%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG370-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : n019.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 04:08:33 PM UTC 2026
% Result : Unsatisfiable 0.96s 1.66s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 635)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
cnf(cls_pCons_1,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__local__XpCons__1(v_cs____,v_e,v_z),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_1) ).
cnf(cls_pCons_Ohyps_1,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__local__XpCons__Xhyps__1(v_cs____,v_e,v_z),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_1) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
cnf(cls_abs__diff__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).
cnf(cls_le__add__iff1_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
cnf(cls_less__add__iff1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
cnf(cls_le__add__iff2_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
cnf(cls_less__add__iff2_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
cnf(cls_CHAINED_0_01,axiom,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
cnf(cls_le__add__iff1_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
cnf(cls_less__add__iff1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
cnf(cls_le__add__iff2_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
cnf(cls_less__add__iff2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
cnf(cls_eq__add__iff2_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
cnf(cls_eq__add__iff1_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
cnf(cls_eq__add__iff1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
cnf(cls_eq__add__iff2_0,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).
cnf(cls_combine__common__factor_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_abs__diff__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
cnf(cls_abs__triangle__ineq3_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).
cnf(cls_sum__squares__le__zero__iff_2,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
cnf(cls_norm__mult__less_0,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).
cnf(cls_mult__mono_H_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
cnf(cls_mult__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).
cnf(cls_mult__less__le__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
cnf(cls_mult__le__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
cnf(cls_mult__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
cnf(cls_abs__mult__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
cnf(cls_abs__diff__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
cnf(cls_abs__diff__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
cnf(cls_left__diff__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).
cnf(cls_left__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).
cnf(cls_right__diff__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).
cnf(cls_right__distrib__number__of_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).
cnf(cls_real__mult__le__cancel__iff1_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).
cnf(cls_real__mult__le__cancel__iff2_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).
cnf(cls_real__mult__less__iff1_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_abs__triangle__ineq2_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).
cnf(cls_abs__triangle__ineq4_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq4_0) ).
cnf(cls_abs__le__mult_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
cnf(cls_abs__triangle__ineq_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).
cnf(cls_le__add__right__mono_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
cnf(cls_norm__mult__ineq_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
cnf(cls_add__le__cancel__right_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
cnf(cls_add__le__cancel__left_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
cnf(cls_add__less__cancel__right_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
cnf(cls_add__less__cancel__left_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
cnf(cls_estimate__by__abs_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).
cnf(cls_norm__ratiotest__lemma_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Otimes__class_Otimes(X3,c_RealVector_Onorm__class_Onorm(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).
cnf(cls_mult__left__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
cnf(cls_mult__mono1_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
cnf(cls_mult__right__mono_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
cnf(cls_mult__left__mono__neg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
cnf(cls_mult__right__mono__neg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_mult__right__le__one__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).
cnf(cls_mult__left__le__one__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).
cnf(cls_smult__diff__right_0,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).
cnf(cls_poly__diff_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__diff_0) ).
cnf(cls_poly__mult_0,axiom,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__mult_0) ).
cnf(cls_add__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).
cnf(cls_add__less__le__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
cnf(cls_add__le__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
cnf(cls_add__strict__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
cnf(cls_smult__diff__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__diff__left_0) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_mult__left_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
cnf(cls_mult_Odiff__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_mult__left_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
cnf(cls_mult_Oadd__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_mult_Odiff__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
cnf(cls_mult__right_Odiff_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
cnf(cls_mult__right_Oadd_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
cnf(cls_mult_Oadd__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_real__mult__le__cancel__iff2_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).
cnf(cls_real__mult__le__cancel__iff1_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).
cnf(cls_real__mult__less__mono2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).
cnf(cls_real__mult__less__iff1_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_abs__eq__mult_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).
cnf(cls_abs__eq__mult_2,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).
cnf(cls_abs__eq__mult_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).
cnf(cls_abs__eq__mult_3,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
cnf(cls_add__cancel__21_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_mult__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
cnf(cls_mult__le__0__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
cnf(cls_mult__le__0__iff_3,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
cnf(cls_mult__le__0__iff_2,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).
cnf(cls_split__mult__neg__le_1,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).
cnf(cls_split__mult__neg__le_0,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
cnf(cls_mult__le__0__iff_5,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
cnf(cls_mult__le__0__iff_4,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
cnf(cls_mult__neg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
cnf(cls_mult__pos__neg2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
cnf(cls_mult__pos__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
cnf(cls_add__neg__nonpos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
cnf(cls_add__nonpos__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
cnf(cls_add__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
cnf(cls_split__mult__pos__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
cnf(cls_less__1__mult_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
cnf(cls_mult__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
cnf(cls_add__pos__nonneg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
cnf(cls_add__nonneg__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
cnf(cls_add__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).
cnf(cls_split__mult__pos__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
cnf(cls_mult__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
cnf(cls_add__left__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
cnf(cls_add__le__cancel__left_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
cnf(cls_add__right__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
cnf(cls_add__le__cancel__right_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
cnf(cls_add__strict__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
cnf(cls_add__less__cancel__left_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
cnf(cls_add__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
cnf(cls_add__less__cancel__right_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
cnf(cls_add__increasing2_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
cnf(cls_add__increasing_0,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).
cnf(cls_add__strict__increasing_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
cnf(cls_add__strict__increasing2_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
cnf(cls_pos__add__strict_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
cnf(cls_le__number__of__eq__not__less_0,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).
cnf(cls_mult__smult__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).
cnf(cls_mult__smult__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X3,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
cnf(cls_abs__add__abs_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
cnf(cls_real__mult__order_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
cnf(cls_even__less__0__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_poly__smult_0,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).
cnf(cls_smult__smult_0,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X1),X1) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__smult_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_add__cancel__21_1,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
cnf(cls_le__eqI_1,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
cnf(cls_le__eqI_0,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
cnf(cls_less__eqI_1,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
cnf(cls_less__eqI_0,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
cnf(cls_real__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
cnf(cls_abs__mult__pos_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
cnf(cls_d1_I1_J_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_d1_I1_J_0) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_not__real__square__gt__zero_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
cnf(cls_even__less__0__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
cnf(cls_th_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_th_0) ).
cnf(cls_H_I5_J_0,axiom,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_H_I5_J_0) ).
cnf(cls_dist__le__zero__iff_0,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_0) ).
cnf(cls_dist__not__less__zero_0,axiom,
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__not__less__zero_0) ).
cnf(cls_zero__less__dist__iff_0,axiom,
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X2,X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_0) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
cnf(cls_norm__minus__commute_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__commute_0) ).
cnf(cls_abs__minus__commute_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
cnf(cls_xt1_I6_J_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
cnf(cls_order__trans_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
cnf(cls_xt1_I8_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
cnf(cls_xt1_I7_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
cnf(cls_xt1_I10_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
cnf(cls_order__less__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
cnf(cls_order__le__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
cnf(cls_order__less__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
cnf(cls_abs__mult_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).
cnf(cls_norm__mult_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).
cnf(cls_of__real__mult_0,axiom,
( c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__mult_0) ).
cnf(cls_le__number__of__eq__not__less_1,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).
cnf(cls_mult__left__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_real__le__trans_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_less__le__not__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_zero__less__two_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
cnf(cls_abs__le__D1_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).
cnf(cls_abs__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_dist__norm_0,axiom,
( c_RealVector_Odist__class_Odist(X2,X3,X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_RealVector_Odist__norm(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__norm_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_less__add__one_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__add__one_0) ).
cnf(cls_eq__eqI_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_eq__eqI_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
cnf(cls_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_zero__less__dist__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X3,X1),tc_RealDef_Oreal)
| X2 = X3
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__dist__iff_1) ).
cnf(cls_real__mult__right__cancel_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).
cnf(cls_real__mult__left__cancel_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
cnf(cls_dist__le__zero__iff_1,axiom,
( c_lessequals(c_RealVector_Odist__class_Odist(X2,X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__le__zero__iff_1) ).
cnf(cls_zero__le__dist_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__dist_0) ).
cnf(cls_real__le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_add__diff__cancel_0,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
cnf(cls_diff__add__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
cnf(cls_dist__complex__def_0,axiom,
c_RealVector_Odist__class_Odist(X1,X2,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__complex__def_0) ).
cnf(cls_abs__mult__self_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(cls_not__real__square__gt__zero_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).
cnf(cls_zero__less__abs__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
cnf(cls_zero__less__norm__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).
cnf(cls_abs__number__of_1,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
cnf(cls_pCons_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__local__XpCons__1(v_cs____,v_e,v_z),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_0) ).
cnf(cls_pCons_Ohyps_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__local__XpCons__Xhyps__1(v_cs____,v_e,v_z),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_0) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
cnf(cls_order__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
cnf(cls_order__le__less_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
cnf(cls_order__le__neq__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
cnf(cls_order__neq__le__trans_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
cnf(cls_xt1_I12_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
cnf(cls_xt1_I11_J_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
cnf(cls_CHAINED_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_abs__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
cnf(cls_order__le__less_1,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_order__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
cnf(cls_abs__not__less__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
cnf(cls_norm__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).
cnf(cls_real__less__def_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_real__less__def_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).
cnf(cls_norm__not__less__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
cnf(cls_linorder__neqE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
cnf(cls_linorder__less__linear_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
cnf(cls_linorder__neqE__ordered__idom_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
cnf(cls_abs__of__nonneg_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).
cnf(cls_abs__of__pos_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
cnf(cls_linorder__linear_0,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
cnf(cls_linorder__not__le_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
cnf(cls_not__leE_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
cnf(cls_linorder__not__less_0,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_dist__commute_0,axiom,
( c_RealVector_Odist__class_Odist(X2,X3,X1) = c_RealVector_Odist__class_Odist(X3,X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__commute_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_not__one__le__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).
cnf(cls_not__one__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_real__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).
cnf(cls_abs__le__zero__iff_1,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_right__minus__eq_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
cnf(cls_norm__le__zero__iff_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).
cnf(cls_zero__less__abs__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
cnf(cls_dist__eq__0__iff_0,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| c_RealVector_Odist__class_Odist(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__eq__0__iff_0) ).
cnf(cls_zero__less__norm__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).
cnf(cls_abs__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_abs__if__lattice_1,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
cnf(cls_norm__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
cnf(cls_abs__ge__self_0,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).
cnf(cls_abs__if_1,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).
cnf(cls_double__eq__0__iff_1,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
cnf(cls_zero__le__one_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).
cnf(cls_zero__less__one_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
cnf(cls_mult__left_Ozero_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
cnf(cls_mult_Ozero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
cnf(cls_mult__zero__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
cnf(cls_mult_Ozero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
cnf(cls_mult__right_Ozero_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).
cnf(cls_mult__zero__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
cnf(cls_mult__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).
cnf(cls_mult__1__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).
cnf(cls_smult__1__left_0,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
cnf(cls_add__0__left_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_diff__0__right_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
cnf(cls_mult__1__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
cnf(cls_diff__self_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__self_0) ).
cnf(cls_right__minus__eq_1,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
cnf(cls_dist__self_0,axiom,
( c_RealVector_Odist__class_Odist(X2,X2,X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dist__self_0) ).
cnf(cls_mult__idem_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_real__mult__is__one_1,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__is__one_1) ).
cnf(cls_abs__idempotent_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
cnf(cls_eq__number__of_0,axiom,
( X2 = X3
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
cnf(cls_one0_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one0_0) ).
cnf(cls_real__mult__1_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__1_0) ).
cnf(cls_d1_I2_J_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_d1_I2_J_0) ).
cnf(cls_ep_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ep_0) ).
cnf(cls_H_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_H_I1_J_0) ).
cnf(cls_H_I2_J_0,axiom,
c_HOL_Oord__class_Oless(v_da____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_H_I2_J_0) ).
cnf(cls_of__real__eq__iff_0,axiom,
( X2 = X3
| ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) != c_RealVector_Oof__real(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
cnf(cls_real__le__refl_0,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(cls_abs__eq__0_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
cnf(cls_of__real__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).
cnf(cls_norm__eq__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X2,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
cnf(cls_of__real_Ozero_0,axiom,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).
cnf(cls_abs__one_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__one_0) ).
cnf(cls_abs__eq__0_1,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
cnf(cls_norm__one_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).
cnf(cls_norm__zero_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).
cnf(cls_of__real__1_0,axiom,
( c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__1_0) ).
cnf(cls_of__real__0_0,axiom,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).
cnf(cls_zero__neq__one_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
cnf(cls_one__neq__zero_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,axiom,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber,axiom,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
cnf(clsarity_Polynomial__Opoly__Int_Oring__char__0,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(cls_real__zero__not__eq__one_0,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Odist__norm,axiom,
class_RealVector_Odist__norm(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Odist__norm) ).
cnf(clsarity_RealDef__Oreal__RealVector_Odist__norm,axiom,
class_RealVector_Odist__norm(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Odist__norm) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Osemiring) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).
cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).
cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
cnf(cls_H_I4_J_0,axiom,
v_w____ != v_z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_H_I4_J_0) ).
cnf(i_0_614,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonneg__eq__0__iff_2 ).
cnf(i_0_615,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__local__XpCons__1(v_cs____,v_e,v_z),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
cls_pCons_1,
[final] ).
cnf(i_0_616,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__local__XpCons__Xhyps__1(v_cs____,v_e,v_z),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal) ),
cls_pCons_Ohyps_1,
[final] ).
cnf(i_0_617,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
cls_conjecture_0,
[final] ).
cnf(i_0_618,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X4,X1),X5,X1),X1),c_HOL_Otimes__class_Otimes(X4,c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oprod__diff__prod_0,
[final] ).
cnf(i_0_619,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X4,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X5,X1),X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__diff__triangle__ineq_0,
[final] ).
cnf(i_0_620,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
cls_le__add__iff1_1,
[final] ).
cnf(i_0_621,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X6,X1) ),
cls_less__add__iff1_1,
[final] ).
cnf(i_0_622,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
cls_le__add__iff2_1,
[final] ).
cnf(i_0_623,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1),X1) ),
cls_less__add__iff2_1,
[final] ).
cnf(i_0_624,axiom,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_CHAINED_0_01,
[final] ).
cnf(i_0_625,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
cls_le__add__iff1_0,
[final] ).
cnf(i_0_626,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1),X5,X1),X6,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),X5,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X1),X6,X1),X1) ),
cls_less__add__iff1_0,
[final] ).
cnf(i_0_627,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
cls_le__add__iff2_0,
[final] ).
cnf(i_0_628,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X1),X5,X1),X6,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X5,X1),X2,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X5,X1),X6,X1),X1) ),
cls_less__add__iff2_0,
[final] ).
cnf(i_0_629,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),X1) ),
cls_sum__squares__gt__zero__iff_0,
[final] ).
cnf(i_0_630,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X2,X1),X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff2_1,
[final] ).
cnf(i_0_631,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_eq__add__iff1_1,
[final] ).
cnf(i_0_632,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_0,
[final] ).
cnf(i_0_633,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_sum__squares__le__zero__iff_1,
[final] ).
cnf(i_0_634,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__sum__squares__lt__zero_0,
[final] ).
cnf(i_0_635,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X5,X1),X3,X1),X4,X1) = X6
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff1_0,
[final] ).
cnf(i_0_636,axiom,
( X4 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X2,X1),X3,X1),X6,X1)
| ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X3,X1),X6,X1) ),
cls_eq__add__iff2_0,
[final] ).
cnf(i_0_637,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X3,X1),X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1),X5,X1)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_638,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_639,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X5,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_640,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X1),X2,X1) ),
cls_abs__diff__less__iff_2,
[final] ).
cnf(i_0_641,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq3_0,
[final] ).
cnf(i_0_642,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__le__zero__iff_2,
[final] ).
cnf(i_0_643,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X3,X1),X5,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),X4,tc_RealDef_Oreal) ),
cls_norm__mult__less_0,
[final] ).
cnf(i_0_644,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X4,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_645,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X5,X1),X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_646,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_H_0,
[final] ).
cnf(i_0_647,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__mono_0,
[final] ).
cnf(i_0_648,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__less__le__imp__less_0,
[final] ).
cnf(i_0_649,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__le__less__imp__less_0,
[final] ).
cnf(i_0_650,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__mono_H_0,
[final] ).
cnf(i_0_651,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__mono_0,
[final] ).
cnf(i_0_652,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X3,X1),X5,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X4,X1) ),
cls_abs__mult__less_0,
[final] ).
cnf(i_0_653,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X4,X2,X1),X1),X3,X1) ),
cls_abs__diff__less__iff_0,
[final] ).
cnf(i_0_654,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X4,X1) ),
cls_abs__diff__less__iff_1,
[final] ).
cnf(i_0_655,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_1,
[final] ).
cnf(i_0_656,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__gt__zero__iff_2,
[final] ).
cnf(i_0_657,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__ge__zero_0,
[final] ).
cnf(i_0_658,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__right__le__imp__le_0,
[final] ).
cnf(i_0_659,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__left__le__imp__le_0,
[final] ).
cnf(i_0_660,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__le__cancel__left__pos_0,
[final] ).
cnf(i_0_661,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__right__less__imp__less_0,
[final] ).
cnf(i_0_662,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__left__less__imp__less_0,
[final] ).
cnf(i_0_663,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) ),
cls_mult__less__imp__less__right_0,
[final] ).
cnf(i_0_664,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) ),
cls_mult__less__imp__less__left_0,
[final] ).
cnf(i_0_665,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X2,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_mult__less__cancel__left__pos_0,
[final] ).
cnf(i_0_666,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__cancel__left__neg_0,
[final] ).
cnf(i_0_667,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__neg_0,
[final] ).
cnf(i_0_668,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
cls_left__diff__distrib__number__of_0,
[final] ).
cnf(i_0_669,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_Int_Onumber__class_Onumber__of(X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Int_Onumber__class_Onumber__of(X4,X1),X1),c_HOL_Otimes__class_Otimes(X3,c_Int_Onumber__class_Onumber__of(X4,X1),X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
cls_left__distrib__number__of_0,
[final] ).
cnf(i_0_670,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Oring(X1)
| ~ class_Int_Onumber(X1) ),
cls_right__diff__distrib__number__of_0,
[final] ).
cnf(i_0_671,axiom,
( c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X3,X1),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(X2,X1),X4,X1),X1)
| ~ class_Ring__and__Field_Osemiring(X1)
| ~ class_Int_Onumber(X1) ),
cls_right__distrib__number__of_0,
[final] ).
cnf(i_0_672,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
cls_real__mult__le__cancel__iff1_0,
[final] ).
cnf(i_0_673,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
cls_real__mult__le__cancel__iff2_0,
[final] ).
cnf(i_0_674,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,tc_RealDef_Oreal) ),
cls_real__mult__less__iff1_0,
[final] ).
cnf(i_0_675,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__left__disj_0,
[final] ).
cnf(i_0_676,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__right__disj_0,
[final] ).
cnf(i_0_677,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_678,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_679,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__right__disj_1,
[final] ).
cnf(i_0_680,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__left__disj_1,
[final] ).
cnf(i_0_681,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__left__disj_2,
[final] ).
cnf(i_0_682,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__right__disj_2,
[final] ).
cnf(i_0_683,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X4,X1),c_HOL_Ominus__class_Ominus(X3,X5,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_Deriv_Oadd__diff__add_0,
[final] ).
cnf(i_0_684,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X5,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_685,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X5,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_686,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1) ),
cls_mult__less__cancel__right__disj_3,
[final] ).
cnf(i_0_687,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X1),c_HOL_Otimes__class_Otimes(X4,X2,X1),X1) ),
cls_mult__less__cancel__left__disj_3,
[final] ).
cnf(i_0_688,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X5,X1),X1) ),
cls_class__ringb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_689,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq2_0,
[final] ).
cnf(i_0_690,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq4_0,
[final] ).
cnf(i_0_691,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
cls_abs__le__mult_0,
[final] ).
cnf(i_0_692,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X2,X3,X1),X1),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__triangle__ineq_0,
[final] ).
cnf(i_0_693,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X5,X4,X1)
| ~ c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X5,X1),X1) ),
cls_le__add__right__mono_0,
[final] ).
cnf(i_0_694,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_norm__mult__ineq_0,
[final] ).
cnf(i_0_695,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__le__cancel__right_0,
[final] ).
cnf(i_0_696,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__le__cancel__left_0,
[final] ).
cnf(i_0_697,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X4,X1),c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) ),
cls_add__less__cancel__right_0,
[final] ).
cnf(i_0_698,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X4,X2,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1) ),
cls_add__less__cancel__left_0,
[final] ).
cnf(i_0_699,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,c_HOL_Oabs__class_Oabs(X4,X1),X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1) ),
cls_estimate__by__abs_0,
[final] ).
cnf(i_0_700,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Otimes__class_Otimes(X3,c_RealVector_Onorm__class_Onorm(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__ratiotest__lemma_0,
[final] ).
cnf(i_0_701,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__left__mono_0,
[final] ).
cnf(i_0_702,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Omult__mono1(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_mult__mono1_0,
[final] ).
cnf(i_0_703,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__le__cancel__left__pos_1,
[final] ).
cnf(i_0_704,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Omult__mono(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_mult__right__mono_0,
[final] ).
cnf(i_0_705,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_mult__strict__left__mono__comm_0,
[final] ).
cnf(i_0_706,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_mult__strict__left__mono_0,
[final] ).
cnf(i_0_707,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__less__cancel__left__pos_1,
[final] ).
cnf(i_0_708,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__less__cancel__left__disj_4,
[final] ).
cnf(i_0_709,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_mult__strict__right__mono_0,
[final] ).
cnf(i_0_710,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__less__cancel__right__disj_4,
[final] ).
cnf(i_0_711,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_mult__left__mono__neg_0,
[final] ).
cnf(i_0_712,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__cancel__left__neg_1,
[final] ).
cnf(i_0_713,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_mult__right__mono__neg_0,
[final] ).
cnf(i_0_714,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__neg_1,
[final] ).
cnf(i_0_715,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_mult__strict__left__mono__neg_0,
[final] ).
cnf(i_0_716,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__left__disj_5,
[final] ).
cnf(i_0_717,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1) ),
cls_mult__strict__right__mono__neg_0,
[final] ).
cnf(i_0_718,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X4,X2,X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__less__cancel__right__disj_5,
[final] ).
cnf(i_0_719,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X3,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__right__le__one__le_0,
[final] ).
cnf(i_0_720,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X2,c_HOL_Oone__class_Oone(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__left__le__one__le_0,
[final] ).
cnf(i_0_721,axiom,
( c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X1)),X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_Osmult(X2,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__diff__right_0,
[final] ).
cnf(i_0_722,axiom,
( c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_poly__diff_0,
[final] ).
cnf(i_0_723,axiom,
( c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X1)),X4,X1) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(X2,X4,X1),c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__mult_0,
[final] ).
cnf(i_0_724,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__mono_0,
[final] ).
cnf(i_0_725,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__le__mono_0,
[final] ).
cnf(i_0_726,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__less__mono_0,
[final] ).
cnf(i_0_727,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X5,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__mono_0,
[final] ).
cnf(i_0_728,axiom,
( c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X2,X4,X1),c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_smult__diff__left_0,
[final] ).
cnf(i_0_729,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_0,
[final] ).
cnf(i_0_730,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Otimes__class_Otimes(X3,X3,X1),X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_1,
[final] ).
cnf(i_0_731,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X4,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_732,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Odiff_0,
[final] ).
cnf(i_0_733,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X3,X1),X4,X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__left_0,
[final] ).
cnf(i_0_734,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_735,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Oadd_0,
[final] ).
cnf(i_0_736,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__left_0,
[final] ).
cnf(i_0_737,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X4,X1),c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_738,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Odiff__right_0,
[final] ).
cnf(i_0_739,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ominus__class_Ominus(X3,X4,X1),X1) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Odiff_0,
[final] ).
cnf(i_0_740,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Oadd_0,
[final] ).
cnf(i_0_741,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__right_0,
[final] ).
cnf(i_0_742,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_743,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_real__mult__le__cancel__iff2_1,
[final] ).
cnf(i_0_744,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__mult__le__cancel__iff1_1,
[final] ).
cnf(i_0_745,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_real__mult__less__mono2_0,
[final] ).
cnf(i_0_746,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X3,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_real__mult__less__iff1_1,
[final] ).
cnf(i_0_747,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__less__mult__pos2_0,
[final] ).
cnf(i_0_748,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__less__mult__pos_0,
[final] ).
cnf(i_0_749,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__eq__mult_0,
[final] ).
cnf(i_0_750,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__eq__mult_2,
[final] ).
cnf(i_0_751,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__eq__mult_1,
[final] ).
cnf(i_0_752,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__eq__mult_3,
[final] ).
cnf(i_0_753,axiom,
( c_HOL_Oplus__class_Oplus(X2,X4,X1) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) != c_HOL_Oplus__class_Oplus(X3,X5,X1) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_754,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_1,
[final] ).
cnf(i_0_755,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_0,
[final] ).
cnf(i_0_756,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_3,
[final] ).
cnf(i_0_757,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__le__mult__iff_0,
[final] ).
cnf(i_0_758,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__le__mult__iff_3,
[final] ).
cnf(i_0_759,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) ),
cls_zero__le__mult__iff_2,
[final] ).
cnf(i_0_760,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) ),
cls_zero__le__mult__iff_1,
[final] ).
cnf(i_0_761,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_2,
[final] ).
cnf(i_0_762,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__nonneg__nonpos2_0,
[final] ).
cnf(i_0_763,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonneg_0,
[final] ).
cnf(i_0_764,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__neg__le_1,
[final] ).
cnf(i_0_765,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonpos_0,
[final] ).
cnf(i_0_766,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__neg__le_0,
[final] ).
cnf(i_0_767,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_5,
[final] ).
cnf(i_0_768,axiom,
( c_lessequals(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__le__0__iff_4,
[final] ).
cnf(i_0_769,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__neg__pos_0,
[final] ).
cnf(i_0_770,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_mult__pos__neg2_0,
[final] ).
cnf(i_0_771,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__pos__neg_0,
[final] ).
cnf(i_0_772,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__nonpos_0,
[final] ).
cnf(i_0_773,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__nonpos_0,
[final] ).
cnf(i_0_774,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__nonpos__neg_0,
[final] ).
cnf(i_0_775,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_add__neg__neg_0,
[final] ).
cnf(i_0_776,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__nonneg__nonneg_0,
[final] ).
cnf(i_0_777,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_split__mult__pos__le_0,
[final] ).
cnf(i_0_778,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__mult__iff_4,
[final] ).
cnf(i_0_779,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__nonneg_0,
[final] ).
cnf(i_0_780,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),X2,X1) ),
cls_less__1__mult_0,
[final] ).
cnf(i_0_781,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__pos__pos_0,
[final] ).
cnf(i_0_782,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__nonneg_0,
[final] ).
cnf(i_0_783,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__pos_0,
[final] ).
cnf(i_0_784,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__pos__pos_0,
[final] ).
cnf(i_0_785,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__nonpos__nonpos_0,
[final] ).
cnf(i_0_786,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_split__mult__pos__le_1,
[final] ).
cnf(i_0_787,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_zero__le__mult__iff_5,
[final] ).
cnf(i_0_788,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__neg__neg_0,
[final] ).
cnf(i_0_789,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__left__mono_0,
[final] ).
cnf(i_0_790,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X3,X4,X1) ),
cls_add__le__cancel__left_1,
[final] ).
cnf(i_0_791,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__right__mono_0,
[final] ).
cnf(i_0_792,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_add__le__cancel__right_1,
[final] ).
cnf(i_0_793,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__strict__left__mono_0,
[final] ).
cnf(i_0_794,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X3,X4,X1) ),
cls_add__less__cancel__left_1,
[final] ).
cnf(i_0_795,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__strict__right__mono_0,
[final] ).
cnf(i_0_796,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X3,X1),c_HOL_Oplus__class_Oplus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_add__less__cancel__right_1,
[final] ).
cnf(i_0_797,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X4,X1) ),
cls_add__increasing2_0,
[final] ).
cnf(i_0_798,axiom,
( c_lessequals(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__increasing_0,
[final] ).
cnf(i_0_799,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing_0,
[final] ).
cnf(i_0_800,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_add__strict__increasing2_0,
[final] ).
cnf(i_0_801,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_pos__add__strict_0,
[final] ).
cnf(i_0_802,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1) ),
cls_le__number__of__eq__not__less_0,
[final] ).
cnf(i_0_803,axiom,
( c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X2,X3,X1),X4,tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__smult__left_0,
[final] ).
cnf(i_0_804,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Osmult(X3,X4,X1),tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X3,c_HOL_Otimes__class_Otimes(X2,X4,tc_Polynomial_Opoly(X1)),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_mult__smult__right_0,
[final] ).
cnf(i_0_805,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X3,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I2_J_0,
[final] ).
cnf(i_0_806,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I3_J_0,
[final] ).
cnf(i_0_807,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__add__abs_0,
[final] ).
cnf(i_0_808,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_real__mult__order_0,
[final] ).
cnf(i_0_809,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_0,
[final] ).
cnf(i_0_810,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_0,
[final] ).
cnf(i_0_811,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_0,
[final] ).
cnf(i_0_812,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_0,
[final] ).
cnf(i_0_813,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_0,
[final] ).
cnf(i_0_814,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_815,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X4,X1),X3,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_816,axiom,
( c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_poly__smult_0,
[final] ).
cnf(i_0_817,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_818,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_819,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_820,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_821,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_822,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_823,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_824,axiom,
( c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X1),X1) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
cls_smult__smult_0,
[final] ).
cnf(i_0_825,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_826,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X4,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_827,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_828,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_829,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_830,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X3,X4,X1),X1) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X2,X4,X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_831,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__eq__zero__iff_2,
[final] ).
cnf(i_0_832,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__iff__diff__le__0_1,
[final] ).
cnf(i_0_833,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__iff__diff__less__0_1,
[final] ).
cnf(i_0_834,axiom,
( c_lessequals(X3,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X5,X4,X1) ),
cls_le__eqI_1,
[final] ).
cnf(i_0_835,axiom,
( c_lessequals(X5,X4,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__eqI_0,
[final] ).
cnf(i_0_836,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X4,X5,X1) ),
cls_less__eqI_1,
[final] ).
cnf(i_0_837,axiom,
( c_HOL_Oord__class_Oless(X4,X5,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X5,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__eqI_0,
[final] ).
cnf(i_0_838,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__mult__assoc_0,
[final] ).
cnf(i_0_839,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1) ),
cls_abs__mult__pos_0,
[final] ).
cnf(i_0_840,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_0,
[final] ).
cnf(i_0_841,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_add__nonneg__eq__0__iff_1,
[final] ).
cnf(i_0_842,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_d1_I1_J_0,
[final] ).
cnf(i_0_843,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__square__less__zero_0,
[final] ).
cnf(i_0_844,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_not__real__square__gt__zero_1,
[final] ).
cnf(i_0_845,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__le__zero__iff__single__add__le__zero_1,
[final] ).
cnf(i_0_846,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_double__add__less__zero__iff__single__less__zero_1,
[final] ).
cnf(i_0_847,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_even__less__0__iff_1,
[final] ).
cnf(i_0_848,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__le__double__add__iff__zero__le__single__add_1,
[final] ).
cnf(i_0_849,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X2,X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_zero__less__double__add__iff__zero__less__single__add_1,
[final] ).
cnf(i_0_850,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
cls_th_0,
[final] ).
cnf(i_0_851,axiom,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_da____,tc_RealDef_Oreal),
cls_H_I5_J_0,
[final] ).
cnf(i_0_852,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_lessequals(c_RealVector_Odist__class_Odist(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_dist__le__zero__iff_0,
[final] ).
cnf(i_0_853,axiom,
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(X2,X3,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_dist__not__less__zero_0,
[final] ).
cnf(i_0_854,axiom,
( ~ class_RealVector_Ometric__space(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X2,X1),tc_RealDef_Oreal) ),
cls_zero__less__dist__iff_0,
[final] ).
cnf(i_0_855,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_le__iff__diff__le__0_0,
[final] ).
cnf(i_0_856,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X2,X3,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_less__iff__diff__less__0_0,
[final] ).
cnf(i_0_857,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__commute_0,
[final] ).
cnf(i_0_858,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__commute_0,
[final] ).
cnf(i_0_859,axiom,
( c_HOL_Oplus__class_Oplus(X2,X2,X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I4_J_0,
[final] ).
cnf(i_0_860,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I6_J_0,
[final] ).
cnf(i_0_861,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__trans_0,
[final] ).
cnf(i_0_862,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_xt1_I8_J_0,
[final] ).
cnf(i_0_863,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I7_J_0,
[final] ).
cnf(i_0_864,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1) ),
cls_xt1_I10_J_0,
[final] ).
cnf(i_0_865,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__le__trans_0,
[final] ).
cnf(i_0_866,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_lessequals(X2,X4,X1) ),
cls_order__le__less__trans_0,
[final] ).
cnf(i_0_867,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X4,X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X4,X1) ),
cls_order__less__trans_0,
[final] ).
cnf(i_0_868,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult_0,
[final] ).
cnf(i_0_869,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
cls_norm__mult_0,
[final] ).
cnf(i_0_870,axiom,
( c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),c_RealVector_Oof__real(X3,X1),X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__mult_0,
[final] ).
cnf(i_0_871,axiom,
( c_lessequals(c_Int_Onumber__class_Onumber__of(X2,X1),c_Int_Onumber__class_Onumber__of(X3,X1),X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X3,X1),c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Int_Onumber(X1) ),
cls_le__number__of__eq__not__less_1,
[final] ).
cnf(i_0_872,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_873,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X3,tc_RealDef_Oreal) ),
cls_real__le__trans_0,
[final] ).
cnf(i_0_874,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_less__le__not__le_2,
[final] ).
cnf(i_0_875,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__two_0,
[final] ).
cnf(i_0_876,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D1_0,
[final] ).
cnf(i_0_877,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__less__iff_0,
[final] ).
cnf(i_0_878,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_879,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
inference(cn,[status(thm)],[i_0_614]),
[final] ).
cnf(i_0_880,axiom,
( c_RealVector_Odist__class_Odist(X2,X3,X1) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
| ~ class_RealVector_Odist__norm(X1) ),
cls_dist__norm_0,
[final] ).
cnf(i_0_881,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_order__antisym__conv_0,
[final] ).
cnf(i_0_882,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__eq__iff_2,
[final] ).
cnf(i_0_883,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__antisym_0,
[final] ).
cnf(i_0_884,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_less__add__one_0,
[final] ).
cnf(i_0_885,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ominus__class_Ominus(X4,X4,X1) ),
cls_eq__eqI_1,
[final] ).
cnf(i_0_886,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X4,X3,X1) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_887,axiom,
( X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X2,X1) != c_HOL_Ominus__class_Ominus(X3,X4,X1) ),
cls_eq__eqI_0,
[final] ).
cnf(i_0_888,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_889,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) != c_HOL_Oplus__class_Oplus(X2,X4,X1) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_890,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X2,X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__antisym__conv2_1,
[final] ).
cnf(i_0_891,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_linorder__not__less_1,
[final] ).
cnf(i_0_892,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_linorder__not__le_1,
[final] ).
cnf(i_0_893,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_not__less__iff__gr__or__eq_1,
[final] ).
cnf(i_0_894,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_xt1_I9_J_0,
[final] ).
cnf(i_0_895,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_less__le__not__le_1,
[final] ).
cnf(i_0_896,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_H_0,
[final] ).
cnf(i_0_897,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_order__less__asym_0,
[final] ).
cnf(i_0_898,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X2,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_zero__le__square_0,
[final] ).
cnf(i_0_899,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X3,X1),tc_RealDef_Oreal)
| X2 = X3
| ~ class_RealVector_Ometric__space(X1) ),
cls_zero__less__dist__iff_1,
[final] ).
cnf(i_0_900,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X3,X2,tc_RealDef_Oreal) ),
cls_real__mult__right__cancel_0,
[final] ).
cnf(i_0_901,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X2 = X3
| c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal) ),
cls_real__mult__left__cancel_0,
[final] ).
cnf(i_0_902,axiom,
( c_lessequals(c_RealVector_Odist__class_Odist(X2,X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
cls_dist__le__zero__iff_1,
[final] ).
cnf(i_0_903,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
cls_zero__le__dist_0,
[final] ).
cnf(i_0_904,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__le__antisym_0,
[final] ).
cnf(i_0_905,axiom,
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__diff__cancel_0,
[final] ).
cnf(i_0_906,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X2,X3,X1),X3,X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__add__cancel_0,
[final] ).
cnf(i_0_907,axiom,
c_RealVector_Odist__class_Odist(X1,X2,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
cls_dist__complex__def_0,
[final] ).
cnf(i_0_908,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult__self_0,
[final] ).
cnf(i_0_909,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_not__real__square__gt__zero_0,
[final] ).
cnf(i_0_910,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),X1) ),
cls_zero__less__abs__iff_0,
[final] ).
cnf(i_0_911,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),tc_RealDef_Oreal) ),
cls_zero__less__norm__iff_0,
[final] ).
cnf(i_0_912,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_Int_Onumber__class_Onumber__of(X2,X1)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_abs__number__of_1,
[final] ).
cnf(i_0_913,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__local__XpCons__1(v_cs____,v_e,v_z),tc_RealDef_Oreal),
cls_pCons_0,
[final] ).
cnf(i_0_914,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__local__XpCons__Xhyps__1(v_cs____,v_e,v_z),tc_RealDef_Oreal),
cls_pCons_Ohyps_0,
[final] ).
cnf(i_0_915,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv1_0,
[final] ).
cnf(i_0_916,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_linorder__antisym__conv2_0,
[final] ).
cnf(i_0_917,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__less__le_2,
[final] ).
cnf(i_0_918,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__less_0,
[final] ).
cnf(i_0_919,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__le__neq__trans_0,
[final] ).
cnf(i_0_920,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_order__neq__le__trans_0,
[final] ).
cnf(i_0_921,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I12_J_0,
[final] ).
cnf(i_0_922,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_xt1_I11_J_0,
[final] ).
cnf(i_0_923,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
cls_CHAINED_0,
[final] ).
cnf(i_0_924,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__le__zero__iff_0,
[final] ).
cnf(i_0_925,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__le__less_1,
[final] ).
cnf(i_0_926,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_order__less__imp__le_0,
[final] ).
cnf(i_0_927,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__not__less__zero_0,
[final] ).
cnf(i_0_928,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__le__zero__iff_0,
[final] ).
cnf(i_0_929,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_2,
[final] ).
cnf(i_0_930,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_RealDef_Oreal) ),
cls_real__less__def_0,
[final] ).
cnf(i_0_931,axiom,
( ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(X2,X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__not__less__zero_0,
[final] ).
cnf(i_0_932,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__neqE_0,
[final] ).
cnf(i_0_933,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__less__linear_0,
[final] ).
cnf(i_0_934,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv3_0,
[final] ).
cnf(i_0_935,axiom,
( X2 = X3
| c_HOL_Oord__class_Oless(X3,X2,X1)
| c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__less__iff__gr__or__eq_0,
[final] ).
cnf(i_0_936,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| X3 = X2
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_linorder__neqE__ordered__idom_0,
[final] ).
cnf(i_0_937,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__of__nonneg_0,
[final] ).
cnf(i_0_938,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_abs__of__pos_0,
[final] ).
cnf(i_0_939,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_940,axiom,
( c_HOL_Oord__class_Oless(X2,X2,X1)
| c_lessequals(X2,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__antisym__conv1_1,
[final] ).
cnf(i_0_941,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__le_0,
[final] ).
cnf(i_0_942,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_not__leE_0,
[final] ).
cnf(i_0_943,axiom,
( c_lessequals(X2,X3,X1)
| c_HOL_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__not__less_0,
[final] ).
cnf(i_0_944,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_945,axiom,
( c_HOL_Otimes__class_Otimes(X2,X3,X1) = c_HOL_Otimes__class_Otimes(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_946,axiom,
( c_RealVector_Odist__class_Odist(X2,X3,X1) = c_RealVector_Odist__class_Odist(X3,X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
cls_dist__commute_0,
[final] ).
cnf(i_0_947,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_948,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_949,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_950,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__le__zero_0,
[final] ).
cnf(i_0_951,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__one__less__zero_0,
[final] ).
cnf(i_0_952,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_953,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_954,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| c_HOL_Otimes__class_Otimes(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_955,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_class__ringb_Osubr0__iff_0,
[final] ).
cnf(i_0_956,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_957,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0,
[final] ).
cnf(i_0_958,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__le__zero__iff_1,
[final] ).
cnf(i_0_959,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
cls_real__mult__commute_0,
[final] ).
cnf(i_0_960,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_961,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_right__minus__eq_0,
[final] ).
cnf(i_0_962,axiom,
( X2 = X3
| ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Ominus__class_Ominus(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__iff__diff__eq__0_1,
[final] ).
cnf(i_0_963,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__le__zero__iff_1,
[final] ).
cnf(i_0_964,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_zero__less__abs__iff_1,
[final] ).
cnf(i_0_965,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| c_RealVector_Odist__class_Odist(X2,X3,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_dist__eq__0__iff_0,
[final] ).
cnf(i_0_966,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_zero__less__norm__iff_1,
[final] ).
cnf(i_0_967,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__zero_0,
[final] ).
cnf(i_0_968,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_969,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_970,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_971,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1) ),
cls_abs__if__lattice_1,
[final] ).
cnf(i_0_972,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__ge__zero_0,
[final] ).
cnf(i_0_973,axiom,
( c_lessequals(X2,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__self_0,
[final] ).
cnf(i_0_974,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
cls_real__less__def_1,
[final] ).
cnf(i_0_975,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = X2
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) ),
cls_abs__if_1,
[final] ).
cnf(i_0_976,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_977,axiom,
( X2 = c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_978,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__le__one_0,
[final] ).
cnf(i_0_979,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ),
cls_zero__less__one_0,
[final] ).
cnf(i_0_980,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Osubr0__iff_1,
[final] ).
cnf(i_0_981,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ozero_0,
[final] ).
cnf(i_0_982,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__left_0,
[final] ).
cnf(i_0_983,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_984,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_1,
[final] ).
cnf(i_0_985,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I9_J_0,
[final] ).
cnf(i_0_986,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__0_0,
[final] ).
cnf(i_0_987,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__right_0,
[final] ).
cnf(i_0_988,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ozero_0,
[final] ).
cnf(i_0_989,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__right_0,
[final] ).
cnf(i_0_990,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1) ),
cls_mult__eq__0__iff_2,
[final] ).
cnf(i_0_991,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I10_J_0,
[final] ).
cnf(i_0_992,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1) ),
cls_mult__1_0,
[final] ).
cnf(i_0_993,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__left_0,
[final] ).
cnf(i_0_994,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I11_J_0,
[final] ).
cnf(i_0_995,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__1_0,
[final] ).
cnf(i_0_996,axiom,
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_smult__1__left_0,
[final] ).
cnf(i_0_997,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_998,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_999,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_1000,axiom,
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X1),X2,X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_1001,axiom,
( c_HOL_Ominus__class_Ominus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__0__right_0,
[final] ).
cnf(i_0_1002,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_mult__1__right_0,
[final] ).
cnf(i_0_1003,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Oone__class_Oone(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I12_J_0,
[final] ).
cnf(i_0_1004,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_1005,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_1006,axiom,
( c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(X1),X1) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_1007,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_diff__self_0,
[final] ).
cnf(i_0_1008,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus__eq_1,
[final] ).
cnf(i_0_1009,axiom,
( c_HOL_Ominus__class_Ominus(X2,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_eq__iff__diff__eq__0_0,
[final] ).
cnf(i_0_1010,axiom,
( c_RealVector_Odist__class_Odist(X2,X2,X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1) ),
cls_dist__self_0,
[final] ).
cnf(i_0_1011,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_1012,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1013,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1014,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_real__mult__is__one_1,
[final] ).
cnf(i_0_1015,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__idempotent_0,
[final] ).
cnf(i_0_1016,axiom,
( X2 = X3
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1)
| c_Int_Onumber__class_Onumber__of(X2,X1) != c_Int_Onumber__class_Onumber__of(X3,X1) ),
cls_eq__number__of_0,
[final] ).
cnf(i_0_1017,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_one0_0,
[final] ).
cnf(i_0_1018,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X1,
cls_real__mult__1_0,
[final] ).
cnf(i_0_1019,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____,tc_RealDef_Oreal),
cls_d1_I2_J_0,
[final] ).
cnf(i_0_1020,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
cls_ep_0,
[final] ).
cnf(i_0_1021,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_da____,tc_RealDef_Oreal),
cls_H_I1_J_0,
[final] ).
cnf(i_0_1022,axiom,
c_HOL_Oord__class_Oless(v_da____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_H_I2_J_0,
[final] ).
cnf(i_0_1023,axiom,
( X2 = X3
| ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) != c_RealVector_Oof__real(X3,X1) ),
cls_of__real__eq__iff_0,
[final] ).
cnf(i_0_1024,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0,
[final] ).
cnf(i_0_1025,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Oabs__class_Oabs(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_abs__eq__0_0,
[final] ).
cnf(i_0_1026,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X1)
| c_RealVector_Oof__real(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_of__real__eq__0__iff_0,
[final] ).
cnf(i_0_1027,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| c_RealVector_Onorm__class_Onorm(X2,X1) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_norm__eq__zero_0,
[final] ).
cnf(i_0_1028,axiom,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real_Ozero_0,
[final] ).
cnf(i_0_1029,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__one_0,
[final] ).
cnf(i_0_1030,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__eq__0_1,
[final] ).
cnf(i_0_1031,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(X1),X1) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
cls_norm__one_0,
[final] ).
cnf(i_0_1032,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__zero_0,
[final] ).
cnf(i_0_1033,axiom,
( c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_HOL_Oone__class_Oone(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__1_0,
[final] ).
cnf(i_0_1034,axiom,
( c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__0_0,
[final] ).
cnf(i_0_1035,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Oone__class_Oone(X1) ),
cls_zero__neq__one_0,
[final] ).
cnf(i_0_1036,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(X1)
| c_HOL_Oone__class_Oone(X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_one__neq__zero_0,
[final] ).
cnf(i_0_1037,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_1038,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_1039,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1040,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1041,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_1042,axiom,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_1043,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_1044,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1045,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1046,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_1047,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_1048,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1049,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_1050,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_1051,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_1052,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1053,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_1054,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1055,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_1056,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_1057,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_1058,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_1059,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_1060,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_1061,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1062,axiom,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_1063,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1064,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1065,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1066,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1067,axiom,
( class_Int_Onumber(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Int_Onumber,
[final] ).
cnf(i_0_1068,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_1069,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Int_Oring__char__0,
[final] ).
cnf(i_0_1070,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1071,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_1072,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_1073,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_1074,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1075,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
clsarity_Polynomial__Opoly__Int_Onumber__ring,
[final] ).
cnf(i_0_1076,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oidom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1077,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1078,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1079,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Olinorder,
[final] ).
cnf(i_0_1080,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_1081,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Oorder,
[final] ).
cnf(i_0_1082,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Opreorder,
[final] ).
cnf(i_0_1083,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1084,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1085,axiom,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal),
cls_real__zero__not__eq__one_0,
[final] ).
cnf(i_0_1086,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_1087,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_1088,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_1089,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_1090,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_1091,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,
[final] ).
cnf(i_0_1092,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1093,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1094,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1095,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_1096,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_1097,axiom,
class_RealVector_Odist__norm(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Odist__norm,
[final] ).
cnf(i_0_1098,axiom,
class_RealVector_Odist__norm(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Odist__norm,
[final] ).
cnf(i_0_1099,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1100,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1101,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1102,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_1103,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_1104,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_1105,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_1106,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_1107,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_1108,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_1109,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_1110,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_1111,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1112,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1113,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_1114,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1115,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1116,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_1117,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_1118,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_1119,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_1120,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_1121,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1122,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1123,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1124,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_1125,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_1126,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_1127,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_1128,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,
[final] ).
cnf(i_0_1129,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_1130,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_1131,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,
[final] ).
cnf(i_0_1132,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1133,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1134,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1135,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_1136,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_1137,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_1138,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_1139,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_1140,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1141,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1142,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1143,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_1144,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_1145,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,
[final] ).
cnf(i_0_1146,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_1147,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_1148,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_1149,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_1150,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_1151,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_1152,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_1153,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_1154,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_1155,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_1156,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1157,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,
[final] ).
cnf(i_0_1158,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_1159,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_1160,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,
[final] ).
cnf(i_0_1162,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_1163,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_1164,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1165,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1166,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,
[final] ).
cnf(i_0_1167,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_1168,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_1169,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_1170,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_1171,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_1172,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_1173,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_1174,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_1175,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1176,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1177,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1178,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1179,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1180,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_1181,axiom,
class_Int_Onumber(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber,
[final] ).
cnf(i_0_1182,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber,
[final] ).
cnf(i_0_1183,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber,
[final] ).
cnf(i_0_1184,axiom,
class_Ring__and__Field_Osemiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_1185,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_1186,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_1187,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
clsarity_Int__Oint__Int_Oring__char__0,
[final] ).
cnf(i_0_1188,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Oring__char__0,
[final] ).
cnf(i_0_1189,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Oring__char__0,
[final] ).
cnf(i_0_1190,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1191,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,
[final] ).
cnf(i_0_1192,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_1193,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_1194,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_1195,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_1196,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_1197,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_1198,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_1199,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Ometric__space,
[final] ).
cnf(i_0_1200,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Ometric__space,
[final] ).
cnf(i_0_1201,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1202,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1203,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_1204,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber__ring,
[final] ).
cnf(i_0_1205,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring,
[final] ).
cnf(i_0_1206,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring,
[final] ).
cnf(i_0_1207,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1208,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1209,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1210,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1212,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_1213,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1214,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1215,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1216,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Olinorder,
[final] ).
cnf(i_0_1217,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder,
[final] ).
cnf(i_0_1218,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_1219,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_1220,axiom,
class_Orderings_Oorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Oorder,
[final] ).
cnf(i_0_1221,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder,
[final] ).
cnf(i_0_1222,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Opreorder,
[final] ).
cnf(i_0_1223,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Opreorder,
[final] ).
cnf(i_0_1224,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1225,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,
[final] ).
cnf(i_0_1226,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,
[final] ).
cnf(i_0_1228,axiom,
v_w____ != v_z,
cls_H_I4_J_0,
[final] ).
cnf(i_0_1229,axiom,
X1 = X1 ).
cnf(i_0_1230,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1231,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1232,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_1233,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_1234,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_1235,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_1236,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_1237,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_1238,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_1239,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_1240,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X1,X3,X4) = c_RealVector_Odist__class_Odist(X2,X3,X4) ) ).
cnf(i_0_1241,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X3,X1,X4) = c_RealVector_Odist__class_Odist(X3,X2,X4) ) ).
cnf(i_0_1242,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X3,X4,X1) = c_RealVector_Odist__class_Odist(X3,X4,X2) ) ).
cnf(i_0_1243,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_1244,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_1245,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1246,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1247,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1248,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_1249,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_1250,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_1251,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1252,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_1253,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_1254,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_1255,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1256,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1257,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1258,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_1259,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_1260,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1261,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1262,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1263,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1264,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1265,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1266,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1267,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1268,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_1269,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_1270,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1271,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_1272,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1273,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1274,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1275,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1276,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1277,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_1278,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1279,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1280,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_1281,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_1282,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1283,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1284,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1285,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1286,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1287,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_1288,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1289,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1290,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1291,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1292,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1293,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1294,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1295,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1296,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1297,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1298,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1299,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1300,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1301,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_1302,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1303,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1304,axiom,
( X1 != X2
| ~ class_RealVector_Odist__norm(X1)
| class_RealVector_Odist__norm(X2) ) ).
cnf(i_0_1305,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1306,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1307,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1308,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1309,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1310,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1311,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1312,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1313,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_1314,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_1315,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1316,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1317,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1318,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1319,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1320,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_1321,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_1322,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1323,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_1324,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1229_001,axiom,
X1 = X1 ).
cnf(i_0_1230_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1231_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1232_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_1233_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_1234_006,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_1235_007,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_1236_008,axiom,
( X1 != X2
| c_HOL_Oone__class_Oone(X1) = c_HOL_Oone__class_Oone(X2) ) ).
cnf(i_0_1237_009,axiom,
( X1 != X2
| c_Polynomial_Osmult(X1,X3,X4) = c_Polynomial_Osmult(X2,X3,X4) ) ).
cnf(i_0_1238_010,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X1,X4) = c_Polynomial_Osmult(X3,X2,X4) ) ).
cnf(i_0_1239_011,axiom,
( X1 != X2
| c_Polynomial_Osmult(X3,X4,X1) = c_Polynomial_Osmult(X3,X4,X2) ) ).
cnf(i_0_1240_012,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X1,X3,X4) = c_RealVector_Odist__class_Odist(X2,X3,X4) ) ).
cnf(i_0_1241_013,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X3,X1,X4) = c_RealVector_Odist__class_Odist(X3,X2,X4) ) ).
cnf(i_0_1242_014,axiom,
( X1 != X2
| c_RealVector_Odist__class_Odist(X3,X4,X1) = c_RealVector_Odist__class_Odist(X3,X4,X2) ) ).
cnf(i_0_1243_015,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_1244_016,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_1245_017,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X1,X3,X4) = c_HOL_Ominus__class_Ominus(X2,X3,X4) ) ).
cnf(i_0_1246_018,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X1,X4) = c_HOL_Ominus__class_Ominus(X3,X2,X4) ) ).
cnf(i_0_1247_019,axiom,
( X1 != X2
| c_HOL_Ominus__class_Ominus(X3,X4,X1) = c_HOL_Ominus__class_Ominus(X3,X4,X2) ) ).
cnf(i_0_1248_020,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_1249_021,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_1250_022,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_1251_023,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1252_024,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_1253_025,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_1254_026,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_1255_027,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X1,X3,X4) = c_HOL_Oplus__class_Oplus(X2,X3,X4) ) ).
cnf(i_0_1256_028,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X1,X4) = c_HOL_Oplus__class_Oplus(X3,X2,X4) ) ).
cnf(i_0_1257_029,axiom,
( X1 != X2
| c_HOL_Oplus__class_Oplus(X3,X4,X1) = c_HOL_Oplus__class_Oplus(X3,X4,X2) ) ).
cnf(i_0_1258_030,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_1259_031,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_1260_032,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1261_033,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1262_034,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1263_035,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1264_036,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1265_037,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1266_038,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1267_039,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1268_040,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_1269_041,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_1270_042,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1271_043,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_1272_044,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1273_045,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1274_046,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2) ) ).
cnf(i_0_1275_047,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1276_048,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1277_049,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_1278_050,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1279_051,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1280_052,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_1281_053,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_1282_054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__ab__semigroup__add(X2) ) ).
cnf(i_0_1283_055,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X1)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1284_056,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1285_057,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1286_058,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1287_059,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_1288_060,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1289_061,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1290_062,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X1)
| class_OrderedGroup_Opordered__comm__monoid__add(X2) ) ).
cnf(i_0_1291_063,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| class_Ring__and__Field_Oordered__semidom(X2) ) ).
cnf(i_0_1292_064,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1293_065,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1294_066,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1295_067,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1296_068,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1297_069,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1298_070,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1299_071,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1300_072,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1301_073,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_1302_074,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1303_075,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1304_076,axiom,
( X1 != X2
| ~ class_RealVector_Odist__norm(X1)
| class_RealVector_Odist__norm(X2) ) ).
cnf(i_0_1305_077,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1306_078,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1307_079,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1308_080,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1309_081,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1310_082,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1311_083,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1312_084,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1313_085,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__mult(X1)
| class_OrderedGroup_Ocomm__monoid__mult(X2) ) ).
cnf(i_0_1314_086,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__mult(X1)
| class_OrderedGroup_Omonoid__mult(X2) ) ).
cnf(i_0_1315_087,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1316_088,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1317_089,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1318_090,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ozero__neq__one(X1)
| class_Ring__and__Field_Ozero__neq__one(X2) ) ).
cnf(i_0_1319_091,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1320_092,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_1321_093,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(X1)
| class_OrderedGroup_Ocancel__comm__monoid__add(X2) ) ).
cnf(i_0_1322_094,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1323_095,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_1324_096,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1325,plain,
( ~ class_Ring__and__Field_Oring(X1)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X2,X1),X3,X1),X4,X1) = X4 ),
inference(equality_inference,[],[635]) ).
cnf(i_0_1326,plain,
( ~ class_Ring__and__Field_Oring(X1)
| X2 = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X3,X1),X4,X1),X2,X1) ),
inference(equality_inference,[],[636]) ).
cnf(i_0_1327,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[639]) ).
cnf(i_0_1328,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[688]) ).
cnf(i_0_1329,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X2,X3,X1) ),
inference(equality_inference,[],[753]) ).
cnf(i_0_1330,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[878]) ).
cnf(i_0_1331,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[885]) ).
cnf(i_0_1332,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[886]) ).
cnf(i_0_1333,plain,
( X1 = X1
| ~ class_OrderedGroup_Oab__group__add(X2) ),
inference(equality_inference,[],[887]) ).
cnf(i_0_1334,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[888]) ).
cnf(i_0_1335,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[889]) ).
cnf(i_0_1336,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[900]) ).
cnf(i_0_1337,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[901]) ).
cnf(i_0_1338,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Int_Oring__char__0(X1) ),
inference(equality_inference,[],[1016]) ).
cnf(i_0_1339,plain,
( X1 = X1
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(equality_inference,[],[1023]) ).
cnf(i_0_1340,plain,
$false,
inference(scs_inference,[],[i_0_617,i_0_1223,i_0_923,i_0_624,i_0_866]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG370-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:33:14 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.96/1.66 % Version : CSE_E---1.7
% 0.96/1.66 % Problem : theBenchmark.p
% 0.96/1.66 % SZS status Unsatisfiable for theBenchmark.p
% 0.96/1.66 % SZS output start CNFRefutation
% See solution above
% 1.02/1.71 % Total time : 1.325s
%------------------------------------------------------------------------------