(i_0_4832,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),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)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657]) ).
cnf(i_0_4833,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ class_Rings_Olinordered__semiring__strict(X1) ),
inference(rename_variables,[],[i_0_2657]) ).
cnf(i_0_4834,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717]) ).
cnf(i_0_4835,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4836,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2717]) ).
cnf(i_0_4837,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718]) ).
cnf(i_0_4838,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4839,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2718]) ).
cnf(i_0_4840,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719]) ).
cnf(i_0_4841,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4842,plain,
( ~ 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))
| 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) ),
inference(rename_variables,[],[i_0_2719]) ).
cnf(i_0_4843,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_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720]) ).
cnf(i_0_4844,plain,
( ~ c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless(X1,X3,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2720]) ).
cnf(i_0_4845,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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724]) ).
cnf(i_0_4846,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X3)
| c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,X2,X3))
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2724]) ).
cnf(i_0_4847,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740]) ).
cnf(i_0_4848,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(rename_variables,[],[i_0_2740]) ).
cnf(i_0_4849,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2)),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765]) ).
cnf(i_0_4850,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4851,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| 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,X3,X4) ),
inference(rename_variables,[],[i_0_2765]) ).
cnf(i_0_4852,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,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766]) ).
cnf(i_0_4853,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4854,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| 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,X3,X4) ),
inference(rename_variables,[],[i_0_2766]) ).
cnf(i_0_4855,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767]) ).
cnf(i_0_4856,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4857,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4858,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| 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,X3,X4) ),
inference(rename_variables,[],[i_0_2767]) ).
cnf(i_0_4859,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768]) ).
cnf(i_0_4860,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4861,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4862,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| 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,X3,X4) ),
inference(rename_variables,[],[i_0_2768]) ).
cnf(i_0_4863,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769]) ).
cnf(i_0_4864,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4865,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4151]) ).
cnf(i_0_4866,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| 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,X3,X4) ),
inference(rename_variables,[],[i_0_2769]) ).
cnf(i_0_4867,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)) = X1,
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788]) ).
cnf(i_0_4868,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X1) = X2,
inference(rename_variables,[],[i_0_3167]) ).
cnf(i_0_4869,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4870,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_3170]) ).
cnf(i_0_4871,plain,
( 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)
| X1 = X3 ),
inference(rename_variables,[],[i_0_2788]) ).
cnf(i_0_4872,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3548,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854]) ).
cnf(i_0_4873,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4874,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)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3) ),
inference(rename_variables,[],[i_0_2854]) ).
cnf(i_0_4875,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,esk9_0)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3550,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879]) ).
cnf(i_0_4876,plain,
( ~ 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))
| c_Orderings_Oord__class_Oless(X1,c_Groups_Oone__class_Oone(X1),c_Rings_Oinverse__class_Oinverse(X1,X2))
| ~ class_Fields_Olinordered__field(X1) ),
inference(rename_variables,[],[i_0_2879]) ).
cnf(i_0_4877,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v_t____)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880]) ).
cnf(i_0_4878,plain,
( ~ 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))
| 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(rename_variables,[],[i_0_2880]) ).
cnf(i_0_4879,plain,
c_Polynomial_Opos__poly(tc_Int_Oint,c_Polynomial_OpCons(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Int_Oint)))))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944]) ).
cnf(i_0_4880,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4881,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(rename_variables,[],[i_0_4123]) ).
cnf(i_0_4882,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
| c_Polynomial_Opos__poly(X2,c_Polynomial_OpCons(X2,X3,X1))
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ class_Rings_Olinordered__idom(X2) ),
inference(rename_variables,[],[i_0_2944]) ).
cnf(i_0_4883,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976]) ).
cnf(i_0_4884,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4154]) ).
cnf(i_0_4885,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X4,X2) ),
inference(rename_variables,[],[i_0_2976]) ).
cnf(i_0_4886,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977]) ).
cnf(i_0_4887,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_4154]) ).
cnf(i_0_4888,plain,
( ~ class_Orderings_Opreorder(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless(X1,X4,X3)
| ~ c_Orderings_Oord__class_Oless(X1,X4,X2) ),
inference(rename_variables,[],[i_0_2977]) ).
cnf(i_0_4889,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk23_0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113]) ).
cnf(i_0_4890,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_3170]) ).
cnf(i_0_4891,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X3 = X2
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3113]) ).
cnf(i_0_4892,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),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(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195]) ).
cnf(i_0_4893,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3400]) ).
cnf(i_0_4894,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Oorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3195]) ).
cnf(i_0_4895,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197]) ).
cnf(i_0_4896,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(rename_variables,[],[i_0_3266]) ).
cnf(i_0_4897,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| X2 = X3
| c_Orderings_Oord__class_Oless(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3197]) ).
cnf(i_0_4898,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324]) ).
cnf(i_0_4899,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != c_Groups_Ozero__class_Ozero(X1)
| X2 = c_Groups_Ozero__class_Ozero(X1)
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__no__zero__divisors(X1) ),
inference(rename_variables,[],[i_0_3324]) ).
cnf(i_0_4900,plain,
c_Polynomial_OpCons(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)),c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal))))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343]) ).
cnf(i_0_4901,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)) = X1,
inference(rename_variables,[],[i_0_3628]) ).
cnf(i_0_4902,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))
| X3 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ozero(X2) ),
inference(rename_variables,[],[i_0_3343]) ).
cnf(i_0_4903,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541]) ).
cnf(i_0_4904,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(rename_variables,[],[i_0_3329]) ).
cnf(i_0_4905,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)) != c_Groups_Oplus__class_Oplus(X1,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X6))
| X3 = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
| X4 = X6
| X2 != X5 ),
inference(rename_variables,[],[i_0_2541]) ).
cnf(i_0_4906,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862]) ).
cnf(i_0_4907,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(rename_variables,[],[i_0_3171]) ).
cnf(i_0_4908,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4909,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(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),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2862]) ).
cnf(i_0_4910,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863]) ).
cnf(i_0_4911,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(rename_variables,[],[i_0_4157]) ).
cnf(i_0_4912,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(rename_variables,[],[i_0_3567]) ).
cnf(i_0_4913,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
| X3 = 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),X2)
| ~ class_Groups_Oordered__comm__monoid__add(X1) ),
inference(rename_variables,[],[i_0_2863]) ).
cnf(i_0_4914,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888]) ).
cnf(i_0_4915,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(rename_variables,[],[i_0_3438]) ).
cnf(i_0_4916,plain,
( X1 != c_Groups_Ozero__class_Ozero(X2)
| X3 != 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(rename_variables,[],[i_0_2888]) ).
cnf(i_0_4917,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk23_0) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140]) ).
cnf(i_0_4918,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ class_Rings_Omult__zero(X2)
| ~ class_Rings_Ono__zero__divisors(X2)
| ~ class_Rings_Ozero__neq__one(X2)
| 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) ),
inference(rename_variables,[],[i_0_4140]) ).
cnf(i_0_4919,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775]) ).
cnf(i_0_4920,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2775]) ).
cnf(i_0_4921,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832]) ).
cnf(i_0_4922,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(rename_variables,[],[i_0_2832]) ).
cnf(i_0_4923,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843]) ).
cnf(i_0_4924,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(rename_variables,[],[i_0_2843]) ).
cnf(i_0_4925,plain,
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844]) ).
cnf(i_0_4926,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(rename_variables,[],[i_0_2844]) ).
cnf(i_0_4927,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934]) ).
cnf(i_0_4928,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(rename_variables,[],[i_0_2934]) ).
cnf(i_0_4929,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935]) ).
cnf(i_0_4930,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(rename_variables,[],[i_0_2935]) ).
cnf(i_0_4931,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955]) ).
cnf(i_0_4932,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(rename_variables,[],[i_0_2955]) ).
cnf(i_0_4933,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957]) ).
cnf(i_0_4934,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,X3) ),
inference(rename_variables,[],[i_0_2957]) ).
cnf(i_0_4935,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157]) ).
cnf(i_0_4936,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 = X3 ),
inference(rename_variables,[],[i_0_3157]) ).
cnf(i_0_4937,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162]) ).
cnf(i_0_4938,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(rename_variables,[],[i_0_3162]) ).
cnf(i_0_4939,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212]) ).
cnf(i_0_4940,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(rename_variables,[],[i_0_3212]) ).
cnf(i_0_4941,plain,
hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1) = hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261]) ).
cnf(i_0_4942,plain,
( hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1))
| X1 = X2 ),
inference(rename_variables,[],[i_0_3261]) ).
cnf(i_0_4943,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk33_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321]) ).
cnf(i_0_4944,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(rename_variables,[],[i_0_3321]) ).
cnf(i_0_4945,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322]) ).
cnf(i_0_4946,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3322]) ).
cnf(i_0_4947,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338]) ).
cnf(i_0_4948,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1) ),
inference(rename_variables,[],[i_0_3338]) ).
cnf(i_0_4949,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371]) ).
cnf(i_0_4950,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(rename_variables,[],[i_0_3371]) ).
cnf(i_0_4951,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,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)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381]) ).
cnf(i_0_4952,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3381]) ).
cnf(i_0_4953,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535]) ).
cnf(i_0_4954,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_4955,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)) ),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545]) ).
cnf(i_0_4956,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X3) ),
inference(rename_variables,[],[i_0_2545]) ).
cnf(i_0_4957,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005]) ).
cnf(i_0_4958,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(rename_variables,[],[i_0_3438]) ).
cnf(i_0_4959,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X1) ),
inference(rename_variables,[],[i_0_3005]) ).
cnf(i_0_4960,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool))),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289]) ).
cnf(i_0_4961,plain,
( c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Olinorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3289]) ).
cnf(i_0_4962,plain,
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3))),X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X3)),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366]) ).
cnf(i_0_4963,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,X3)),X4),X5),X6)
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2366]) ).
cnf(i_0_4964,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2))),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378]) ).
cnf(i_0_4965,plain,
( ~ 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))
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2378]) ).
cnf(i_0_4966,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641]) ).
cnf(i_0_4967,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4968,plain,
( 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,X3,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X4) ),
inference(rename_variables,[],[i_0_2641]) ).
cnf(i_0_4969,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642]) ).
cnf(i_0_4970,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X4) ),
inference(rename_variables,[],[i_0_2642]) ).
cnf(i_0_4971,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))),X2),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751]) ).
cnf(i_0_4972,plain,
( 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(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2751]) ).
cnf(i_0_4973,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755]) ).
cnf(i_0_4974,plain,
( 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__cancel__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2755]) ).
cnf(i_0_4975,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_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990]) ).
cnf(i_0_4976,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X3,X2) ),
inference(rename_variables,[],[i_0_2990]) ).
cnf(i_0_4977,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_4893,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990,i_0_3317]) ).
cnf(i_0_4978,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rename_variables,[],[i_0_3400]) ).
cnf(i_0_4979,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3317]) ).
cnf(i_0_4980,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_4893,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_4908,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3750,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3937,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3716,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990,i_0_3317,i_0_3364,i_0_3048]) ).
cnf(i_0_4981,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4982,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X3)
| ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2) ),
inference(rename_variables,[],[i_0_3048]) ).
cnf(i_0_4983,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_4893,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_4908,i_0_4981,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3750,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3937,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3716,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990,i_0_3317,i_0_3364,i_0_3048,i_0_2623]) ).
cnf(i_0_4984,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),
inference(rename_variables,[],[i_0_3538]) ).
cnf(i_0_4985,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X5))
| ~ class_Groups_Oordered__ab__semigroup__add(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X5) ),
inference(rename_variables,[],[i_0_2623]) ).
cnf(i_0_4986,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))))) ),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_4893,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_4908,i_0_4981,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3750,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3937,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3716,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990,i_0_3317,i_0_3364,i_0_3048,i_0_2623,i_0_2882]) ).
cnf(i_0_4987,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rename_variables,[],[i_0_2882]) ).
cnf(i_0_4988,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_t____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(scs_inference,[],[i_0_2344,i_0_4137,i_0_4358,i_0_4658,i_0_4138,i_0_4183,i_0_4151,i_0_4252,i_0_4255,i_0_4281,i_0_4336,i_0_4857,i_0_4861,i_0_4154,i_0_4339,i_0_4731,i_0_4815,i_0_4884,i_0_3427,i_0_4258,i_0_4402,i_0_4470,i_0_4490,i_0_3565,i_0_4235,i_0_4367,i_0_4387,i_0_4390,i_0_4393,i_0_4405,i_0_4410,i_0_4476,i_0_4483,i_0_4496,i_0_4516,i_0_4519,i_0_4528,i_0_4838,i_0_4841,i_0_4860,i_0_3566,i_0_4221,i_0_4224,i_0_4229,i_0_4413,i_0_4444,i_0_4500,i_0_4508,i_0_4819,i_0_4850,i_0_4869,i_0_3567,i_0_4206,i_0_4272,i_0_4275,i_0_4288,i_0_4297,i_0_4473,i_0_4489,i_0_4499,i_0_4543,i_0_4546,i_0_4555,i_0_4558,i_0_4563,i_0_4566,i_0_4577,i_0_4835,i_0_4853,i_0_4157,i_0_4420,i_0_4702,i_0_4123,i_0_4303,i_0_4396,i_0_4438,i_0_4441,i_0_4486,i_0_4522,i_0_4525,i_0_4552,i_0_4569,i_0_4584,i_0_4589,i_0_4856,i_0_4864,i_0_4124,i_0_4108,i_0_4155,i_0_4156,i_0_4110,i_0_3329,i_0_4423,i_0_4432,i_0_4435,i_0_3640,i_0_2938,i_0_4261,i_0_2939,i_0_4399,i_0_4812,i_0_3169,i_0_3170,i_0_4238,i_0_4241,i_0_4447,i_0_4870,i_0_3171,i_0_4417,i_0_4448,i_0_4820,i_0_3400,i_0_4493,i_0_4893,i_0_3538,i_0_4414,i_0_4504,i_0_4627,i_0_4908,i_0_4981,i_0_3541,i_0_3266,i_0_3438,i_0_4620,i_0_4630,i_0_4915,i_0_3736,i_0_3737,i_0_3738,i_0_3739,i_0_3741,i_0_3742,i_0_3743,i_0_3748,i_0_3749,i_0_3750,i_0_3751,i_0_3761,i_0_3762,i_0_3769,i_0_3770,i_0_3771,i_0_3798,i_0_3799,i_0_3823,i_0_3845,i_0_3847,i_0_3848,i_0_3851,i_0_3852,i_0_3856,i_0_3890,i_0_3892,i_0_3937,i_0_3520,i_0_3522,i_0_3632,i_0_2826,i_0_3125,i_0_3628,i_0_4309,i_0_4382,i_0_4384,i_0_4503,i_0_4667,i_0_4670,i_0_4681,i_0_4684,i_0_4693,i_0_4711,i_0_4726,i_0_4729,i_0_4764,i_0_4766,i_0_4768,i_0_4880,i_0_3401,i_0_4215,i_0_4267,i_0_2803,i_0_4246,i_0_4460,i_0_4826,i_0_2984,i_0_4218,i_0_4232,i_0_4249,i_0_4291,i_0_4294,i_0_4300,i_0_4451,i_0_4549,i_0_4572,i_0_4830,i_0_3167,i_0_4306,i_0_4613,i_0_3528,i_0_3529,i_0_4469,i_0_3214,i_0_3545,i_0_3546,i_0_3548,i_0_3549,i_0_3550,i_0_3551,i_0_3028,i_0_3024,i_0_3166,i_0_3524,i_0_4647,i_0_3564,i_0_2816,i_0_2432,i_0_2358,i_0_2422,i_0_4426,i_0_2352,i_0_2339,i_0_2581,i_0_3744,i_0_3745,i_0_3938,i_0_3309,i_0_3717,i_0_3721,i_0_3725,i_0_3726,i_0_3727,i_0_3731,i_0_3752,i_0_3754,i_0_3755,i_0_3756,i_0_3758,i_0_3759,i_0_3760,i_0_3763,i_0_3764,i_0_3765,i_0_3766,i_0_3767,i_0_3772,i_0_3773,i_0_3774,i_0_3778,i_0_3782,i_0_3786,i_0_3789,i_0_3790,i_0_3792,i_0_3794,i_0_3800,i_0_3803,i_0_3806,i_0_3809,i_0_3813,i_0_3817,i_0_3824,i_0_3828,i_0_3829,i_0_3830,i_0_3832,i_0_3835,i_0_3837,i_0_3841,i_0_3842,i_0_3853,i_0_3858,i_0_3860,i_0_3862,i_0_3863,i_0_3865,i_0_3868,i_0_3870,i_0_3874,i_0_3878,i_0_3879,i_0_3881,i_0_3883,i_0_3884,i_0_3885,i_0_3886,i_0_3887,i_0_3893,i_0_3894,i_0_3897,i_0_3901,i_0_3905,i_0_3909,i_0_3913,i_0_3917,i_0_3920,i_0_3922,i_0_3926,i_0_3934,i_0_3936,i_0_3708,i_0_3711,i_0_3716,i_0_3504,i_0_2914,i_0_2363,i_0_3147,i_0_3246,i_0_3323,i_0_3536,i_0_2665,i_0_2666,i_0_2685,i_0_2687,i_0_2688,i_0_2764,i_0_2805,i_0_2845,i_0_2858,i_0_2859,i_0_2860,i_0_2883,i_0_2926,i_0_2936,i_0_2937,i_0_2953,i_0_2959,i_0_2961,i_0_3032,i_0_3033,i_0_3059,i_0_3136,i_0_3137,i_0_3163,i_0_3173,i_0_3174,i_0_3179,i_0_3180,i_0_3181,i_0_3182,i_0_3209,i_0_3211,i_0_3222,i_0_3234,i_0_3239,i_0_3244,i_0_3299,i_0_3303,i_0_3361,i_0_3362,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_3506,i_0_4093,i_0_4094,i_0_4097,i_0_4098,i_0_4113,i_0_3940,i_0_3960,i_0_3972,i_0_3995,i_0_3285,i_0_3505,i_0_2571,i_0_2675,i_0_3093,i_0_3206,i_0_3208,i_0_3294,i_0_3495,i_0_3496,i_0_3497,i_0_3999,i_0_4000,i_0_4001,i_0_2357,i_0_2365,i_0_2367,i_0_2368,i_0_2370,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2379,i_0_2381,i_0_2403,i_0_2404,i_0_2410,i_0_2411,i_0_2412,i_0_2413,i_0_2466,i_0_2467,i_0_2562,i_0_2563,i_0_2575,i_0_2577,i_0_2643,i_0_2645,i_0_2753,i_0_2763,i_0_2789,i_0_2813,i_0_2850,i_0_2881,i_0_2893,i_0_2894,i_0_2895,i_0_2896,i_0_2897,i_0_2900,i_0_2913,i_0_2915,i_0_2916,i_0_2998,i_0_2999,i_0_3003,i_0_3004,i_0_3013,i_0_3015,i_0_3016,i_0_3018,i_0_3020,i_0_3022,i_0_3034,i_0_3039,i_0_3045,i_0_3047,i_0_3061,i_0_3070,i_0_3071,i_0_3072,i_0_3073,i_0_3074,i_0_3075,i_0_3076,i_0_3077,i_0_3080,i_0_3081,i_0_3082,i_0_3083,i_0_3084,i_0_3085,i_0_3086,i_0_3094,i_0_3101,i_0_3102,i_0_3103,i_0_3104,i_0_3120,i_0_3121,i_0_3123,i_0_3126,i_0_3129,i_0_3130,i_0_3131,i_0_3135,i_0_3139,i_0_3150,i_0_3151,i_0_3152,i_0_3177,i_0_3204,i_0_3226,i_0_3228,i_0_3296,i_0_3297,i_0_3298,i_0_3314,i_0_3318,i_0_3334,i_0_3335,i_0_3336,i_0_3339,i_0_3340,i_0_3353,i_0_3355,i_0_3356,i_0_3357,i_0_3388,i_0_3389,i_0_3391,i_0_3392,i_0_3451,i_0_3462,i_0_3475,i_0_3540,i_0_3576,i_0_3578,i_0_3579,i_0_3580,i_0_3582,i_0_3590,i_0_3591,i_0_3603,i_0_3604,i_0_3605,i_0_3606,i_0_3607,i_0_3608,i_0_3609,i_0_3610,i_0_3621,i_0_3622,i_0_3623,i_0_3941,i_0_4003,i_0_4012,i_0_4013,i_0_4014,i_0_4017,i_0_4027,i_0_4028,i_0_4035,i_0_4037,i_0_4050,i_0_4055,i_0_4062,i_0_4064,i_0_4067,i_0_4071,i_0_4002,i_0_4005,i_0_4006,i_0_4036,i_0_4060,i_0_4063,i_0_4068,i_0_4069,i_0_4070,i_0_4072,i_0_4073,i_0_4074,i_0_4075,i_0_4076,i_0_4077,i_0_4078,i_0_4079,i_0_4080,i_0_4082,i_0_4083,i_0_4084,i_0_4085,i_0_4086,i_0_4087,i_0_2846,i_0_3090,i_0_3091,i_0_3327,i_0_4008,i_0_4009,i_0_4010,i_0_4011,i_0_4016,i_0_4018,i_0_4019,i_0_4020,i_0_4021,i_0_4022,i_0_4023,i_0_4024,i_0_4026,i_0_4029,i_0_4030,i_0_4031,i_0_4032,i_0_4033,i_0_4038,i_0_4039,i_0_4040,i_0_4041,i_0_4042,i_0_4043,i_0_4045,i_0_4046,i_0_4052,i_0_4053,i_0_4056,i_0_2604,i_0_3275,i_0_2438,i_0_2468,i_0_2624,i_0_2625,i_0_2626,i_0_2657,i_0_2717,i_0_2718,i_0_2719,i_0_2720,i_0_2724,i_0_2740,i_0_2765,i_0_2766,i_0_2767,i_0_2768,i_0_2769,i_0_2788,i_0_2854,i_0_2879,i_0_2880,i_0_2944,i_0_2976,i_0_2977,i_0_3113,i_0_3195,i_0_3197,i_0_3324,i_0_3343,i_0_2541,i_0_2862,i_0_2863,i_0_2888,i_0_4140,i_0_2775,i_0_2832,i_0_2843,i_0_2844,i_0_2934,i_0_2935,i_0_2955,i_0_2957,i_0_3157,i_0_3162,i_0_3212,i_0_3261,i_0_3321,i_0_3322,i_0_3338,i_0_3371,i_0_3381,i_0_3535,i_0_2545,i_0_3005,i_0_3289,i_0_2366,i_0_2378,i_0_2641,i_0_2642,i_0_2751,i_0_2755,i_0_2903,i_0_2990,i_0_3317,i_0_3364,i_0_3048,i_0_2623,i_0_2882,i_0_2941]) ).
cnf(i_0_4989,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(rename_variables,[],[i_0_2941]) ).
cnf(i_0_4990,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X1),
inference(rename_variables,[],[i_0_3169]) ).
cnf(i_0_4991,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4992,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_3565]) ).
cnf(i_0_4993,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4994,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X1),
inference(rename_variables,[],[i_0_3566]) ).
cnf(i_0_4996,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,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4228,i_0_3114]) ).
cnf(i_0_4997,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rename_variables,[],[i_0_4228]) ).
cnf(i_0_4998,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(rename_variables,[],[i_0_3114]) ).
cnf(i_0_4999,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4208,i_0_4228,i_0_3114,i_0_2804]) ).
cnf(i_0_5000,plain,
c_Orderings_Oord__class_Oless__eq(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(rename_variables,[],[i_0_4208]) ).
cnf(i_0_5001,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(rename_variables,[],[i_0_2804]) ).
cnf(i_0_5002,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X1)),X2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4208,i_0_4347,i_0_4228,i_0_3114,i_0_2804,i_0_3380]) ).
cnf(i_0_5003,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,X1)),X2),X3) = X3,
inference(rename_variables,[],[i_0_4347]) ).
cnf(i_0_5004,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) ),
inference(rename_variables,[],[i_0_3380]) ).
cnf(i_0_5005,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),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)),X2),X3)),X3),
inference(scs_inference,[],[i_0_4208,i_0_4347,i_0_4398,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779]) ).
cnf(i_0_5006,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,X1)),X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2),X3)),X3),
inference(rename_variables,[],[i_0_4398]) ).
cnf(i_0_5007,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2779]) ).
cnf(i_0_5008,plain,
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),X2),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,X2)),X3),X1))),
inference(scs_inference,[],[i_0_4208,i_0_4347,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585]) ).
cnf(i_0_5009,plain,
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,X2)),X3),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3),X1))),
inference(rename_variables,[],[i_0_4416]) ).
cnf(i_0_5010,plain,
( ~ 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))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2585]) ).
cnf(i_0_5011,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X2),
inference(scs_inference,[],[i_0_4208,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778]) ).
cnf(i_0_5012,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X2),
inference(rename_variables,[],[i_0_4263]) ).
cnf(i_0_5013,plain,
( 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,X3,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2778]) ).
cnf(i_0_5014,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk2_0),
inference(scs_inference,[],[i_0_4208,i_0_3547,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246]) ).
cnf(i_0_5015,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3246]) ).
cnf(i_0_5016,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4208,i_0_3547,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323]) ).
cnf(i_0_5017,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(rename_variables,[],[i_0_3323]) ).
cnf(i_0_5018,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)),
inference(scs_inference,[],[i_0_4809,i_0_4208,i_0_3547,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536]) ).
cnf(i_0_5019,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3536]) ).
cnf(i_0_5020,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2),X2))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_3547,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764]) ).
cnf(i_0_5021,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(rename_variables,[],[i_0_4362]) ).
cnf(i_0_5022,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2)) ),
inference(rename_variables,[],[i_0_2764]) ).
cnf(i_0_5023,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_3547,i_0_4347,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805]) ).
cnf(i_0_5024,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(rename_variables,[],[i_0_2805]) ).
cnf(i_0_5025,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_3547,i_0_4347,i_0_4214,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860]) ).
cnf(i_0_5026,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rename_variables,[],[i_0_4214]) ).
cnf(i_0_5027,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2860]) ).
cnf(i_0_5028,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1))))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4263,i_0_4398,i_0_4416,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882]) ).
cnf(i_0_5029,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rename_variables,[],[i_0_2882]) ).
cnf(i_0_5030,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4263,i_0_4398,i_0_4416,i_0_4886,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883]) ).
cnf(i_0_5031,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),X1),
inference(rename_variables,[],[i_0_4886]) ).
cnf(i_0_5032,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) ),
inference(rename_variables,[],[i_0_2883]) ).
cnf(i_0_5033,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_4263,i_0_4398,i_0_4416,i_0_4886,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937]) ).
cnf(i_0_5034,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(rename_variables,[],[i_0_4863]) ).
cnf(i_0_5035,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(rename_variables,[],[i_0_2937]) ).
cnf(i_0_5036,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941]) ).
cnf(i_0_5037,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(rename_variables,[],[i_0_4973]) ).
cnf(i_0_5038,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(rename_variables,[],[i_0_2941]) ).
cnf(i_0_5039,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X2),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955]) ).
cnf(i_0_5040,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X2),
inference(rename_variables,[],[i_0_4822]) ).
cnf(i_0_5041,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(rename_variables,[],[i_0_2955]) ).
cnf(i_0_5042,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033]) ).
cnf(i_0_5043,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(rename_variables,[],[i_0_3033]) ).
cnf(i_0_5044,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059]) ).
cnf(i_0_5045,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5046,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2),X1) ),
inference(rename_variables,[],[i_0_3059]) ).
cnf(i_0_5047,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) != X1,
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163]) ).
cnf(i_0_5048,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(rename_variables,[],[i_0_4863]) ).
cnf(i_0_5049,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(rename_variables,[],[i_0_3163]) ).
cnf(i_0_5050,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173]) ).
cnf(i_0_5051,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,X1))))),
inference(rename_variables,[],[i_0_4277]) ).
cnf(i_0_5052,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(rename_variables,[],[i_0_3173]) ).
cnf(i_0_5053,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(esk2_0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181]) ).
cnf(i_0_5054,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rename_variables,[],[i_0_3181]) ).
cnf(i_0_5055,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(esk2_0),esk2_0),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209]) ).
cnf(i_0_5056,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,esk3_1(X1),X1) ),
inference(rename_variables,[],[i_0_3209]) ).
cnf(i_0_5057,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4347,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211]) ).
cnf(i_0_5058,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(rename_variables,[],[i_0_3211]) ).
cnf(i_0_5059,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4809,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4478,i_0_4347,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239]) ).
cnf(i_0_5060,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2) ),
inference(rename_variables,[],[i_0_3239]) ).
cnf(i_0_5061,plain,
~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X1,X2,hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____)),v_k____)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4478,i_0_4347,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299]) ).
cnf(i_0_5062,plain,
( hAPP(X1,X2) = hAPP(X1,X3)
| ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X4,X5,X1) ),
inference(rename_variables,[],[i_0_3299]) ).
cnf(i_0_5063,plain,
c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_4478,i_0_4347,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303]) ).
cnf(i_0_5064,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) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1) ),
inference(rename_variables,[],[i_0_3303]) ).
cnf(i_0_5065,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),X2)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390]) ).
cnf(i_0_5066,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = X1,
inference(rename_variables,[],[i_0_3168]) ).
cnf(i_0_5067,plain,
( X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3390]) ).
cnf(i_0_5068,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))) != X1,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397]) ).
cnf(i_0_5069,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) != X1,
inference(rename_variables,[],[i_0_4280]) ).
cnf(i_0_5070,plain,
( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) != X2 ),
inference(rename_variables,[],[i_0_3397]) ).
cnf(i_0_5071,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406]) ).
cnf(i_0_5072,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3406]) ).
cnf(i_0_5073,plain,
c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) != X1,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410]) ).
cnf(i_0_5074,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X2 != X1 ),
inference(rename_variables,[],[i_0_3410]) ).
cnf(i_0_5075,plain,
X1 != c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411]) ).
cnf(i_0_5076,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3411]) ).
cnf(i_0_5077,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != esk2_0,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412]) ).
cnf(i_0_5078,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3412]) ).
cnf(i_0_5079,plain,
c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463]) ).
cnf(i_0_5080,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(rename_variables,[],[i_0_4863]) ).
cnf(i_0_5081,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(rename_variables,[],[i_0_3463]) ).
cnf(i_0_5082,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465]) ).
cnf(i_0_5083,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),X1),
inference(rename_variables,[],[i_0_4886]) ).
cnf(i_0_5084,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(rename_variables,[],[i_0_3465]) ).
cnf(i_0_5085,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),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3),X1)),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(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094]) ).
cnf(i_0_5086,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(rename_variables,[],[i_0_4094]) ).
cnf(i_0_5087,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),X1),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113]) ).
cnf(i_0_5088,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(rename_variables,[],[i_0_4113]) ).
cnf(i_0_5089,plain,
c_Rings_Odvd__class_Odvd(tc_RealDef_Oreal,X1,X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505]) ).
cnf(i_0_5090,plain,
( ~ class_Rings_Ocomm__semiring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3505]) ).
cnf(i_0_5091,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147]) ).
cnf(i_0_5092,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5093,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2) ),
inference(rename_variables,[],[i_0_3147]) ).
cnf(i_0_5094,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),X2),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685]) ).
cnf(i_0_5095,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_5096,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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X3),X2) ),
inference(rename_variables,[],[i_0_2685]) ).
cnf(i_0_5097,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3),X3),X2)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687]) ).
cnf(i_0_5098,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(rename_variables,[],[i_0_4362]) ).
cnf(i_0_5099,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2687]) ).
cnf(i_0_5100,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),X2)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688]) ).
cnf(i_0_5101,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rename_variables,[],[i_0_4214]) ).
cnf(i_0_5102,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X3,X2)) ),
inference(rename_variables,[],[i_0_2688]) ).
cnf(i_0_5103,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X3),X2),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775]) ).
cnf(i_0_5104,plain,
( 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))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ),
inference(rename_variables,[],[i_0_2775]) ).
cnf(i_0_5105,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,c_Groups_Oone__class_Oone(tc_Int_Oint))),X3),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845]) ).
cnf(i_0_5106,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),X3),X3),
inference(rename_variables,[],[i_0_4404]) ).
cnf(i_0_5107,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(rename_variables,[],[i_0_2845]) ).
cnf(i_0_5108,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935]) ).
cnf(i_0_5109,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)),X1),
inference(rename_variables,[],[i_0_4251]) ).
cnf(i_0_5110,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(rename_variables,[],[i_0_2935]) ).
cnf(i_0_5111,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936]) ).
cnf(i_0_5112,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_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),X1),
inference(rename_variables,[],[i_0_4863]) ).
cnf(i_0_5113,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(rename_variables,[],[i_0_2936]) ).
cnf(i_0_5114,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X2),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961]) ).
cnf(i_0_5115,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)),X1),
inference(rename_variables,[],[i_0_4921]) ).
cnf(i_0_5116,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,X3) ),
inference(rename_variables,[],[i_0_2961]) ).
cnf(i_0_5117,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136]) ).
cnf(i_0_5118,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),X1),
inference(rename_variables,[],[i_0_4271]) ).
cnf(i_0_5119,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) ),
inference(rename_variables,[],[i_0_3136]) ).
cnf(i_0_5120,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179]) ).
cnf(i_0_5121,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5122,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(rename_variables,[],[i_0_3179]) ).
cnf(i_0_5123,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182]) ).
cnf(i_0_5124,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),X1),
inference(rename_variables,[],[i_0_4271]) ).
cnf(i_0_5125,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(rename_variables,[],[i_0_3182]) ).
cnf(i_0_5126,plain,
c_RComplete_Onatfloor(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))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361]) ).
cnf(i_0_5127,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatfloor(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3361]) ).
cnf(i_0_5128,plain,
c_RComplete_Onatceiling(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))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362]) ).
cnf(i_0_5129,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_RComplete_Onatceiling(X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(rename_variables,[],[i_0_3362]) ).
cnf(i_0_5130,plain,
c_Orderings_Oord__class_Oless__eq(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,tc_HOL_Obool,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))),X1,X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506]) ).
cnf(i_0_5131,plain,
( ~ class_Orderings_Opreorder(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X2,X2) ),
inference(rename_variables,[],[i_0_3506]) ).
cnf(i_0_5132,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) != X2,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535]) ).
cnf(i_0_5133,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| X1 != X2 ),
inference(rename_variables,[],[i_0_3535]) ).
cnf(i_0_5134,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843]) ).
cnf(i_0_5135,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3),X1)),
inference(rename_variables,[],[i_0_4409]) ).
cnf(i_0_5136,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(rename_variables,[],[i_0_2843]) ).
cnf(i_0_5137,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844]) ).
cnf(i_0_5138,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(rename_variables,[],[i_0_2844]) ).
cnf(i_0_5139,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3),X3)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858]) ).
cnf(i_0_5140,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(rename_variables,[],[i_0_4362]) ).
cnf(i_0_5141,plain,
( ~ 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,X1,X3) ),
inference(rename_variables,[],[i_0_2858]) ).
cnf(i_0_5142,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X3),X3)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859]) ).
cnf(i_0_5143,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(rename_variables,[],[i_0_4362]) ).
cnf(i_0_5144,plain,
( ~ 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(rename_variables,[],[i_0_2859]) ).
cnf(i_0_5145,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_3(X1,X2,esk2_0)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926]) ).
cnf(i_0_5146,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk35_3(X2,X3,X1)) ),
inference(rename_variables,[],[i_0_2926]) ).
cnf(i_0_5147,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137]) ).
cnf(i_0_5148,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5149,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)) ),
inference(rename_variables,[],[i_0_3137]) ).
cnf(i_0_5150,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X3)),X2),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157]) ).
cnf(i_0_5151,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X2)
| X1 = X3 ),
inference(rename_variables,[],[i_0_3157]) ).
cnf(i_0_5152,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(esk2_0)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180]) ).
cnf(i_0_5153,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),esk3_1(X1)) ),
inference(rename_variables,[],[i_0_3180]) ).
cnf(i_0_5154,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212]) ).
cnf(i_0_5155,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),
inference(rename_variables,[],[i_0_4366]) ).
cnf(i_0_5156,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(rename_variables,[],[i_0_3212]) ).
cnf(i_0_5157,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222]) ).
cnf(i_0_5158,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_4502]) ).
cnf(i_0_5159,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(rename_variables,[],[i_0_3222]) ).
cnf(i_0_5160,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234]) ).
cnf(i_0_5161,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rename_variables,[],[i_0_3530]) ).
cnf(i_0_5162,plain,
( X1 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3234]) ).
cnf(i_0_5163,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244]) ).
cnf(i_0_5164,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(rename_variables,[],[i_0_3244]) ).
cnf(i_0_5165,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321]) ).
cnf(i_0_5166,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X2,X1) ),
inference(rename_variables,[],[i_0_3321]) ).
cnf(i_0_5167,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322]) ).
cnf(i_0_5168,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X1) ),
inference(rename_variables,[],[i_0_3322]) ).
cnf(i_0_5169,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),X3),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957]) ).
cnf(i_0_5170,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2),X2),
inference(rename_variables,[],[i_0_4822]) ).
cnf(i_0_5171,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,X3) ),
inference(rename_variables,[],[i_0_2957]) ).
cnf(i_0_5172,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959]) ).
cnf(i_0_5173,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,X1)),X1),
inference(rename_variables,[],[i_0_4921]) ).
cnf(i_0_5174,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(rename_variables,[],[i_0_2959]) ).
cnf(i_0_5175,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953]) ).
cnf(i_0_5176,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2)),
inference(rename_variables,[],[i_0_4257]) ).
cnf(i_0_5177,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X3) ),
inference(rename_variables,[],[i_0_2953]) ).
cnf(i_0_5178,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371]) ).
cnf(i_0_5179,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(rename_variables,[],[i_0_3371]) ).
cnf(i_0_5180,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,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____))) != v_m____,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995]) ).
cnf(i_0_5181,plain,
X1 = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940]) ).
cnf(i_0_5182,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3812,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725]) ).
cnf(i_0_5183,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)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) ),
inference(rename_variables,[],[i_0_2725]) ).
cnf(i_0_5184,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3812,i_0_3768,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749]) ).
cnf(i_0_5185,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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)),X1),
inference(rename_variables,[],[i_0_4883]) ).
cnf(i_0_5186,plain,
( 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(X1)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,X4) ),
inference(rename_variables,[],[i_0_2749]) ).
cnf(i_0_5187,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3812,i_0_3768,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752]) ).
cnf(i_0_5188,plain,
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_2752]) ).
cnf(i_0_5189,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3812,i_0_3768,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795]) ).
cnf(i_0_5190,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(rename_variables,[],[i_0_2795]) ).
cnf(i_0_5191,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_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4347,i_0_4741,i_0_4280,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3761,i_0_3812,i_0_3768,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035]) ).
cnf(i_0_5192,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),
inference(rename_variables,[],[i_0_4524]) ).
cnf(i_0_5193,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(rename_variables,[],[i_0_3035]) ).
cnf(i_0_5194,plain,
X1 = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3761,i_0_3812,i_0_3768,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183]) ).
cnf(i_0_5195,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X3,X1))),X2),
inference(rename_variables,[],[i_0_4935]) ).
cnf(i_0_5196,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) != X1,
inference(rename_variables,[],[i_0_4280]) ).
cnf(i_0_5197,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)
| X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1 = X3 ),
inference(rename_variables,[],[i_0_3183]) ).
cnf(i_0_5198,plain,
class_Fields_Olinordered__field(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),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054]) ).
cnf(i_0_5199,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5200,plain,
class_Rings_Odivision__ring(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3836,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004]) ).
cnf(i_0_5201,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5202,plain,
class_Fields_Ofield(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3821,i_0_3836,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007]) ).
cnf(i_0_5203,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5204,plain,
class_RealVector_Oreal__normed__vector(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3821,i_0_3836,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025]) ).
cnf(i_0_5205,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5206,plain,
class_Fields_Ofield__inverse__zero(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),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061]) ).
cnf(i_0_5207,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5208,plain,
class_Rings_Odivision__ring__inverse__zero(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3840,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065]) ).
cnf(i_0_5209,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5210,plain,
class_RealVector_Oreal__div__algebra(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081]) ).
cnf(i_0_5211,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5212,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,X1),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3800,i_0_3772,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095]) ).
cnf(i_0_5213,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4360]) ).
cnf(i_0_5214,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Ouminus__class_Ouminus(X1,X3))
| ~ class_Rings_Ocomm__ring__1(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3095]) ).
cnf(i_0_5215,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3800,i_0_3772,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096]) ).
cnf(i_0_5216,plain,
c_Rings_Odvd__class_Odvd(tc_Int_Oint,X1,X1),
inference(rename_variables,[],[i_0_4360]) ).
cnf(i_0_5217,plain,
( ~ c_Rings_Odvd__class_Odvd(X1,X2,c_Groups_Oabs__class_Oabs(X1,X3))
| ~ class_Rings_Olinordered__idom(X1)
| c_Rings_Odvd__class_Odvd(X1,X2,X3) ),
inference(rename_variables,[],[i_0_3096]) ).
cnf(i_0_5218,plain,
class_RealVector_Oreal__normed__algebra__1(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3932,i_0_3800,i_0_3772,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034]) ).
cnf(i_0_5219,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5220,plain,
class_RealVector_Oreal__normed__div__algebra(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3932,i_0_3800,i_0_3772,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044]) ).
cnf(i_0_5221,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5222,plain,
class_RealVector_Oreal__normed__algebra(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),tc_Complex_Ocomplex)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047]) ).
cnf(i_0_5223,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5224,plain,
class_RealVector_Oreal__algebra__1(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),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051]) ).
cnf(i_0_5225,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5226,plain,
class_Fields_Olinordered__field__inverse__zero(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),tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057]) ).
cnf(i_0_5227,plain,
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,X2)),X3),X1),
inference(rename_variables,[],[i_0_4349]) ).
cnf(i_0_5228,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644]) ).
cnf(i_0_5229,plain,
( 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,X1,X3))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X1) ),
inference(rename_variables,[],[i_0_2644]) ).
cnf(i_0_5230,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223]) ).
cnf(i_0_5231,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk34_2(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),tc_HOL_Obool)))),
inference(rename_variables,[],[i_0_4927]) ).
cnf(i_0_5232,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3),X1)),
inference(rename_variables,[],[i_0_4409]) ).
cnf(i_0_5233,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X2)
| X1 = X2 ),
inference(rename_variables,[],[i_0_3223]) ).
cnf(i_0_5234,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_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756]) ).
cnf(i_0_5235,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X2,X4))
| ~ c_Orderings_Oord__class_Oless(X1,X3,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_2756]) ).
cnf(i_0_5236,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),X1),X1))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917]) ).
cnf(i_0_5237,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5238,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X2)),
inference(rename_variables,[],[i_0_4362]) ).
cnf(i_0_5239,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_RealDef_Oreal(tc_Nat_Onat,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X2) ),
inference(rename_variables,[],[i_0_2917]) ).
cnf(i_0_5240,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),X1),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754]) ).
cnf(i_0_5241,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)),X1),
inference(rename_variables,[],[i_0_4886]) ).
cnf(i_0_5242,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Oplus__class_Oplus(X1,X2,X3),c_Groups_Oplus__class_Oplus(X1,X4,X3))
| ~ c_Orderings_Oord__class_Oless(X1,X2,X4)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
inference(rename_variables,[],[i_0_2754]) ).
cnf(i_0_5243,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3547,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093]) ).
cnf(i_0_5244,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),
inference(rename_variables,[],[i_0_4366]) ).
cnf(i_0_5245,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) ),
inference(rename_variables,[],[i_0_3093]) ).
cnf(i_0_5246,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,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(scs_inference,[],[i_0_4809,i_0_4212,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3761,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495]) ).
cnf(i_0_5247,plain,
( X1 != X2
| ~ class_Orderings_Oorder(X3)
| c_Orderings_Oord__class_Oless__eq(X3,X2,X1) ),
inference(rename_variables,[],[i_0_3495]) ).
cnf(i_0_5248,plain,
c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357]) ).
cnf(i_0_5249,plain,
c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,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(rename_variables,[],[i_0_4375]) ).
cnf(i_0_5250,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk22_4(X3,X2,X4,X1)),hAPP(X3,esk22_4(X3,X2,X4,X1)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X1),X2,X3)
| ~ class_Orderings_Oord(X1) ),
inference(rename_variables,[],[i_0_2357]) ).
cnf(i_0_5251,plain,
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X4))),X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X4),X2),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366]) ).
cnf(i_0_5252,plain,
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X1)),X2)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rename_variables,[],[i_0_4395]) ).
cnf(i_0_5253,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,X3)),X4),X5),X6)
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2366]) ).
cnf(i_0_5254,plain,
~ 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,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2)))),X3),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X2,X2))),X3),X1))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372]) ).
cnf(i_0_5255,plain,
~ 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,X2)),X3),X1)),
inference(rename_variables,[],[i_0_4401]) ).
cnf(i_0_5256,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1),X1),
inference(rename_variables,[],[i_0_4811]) ).
cnf(i_0_5257,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),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(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,X1,X4) ),
inference(rename_variables,[],[i_0_2372]) ).
cnf(i_0_5258,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1),X2)),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3),X4)),X4),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375]) ).
cnf(i_0_5259,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),X3),X3),
inference(rename_variables,[],[i_0_4404]) ).
cnf(i_0_5260,plain,
( ~ 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))
| 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)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2375]) ).
cnf(i_0_5261,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),X4),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3),X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376]) ).
cnf(i_0_5262,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(rename_variables,[],[i_0_4440]) ).
cnf(i_0_5263,plain,
( ~ 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))
| 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)
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2376]) ).
cnf(i_0_5264,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X4,X4))),X2),X3)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377]) ).
cnf(i_0_5265,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X1)),X2),X3),X3),
inference(rename_variables,[],[i_0_4404]) ).
cnf(i_0_5266,plain,
( ~ 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))
| 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))
| ~ class_Rings_Oordered__ring(X1) ),
inference(rename_variables,[],[i_0_2377]) ).
cnf(i_0_5267,plain,
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),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X3)),X4)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X5),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X5)),X2)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403]) ).
cnf(i_0_5268,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X2)),X3)) = X1,
inference(rename_variables,[],[i_0_4599]) ).
cnf(i_0_5269,plain,
( 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
| 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)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2403]) ).
cnf(i_0_5270,plain,
c_Groups_Oplus__class_Oplus(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),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,X1)),X2)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X3),X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X4))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404]) ).
cnf(i_0_5271,plain,
X1 = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2))),
inference(rename_variables,[],[i_0_4678]) ).
cnf(i_0_5272,plain,
( 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)
| 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)
| ~ class_Rings_Oring(X2) ),
inference(rename_variables,[],[i_0_2404]) ).
cnf(i_0_5273,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,X2,X1)),X3))) = X4,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412]) ).
cnf(i_0_5274,plain,
( 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)
| 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
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2412]) ).
cnf(i_0_5275,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2)),X3)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1)),X3),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413]) ).
cnf(i_0_5276,plain,
( 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)
| 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)
| ~ class_Rings_Oring(X1) ),
inference(rename_variables,[],[i_0_2413]) ).
cnf(i_0_5277,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X3,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467]) ).
cnf(i_0_5278,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(rename_variables,[],[i_0_4440]) ).
cnf(i_0_5279,plain,
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,c_Groups_Ominus__class_Ominus(X1,X2,X3)),X4)
| c_Orderings_Oord__class_Oless(X1,X2,c_Groups_Oplus__class_Oplus(X1,X3,X4))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(rename_variables,[],[i_0_2467]) ).
cnf(i_0_5280,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),X2)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_5278,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467,i_0_2577]) ).
cnf(i_0_5281,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(rename_variables,[],[i_0_4440]) ).
cnf(i_0_5282,plain,
( ~ 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)
| c_Orderings_Oord__class_Oless(X1,X3,X4) ),
inference(rename_variables,[],[i_0_2577]) ).
cnf(i_0_5283,plain,
c_SEQ_Odecseq(tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4377,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3738,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_5278,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467,i_0_2577,i_0_2763]) ).
cnf(i_0_5284,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,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(rename_variables,[],[i_0_4377]) ).
cnf(i_0_5285,plain,
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X2,esk34_2(X2,X1)),hAPP(X2,esk33_2(X2,X1)))
| ~ class_Orderings_Oorder(X1)
| c_SEQ_Odecseq(X1,X2) ),
inference(rename_variables,[],[i_0_2763]) ).
cnf(i_0_5286,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4377,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3738,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_5278,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467,i_0_2577,i_0_2763,i_0_2789]) ).
cnf(i_0_5287,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rename_variables,[],[i_0_4214]) ).
cnf(i_0_5288,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_Ominus__class_Ominus(tc_Nat_Onat,X2,X1),X2) ),
inference(rename_variables,[],[i_0_2789]) ).
cnf(i_0_5289,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4377,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_5237,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3738,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_5278,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4472,i_0_4450,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467,i_0_2577,i_0_2763,i_0_2789,i_0_2881]) ).
cnf(i_0_5290,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)),
inference(rename_variables,[],[i_0_4205]) ).
cnf(i_0_5291,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)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(rename_variables,[],[i_0_2881]) ).
cnf(i_0_5292,plain,
$false,
inference(scs_inference,[],[i_0_4809,i_0_4212,i_0_4375,i_0_4377,i_0_4362,i_0_5021,i_0_5098,i_0_5140,i_0_5143,i_0_4205,i_0_5045,i_0_5092,i_0_5121,i_0_5148,i_0_5237,i_0_4366,i_0_5155,i_0_4811,i_0_5095,i_0_4385,i_0_4208,i_0_4373,i_0_4957,i_0_3740,i_0_3738,i_0_3547,i_0_2836,i_0_3168,i_0_5066,i_0_3530,i_0_4847,i_0_4478,i_0_4935,i_0_4347,i_0_4349,i_0_5199,i_0_5201,i_0_5203,i_0_5205,i_0_5207,i_0_5209,i_0_5211,i_0_5219,i_0_5221,i_0_5223,i_0_5225,i_0_4599,i_0_4678,i_0_4741,i_0_4280,i_0_5069,i_0_4502,i_0_4428,i_0_4975,i_0_4422,i_0_4419,i_0_4921,i_0_5115,i_0_4588,i_0_4277,i_0_4214,i_0_5026,i_0_5101,i_0_4257,i_0_4863,i_0_5034,i_0_5048,i_0_5080,i_0_4401,i_0_4404,i_0_5106,i_0_5259,i_0_4409,i_0_5135,i_0_4927,i_0_4822,i_0_5040,i_0_4263,i_0_4398,i_0_4416,i_0_4440,i_0_5262,i_0_5278,i_0_4971,i_0_4251,i_0_4973,i_0_4883,i_0_4886,i_0_5031,i_0_5083,i_0_4271,i_0_5118,i_0_4228,i_0_4524,i_0_4395,i_0_4472,i_0_4450,i_0_4540,i_0_4937,i_0_3170,i_0_3771,i_0_3937,i_0_3028,i_0_3769,i_0_3823,i_0_3798,i_0_3851,i_0_3761,i_0_3744,i_0_3812,i_0_4360,i_0_5213,i_0_3768,i_0_3821,i_0_3825,i_0_3836,i_0_3838,i_0_3840,i_0_3895,i_0_3921,i_0_3930,i_0_3932,i_0_3883,i_0_3936,i_0_3800,i_0_3881,i_0_3772,i_0_3829,i_0_3893,i_0_3114,i_0_2804,i_0_3380,i_0_2779,i_0_2585,i_0_2778,i_0_3246,i_0_3323,i_0_3536,i_0_2764,i_0_2805,i_0_2860,i_0_2882,i_0_2883,i_0_2937,i_0_2941,i_0_2955,i_0_3033,i_0_3059,i_0_3163,i_0_3173,i_0_3181,i_0_3209,i_0_3211,i_0_3239,i_0_3299,i_0_3303,i_0_3390,i_0_3397,i_0_3406,i_0_3410,i_0_3411,i_0_3412,i_0_3463,i_0_3465,i_0_4094,i_0_4113,i_0_3505,i_0_3147,i_0_2685,i_0_2687,i_0_2688,i_0_2775,i_0_2845,i_0_2935,i_0_2936,i_0_2961,i_0_3136,i_0_3179,i_0_3182,i_0_3361,i_0_3362,i_0_3506,i_0_3535,i_0_2843,i_0_2844,i_0_2858,i_0_2859,i_0_2926,i_0_3137,i_0_3157,i_0_3180,i_0_3212,i_0_3222,i_0_3234,i_0_3244,i_0_3321,i_0_3322,i_0_2957,i_0_2959,i_0_2953,i_0_3371,i_0_3995,i_0_3940,i_0_2725,i_0_2749,i_0_2752,i_0_2795,i_0_3035,i_0_3183,i_0_4054,i_0_4004,i_0_4007,i_0_4025,i_0_4061,i_0_4065,i_0_4081,i_0_3095,i_0_3096,i_0_4034,i_0_4044,i_0_4047,i_0_4051,i_0_4057,i_0_2644,i_0_3223,i_0_2756,i_0_2917,i_0_2754,i_0_3093,i_0_3495,i_0_2357,i_0_2366,i_0_2372,i_0_2375,i_0_2376,i_0_2377,i_0_2403,i_0_2404,i_0_2412,i_0_2413,i_0_2467,i_0_2577,i_0_2763,i_0_2789,i_0_2881,i_0_2903]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW265+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n018.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 06:31:32 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 7.15/5.80 % Version : CSE_E---1.7
% 7.15/5.80 % Problem : theBenchmark.p
% 7.15/5.80 % SZS status Theorem for theBenchmark.p
% 7.15/5.80 % SZS output start CNFRefutation
% See solution above
% 46.01/31.36 % Total time : 5.455s
%------------------------------------------------------------------------------