%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG373-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.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 04:08:34 PM UTC 2026
% Result : Unsatisfiable 0.94s 1.68s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 666)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_mult_Obounded_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded_0) ).
cnf(cls_mult_Ononneg__bounded_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_1) ).
cnf(cls_mult_Opos__bounded_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Opos__bounded_1) ).
cnf(cls_calculation_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__unknown__thm__rW8__1(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).
cnf(cls_scaleR__right_Obounded_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Obounded_0) ).
cnf(cls_scaleR__right_Ononneg__bounded_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Ononneg__bounded_1) ).
cnf(cls_scaleR__right_Opos__bounded_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Opos__bounded_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
cnf(cls_mult__left_Obounded_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_Osko__RealVector__Xmult__left__Xbounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Obounded_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/sandbox/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).
cnf(cls_mult__left_Ononneg__bounded_1,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_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_1) ).
cnf(cls_mult__left_Opos__bounded_1,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_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_1) ).
cnf(cls_mult__right_Obounded_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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Obounded_0) ).
cnf(cls_mult__right_Ononneg__bounded_1,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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_1) ).
cnf(cls_mult__right_Opos__bounded_1,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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
cnf(cls_rabs__ratiotest__lemma_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rabs__ratiotest__lemma_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).
cnf(cls_poly__bound__exists_1,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_real__minus__mult__self__le_0,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).
cnf(cls_CHAINED_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_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/sandbox/benchmark/theBenchmark.p',cls_mult__pos__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult__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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_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/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_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/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
cnf(cls_mult__scaleR__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
cnf(cls_mult__left_OscaleR_0,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).
cnf(cls_mult_OscaleR__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__left_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
cnf(cls_scaleR__left__commute_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
cnf(cls_scaleR__right_OscaleR_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).
cnf(cls_scaleR_OscaleR__right_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
cnf(cls_mult__scaleR__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
cnf(cls_mult__right_OscaleR_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OscaleR_0) ).
cnf(cls_mult_OscaleR__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__right_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
cnf(cls_real__vector_Oscale__scale_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),X4,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__vector_Oscale__scale_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).
cnf(cls_abs__leI_0,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__leI_0) ).
cnf(cls_abs__le__iff_2,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
cnf(cls_abs__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
cnf(cls_abs__le__interval__iff_2,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).
cnf(cls_real__sum__squares__cancel__a_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).
cnf(cls_real__sum__squares__cancel__a_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_order__trans_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/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__less__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_of__real__mult_0) ).
cnf(cls_abs__number__of_0,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
cnf(cls_neg__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_norm__scaleR_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__scaleR_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).
cnf(cls_poly__minus_0,axiom,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).
cnf(cls_minus__le__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_abs__le__D2_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
cnf(cls_minus__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
cnf(cls_minus__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_abs__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),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/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
cnf(cls_less__minus__iff_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
cnf(cls_less__minus__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_mult_Ominus__left_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
cnf(cls_scaleR__minus__right_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
cnf(cls_scaleR_Ominus__right_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
cnf(cls_mult_Ominus__right_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
cnf(cls_minus__mult__left_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_minus__mult__right_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_scaleR__left_Ominus_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Ominus_0) ).
cnf(cls_scaleR__minus__left_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__left_0) ).
cnf(cls_scaleR_Ominus__left_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__left_0) ).
cnf(cls_neg__le__0__iff__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_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/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
cnf(cls_le__imp__neg__le_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
cnf(cls_neg__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
cnf(cls_square__eq__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_abs__le__interval__iff_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).
cnf(cls_minus__le__self__iff_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
cnf(cls_le__minus__self__iff_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).
cnf(cls_less__eq__neg__nonpos_0,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
cnf(cls_less__minus__self__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(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
cnf(cls_neg__le__0__iff__le_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
cnf(cls_neg__0__le__iff__le_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
cnf(cls_neg__0__less__iff__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
cnf(cls_scaleR__cancel__right_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_RealVector_OscaleR__class_OscaleR(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
cnf(cls_mth1_1,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mth1_1) ).
cnf(cls_scaleR__cancel__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3 = X4
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_RealVector_OscaleR__class_OscaleR(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
cnf(cls_minus__le__self__iff_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).
cnf(cls_neg__less__eq__nonneg_1,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
cnf(cls_le__minus__self__iff_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).
cnf(cls_less__eq__neg__nonpos_1,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
cnf(cls_less__minus__self__iff_1,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,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/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_order__antisym_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/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_abs__le__interval__iff_1,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).
cnf(cls_scaleR__right_Ononneg__bounded_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Ononneg__bounded_0) ).
cnf(cls_scaleR__right_Opos__bounded_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Opos__bounded_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/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
cnf(cls_square__eq__iff_1,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
cnf(cls_minus__mult__minus_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_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/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_1) ).
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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_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/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_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/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
cnf(cls_abs__minus__le__zero_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).
cnf(cls_complex__mod__minus__le__complex__mod_0,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
cnf(cls_scaleR__conv__of__real_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),X3,X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).
cnf(cls_abs__if__lattice_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).
cnf(cls_abs__if_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
cnf(cls_abs__of__nonpos_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).
cnf(cls_abs__of__neg_0,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
cnf(cls_scaleR__cancel__right_1,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
cnf(cls_scaleR__cancel__left_1,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_mth1_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mth1_0) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_real__abs__def_0,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_0) ).
cnf(cls_abs__Re__le__cmod_0,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X1),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_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/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_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/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_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/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_scaleR__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_HOL_Oord__class_Oless(v_x(X1),X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_of__real_Ominus_0,axiom,
( c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Ominus_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
cnf(cls_mult_Ononneg__bounded_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_0) ).
cnf(cls_mult__right_Ononneg__bounded_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_0) ).
cnf(cls_mult__left_Ononneg__bounded_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_0) ).
cnf(cls_mult_Opos__bounded_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).
cnf(cls_mult__left_Opos__bounded_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).
cnf(cls_mult__right_Opos__bounded_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_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/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_of__real__minus_0,axiom,
( c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X2,X1),X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__minus_0) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
cnf(cls_poly__bound__exists_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X2),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).
cnf(cls_complex__Re__le__cmod_0,axiom,
c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_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/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_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/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).
cnf(cls_scaleR__eq__0__iff_2,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
cnf(cls_scaleR_Ozero__right_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_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/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_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/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_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/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
cnf(cls_real__abs__def_1,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
cnf(cls_scaleR__eq__0__iff_1,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).
cnf(cls_scaleR_Ozero__left_0,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_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/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_order__eq__refl_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
cnf(cls_order__eq__iff_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
cnf(cls_norm__minus__cancel_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
cnf(cls_abs__minus__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).
cnf(cls_abs__norm__cancel_0,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).
cnf(cls_norm__of__real_0,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__of__real_0) ).
cnf(cls_rp_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).
cnf(cls_double__compl_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__minus_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
cnf(cls_equation__minus__iff_0,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
cnf(cls_equation__minus__iff_1,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
cnf(cls_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__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/sandbox/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).
cnf(cls_minus__zero_0,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
cnf(cls_neg__equal__zero_1,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_norm__zero_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/sandbox/benchmark/theBenchmark.p',cls_of__real__0_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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).
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/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).
cnf(clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__vector,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).
cnf(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).
cnf(clsarity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).
cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
cnf(i_0_485,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Obounded_0,
[final] ).
cnf(i_0_486,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ononneg__bounded_1,
[final] ).
cnf(i_0_487,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X2,X1),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X4,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Opos__bounded_1,
[final] ).
cnf(i_0_488,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__unknown__thm__rW8__1(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
| c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
cls_calculation_0,
[final] ).
cnf(i_0_489,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Obounded_0,
[final] ).
cnf(i_0_490,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Ononneg__bounded_1,
[final] ).
cnf(i_0_491,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X3,X1),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X4,X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Opos__bounded_1,
[final] ).
cnf(i_0_492,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_493,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_494,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_495,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_496,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_497,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_498,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_499,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_500,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_501,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_502,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_503,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_504,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_505,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_506,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_507,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_508,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_509,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_510,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_511,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_512,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_513,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_514,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_515,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_516,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_517,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_518,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_519,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_520,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_521,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_522,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_523,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_524,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_525,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_Osko__RealVector__Xmult__left__Xbounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Obounded_0,
[final] ).
cnf(i_0_526,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_527,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_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ononneg__bounded_1,
[final] ).
cnf(i_0_528,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_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X3,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Opos__bounded_1,
[final] ).
cnf(i_0_529,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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Obounded_0,
[final] ).
cnf(i_0_530,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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ononneg__bounded_1,
[final] ).
cnf(i_0_531,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(X3,X1),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Opos__bounded_1,
[final] ).
cnf(i_0_532,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_533,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_534,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_535,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_536,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_537,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_538,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_539,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_540,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_541,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_542,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_543,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_544,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_545,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_546,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_547,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_548,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_549,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_550,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_551,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,c_HOL_Oabs__class_Oabs(X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_rabs__ratiotest__lemma_0,
[final] ).
cnf(i_0_552,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_553,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_554,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_555,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_556,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X2,tc_Complex_Ocomplex),X3,tc_RealDef_Oreal) ),
cls_poly__bound__exists_1,
[final] ).
cnf(i_0_557,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_558,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_559,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_560,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_561,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_562,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_563,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_564,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_565,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_566,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_567,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_568,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_569,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_570,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_571,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__minus__mult__self__le_0,
[final] ).
cnf(i_0_572,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal) ),
cls_CHAINED_0,
[final] ).
cnf(i_0_573,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_574,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_575,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_576,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_577,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_578,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_579,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_580,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_581,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_582,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_583,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_584,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_585,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_586,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_587,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_588,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_589,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_590,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_591,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_592,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_593,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_594,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__left_0,
[final] ).
cnf(i_0_595,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_OscaleR_0,
[final] ).
cnf(i_0_596,axiom,
( c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X4,X1) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Otimes__class_Otimes(X3,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__left_0,
[final] ).
cnf(i_0_597,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_598,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_599,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_600,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_601,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left__commute_0,
[final] ).
cnf(i_0_602,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OscaleR_0,
[final] ).
cnf(i_0_603,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_RealVector_OscaleR__class_OscaleR(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_OscaleR__right_0,
[final] ).
cnf(i_0_604,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__right_0,
[final] ).
cnf(i_0_605,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OscaleR_0,
[final] ).
cnf(i_0_606,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Otimes__class_Otimes(X2,X4,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__right_0,
[final] ).
cnf(i_0_607,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_608,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X3,X4,X1),X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),X4,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_real__vector_Oscale__scale_0,
[final] ).
cnf(i_0_609,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_610,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_611,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__leI_0,
[final] ).
cnf(i_0_612,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__le__iff_2,
[final] ).
cnf(i_0_613,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_abs__less__iff_2,
[final] ).
cnf(i_0_614,axiom,
( c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_2,
[final] ).
cnf(i_0_615,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_616,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_617,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__sum__squares__cancel__a_0,
[final] ).
cnf(i_0_618,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__sum__squares__cancel__a_1,
[final] ).
cnf(i_0_619,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_620,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_621,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_622,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_623,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_624,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_625,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_626,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_627,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_628,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_629,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_630,axiom,
( c_HOL_Oabs__class_Oabs(c_Int_Onumber__class_Onumber__of(X2,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_Int_Onumber__class_Onumber__of(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Int_Onumber__ring(X1)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__number__of_0,
[final] ).
cnf(i_0_631,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_632,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_633,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__scaleR_0,
[final] ).
cnf(i_0_634,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_635,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_636,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_637,axiom,
( c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring(X1) ),
cls_poly__minus_0,
[final] ).
cnf(i_0_638,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_639,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_640,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,X1),X3,X1) ),
cls_abs__le__D2_0,
[final] ).
cnf(i_0_641,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_642,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X1),X2,X1) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_643,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),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_1,
[final] ).
cnf(i_0_644,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_645,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_646,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_647,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_648,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__left_0,
[final] ).
cnf(i_0_649,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ominus_0,
[final] ).
cnf(i_0_650,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__minus__right_0,
[final] ).
cnf(i_0_651,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ominus__right_0,
[final] ).
cnf(i_0_652,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__right_0,
[final] ).
cnf(i_0_653,axiom,
( c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ominus_0,
[final] ).
cnf(i_0_654,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_655,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X2,X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_656,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left_Ominus_0,
[final] ).
cnf(i_0_657,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__minus__left_0,
[final] ).
cnf(i_0_658,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X3,X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X2,X3,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ominus__left_0,
[final] ).
cnf(i_0_659,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__le__0__iff__le_0,
[final] ).
cnf(i_0_660,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__less__0__iff__less_0,
[final] ).
cnf(i_0_661,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__0__le__iff__le_0,
[final] ).
cnf(i_0_662,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_neg__0__less__iff__less_0,
[final] ).
cnf(i_0_663,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_664,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_665,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,X2,X1) ),
cls_neg__less__iff__less_1,
[final] ).
cnf(i_0_666,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(X3,X1)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| c_HOL_Otimes__class_Otimes(X2,X2,X1) != c_HOL_Otimes__class_Otimes(X3,X3,X1) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_667,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_0,
[final] ).
cnf(i_0_668,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
cls_minus__le__self__iff_0,
[final] ).
cnf(i_0_669,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1) ),
cls_neg__less__eq__nonneg_0,
[final] ).
cnf(i_0_670,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_le__minus__self__iff_0,
[final] ).
cnf(i_0_671,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__eq__neg__nonpos_0,
[final] ).
cnf(i_0_672,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(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1) ),
cls_less__minus__self__iff_0,
[final] ).
cnf(i_0_673,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__le__0__iff__le_1,
[final] ).
cnf(i_0_674,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__less__0__iff__less_1,
[final] ).
cnf(i_0_675,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__0__le__iff__le_1,
[final] ).
cnf(i_0_676,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__0__less__iff__less_1,
[final] ).
cnf(i_0_677,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_678,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_679,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_RealVector_OscaleR__class_OscaleR(X4,X3,X1) ),
cls_scaleR__cancel__right_0,
[final] ).
cnf(i_0_680,axiom,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_sko__local__Xmth1__1(v_p,v_r),tc_RealDef_Oreal),
cls_mth1_1,
[final] ).
cnf(i_0_681,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3 = X4
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_RealVector_OscaleR__class_OscaleR(X2,X4,X1) ),
cls_scaleR__cancel__left_0,
[final] ).
cnf(i_0_682,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_minus__le__self__iff_1,
[final] ).
cnf(i_0_683,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_neg__less__eq__nonneg_1,
[final] ).
cnf(i_0_684,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_le__minus__self__iff_1,
[final] ).
cnf(i_0_685,axiom,
( c_lessequals(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__eq__neg__nonpos_1,
[final] ).
cnf(i_0_686,axiom,
( c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_less__minus__self__iff_1,
[final] ).
cnf(i_0_687,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_688,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_689,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_690,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_691,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_692,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_693,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_694,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_695,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_696,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_697,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_698,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_699,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_abs__le__interval__iff_1,
[final] ).
cnf(i_0_700,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_701,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_702,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Ononneg__bounded_0,
[final] ).
cnf(i_0_703,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(X2,X3,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Opos__bounded_0,
[final] ).
cnf(i_0_704,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_705,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X2,X1)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_706,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Ouminus__class_Ouminus(X3,X1),X1) = c_HOL_Otimes__class_Otimes(X2,X3,X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_707,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_708,axiom,
( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X1),X3,X1) = c_HOL_Otimes__class_Otimes(X2,c_HOL_Ouminus__class_Ouminus(X3,X1),X1)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_709,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_710,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_711,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_712,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_713,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_714,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_715,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_716,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_717,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_718,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_719,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_720,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_721,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_722,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_723,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_724,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X2,X1),X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__le__zero_0,
[final] ).
cnf(i_0_725,axiom,
c_lessequals(c_HOL_Ouminus__class_Ouminus(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_complex__mod__minus__le__complex__mod_0,
[final] ).
cnf(i_0_726,negated_conjecture,
c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_xa(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(v_x(X1),tc_RealDef_Oreal),
cls_conjecture_1,
[final] ).
cnf(i_0_727,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_728,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(X2,X1),X3,X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_scaleR__conv__of__real_0,
[final] ).
cnf(i_0_729,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_730,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_731,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__if__lattice_0,
[final] ).
cnf(i_0_732,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_733,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_734,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__if_0,
[final] ).
cnf(i_0_735,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__of__nonpos_0,
[final] ).
cnf(i_0_736,axiom,
( c_HOL_Oabs__class_Oabs(X2,X1) = c_HOL_Ouminus__class_Ouminus(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__of__neg_0,
[final] ).
cnf(i_0_737,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_RealVector_OscaleR__class_OscaleR(X3,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__right_1,
[final] ).
cnf(i_0_738,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X3,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__left_1,
[final] ).
cnf(i_0_739,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_740,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_741,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_742,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_743,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_744,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_745,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_746,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_747,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_748,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_749,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_750,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_751,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_752,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_753,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_sko__local__Xmth1__2(v_p,v_r),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_mth1_0,
[final] ).
cnf(i_0_754,axiom,
( c_lessequals(c_HOL_Ouminus__class_Ouminus(X2,X1),c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__minus__self_0,
[final] ).
cnf(i_0_755,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_0,
[final] ).
cnf(i_0_756,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(X1),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_abs__Re__le__cmod_0,
[final] ).
cnf(i_0_757,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_758,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_759,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_760,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__vector(X1)
| c_RealVector_OscaleR__class_OscaleR(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_scaleR__eq__0__iff_0,
[final] ).
cnf(i_0_761,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0,
[final] ).
cnf(i_0_762,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_763,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_764,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_765,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_766,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_767,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_768,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_769,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_770,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_771,negated_conjecture,
~ c_HOL_Oord__class_Oless(v_x(X1),X1,tc_RealDef_Oreal),
cls_conjecture_2,
[final] ).
cnf(i_0_772,axiom,
( c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real_Ominus_0,
[final] ).
cnf(i_0_773,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_774,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_775,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ononneg__bounded_0,
[final] ).
cnf(i_0_776,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ononneg__bounded_0,
[final] ).
cnf(i_0_777,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ononneg__bounded_0,
[final] ).
cnf(i_0_778,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Opos__bounded_0,
[final] ).
cnf(i_0_779,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Opos__bounded_0,
[final] ).
cnf(i_0_780,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(X2,X1),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Opos__bounded_0,
[final] ).
cnf(i_0_781,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_782,negated_conjecture,
c_lessequals(c_RealVector_Onorm__class_Onorm(v_xa(X1),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
cls_conjecture_0,
[final] ).
cnf(i_0_783,axiom,
( c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(X2,tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(X2,X1),X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__minus_0,
[final] ).
cnf(i_0_784,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_RealDef_Oreal),
cls_real__less__def_1,
[final] ).
cnf(i_0_785,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_786,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(X1,X2),tc_RealDef_Oreal),
cls_poly__bound__exists_0,
[final] ).
cnf(i_0_787,axiom,
c_lessequals(c_Complex_ORe(X1),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
cls_complex__Re__le__cmod_0,
[final] ).
cnf(i_0_788,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_789,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_790,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_791,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_792,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_793,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_794,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__eq__0__iff_2,
[final] ).
cnf(i_0_795,axiom,
( c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ozero__right_0,
[final] ).
cnf(i_0_796,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_797,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_798,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_799,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_800,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_801,axiom,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_real__abs__def_1,
[final] ).
cnf(i_0_802,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__eq__0__iff_1,
[final] ).
cnf(i_0_803,axiom,
( c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ozero__left_0,
[final] ).
cnf(i_0_804,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_805,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_806,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_807,axiom,
( c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__cancel_0,
[final] ).
cnf(i_0_808,axiom,
( c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__cancel_0,
[final] ).
cnf(i_0_809,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_810,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_811,axiom,
( c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(X2,X1),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_abs__norm__cancel_0,
[final] ).
cnf(i_0_812,axiom,
( c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(X2,X1),X1) = c_HOL_Oabs__class_Oabs(X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
cls_norm__of__real_0,
[final] ).
cnf(i_0_813,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
cls_rp_0,
[final] ).
cnf(i_0_814,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_815,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ouminus__class_Ouminus(X3,X1) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_816,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_817,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0,
[final] ).
cnf(i_0_818,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_819,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_820,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_821,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_822,axiom,
( X2 = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_823,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != c_HOL_Ouminus__class_Ouminus(X2,X1) ),
cls_neg__0__equal__iff__equal_0,
[final] ).
cnf(i_0_824,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0,
[final] ).
cnf(i_0_825,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_826,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_827,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_828,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| c_HOL_Ouminus__class_Ouminus(X2,X1) != X2 ),
cls_neg__equal__zero_0,
[final] ).
cnf(i_0_829,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_830,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__zero_0,
[final] ).
cnf(i_0_831,axiom,
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
cls_neg__equal__zero_1,
[final] ).
cnf(i_0_832,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_833,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1,
[final] ).
cnf(i_0_834,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_835,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_836,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_837,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_838,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_839,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Opreorder,
[final] ).
cnf(i_0_840,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Oorder,
[final] ).
cnf(i_0_841,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_842,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_843,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_844,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_845,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_846,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_847,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_848,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_849,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_850,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_851,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_852,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_853,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_854,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_855,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_856,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_857,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_858,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_859,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_860,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_861,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_862,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_863,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_864,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_865,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_866,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_867,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_868,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsarity_Polynomial__Opoly__Orderings_Olinorder,
[final] ).
cnf(i_0_869,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_870,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_871,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,
[final] ).
cnf(i_0_872,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_873,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_874,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_875,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_876,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_877,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,
[final] ).
cnf(i_0_878,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Opreorder,
[final] ).
cnf(i_0_879,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Opreorder,
[final] ).
cnf(i_0_880,axiom,
class_Orderings_Oorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Oorder,
[final] ).
cnf(i_0_881,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder,
[final] ).
cnf(i_0_882,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_883,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_884,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,
[final] ).
cnf(i_0_885,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_886,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_887,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_888,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_889,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_890,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_891,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_892,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_893,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_894,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_895,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_896,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_897,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_898,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_899,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_900,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_901,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_902,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_903,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_904,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_905,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_906,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_907,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_908,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_909,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_910,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_911,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_912,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_913,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_914,axiom,
class_Ring__and__Field_Oring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oring,
[final] ).
cnf(i_0_915,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_916,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring,
[final] ).
cnf(i_0_917,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_918,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_919,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_920,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_921,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_922,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_923,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_924,axiom,
class_Ring__and__Field_Oabs__if(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_925,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_926,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_927,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_928,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_929,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_930,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__vector,
[final] ).
cnf(i_0_931,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__vector,
[final] ).
cnf(i_0_932,axiom,
class_Ring__and__Field_Olordered__ring(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_933,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_934,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_935,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_936,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_Int_Oint),
clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_937,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_938,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_939,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_940,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_941,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_942,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_943,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_944,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_945,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_946,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_947,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_948,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_949,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_950,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_951,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_952,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_953,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
clsarity_Int__Oint__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_954,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_955,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber__ring,
[final] ).
cnf(i_0_956,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring,
[final] ).
cnf(i_0_957,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring,
[final] ).
cnf(i_0_958,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
clsarity_Int__Oint__Int_Oring__char__0,
[final] ).
cnf(i_0_959,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Oring__char__0,
[final] ).
cnf(i_0_960,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Oring__char__0,
[final] ).
cnf(i_0_961,axiom,
class_Int_Onumber(tc_Int_Oint),
clsarity_Int__Oint__Int_Onumber,
[final] ).
cnf(i_0_962,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber,
[final] ).
cnf(i_0_963,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber,
[final] ).
cnf(i_0_964,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
clsarity_Int__Oint__Orderings_Olinorder,
[final] ).
cnf(i_0_965,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder,
[final] ).
cnf(i_0_966,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_967,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_968,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_969,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_970,axiom,
X1 = X1 ).
cnf(i_0_971,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_972,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_973,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_974,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_975,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_976,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_977,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_978,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_979,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_980,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_981,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_982,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_983,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_984,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_985,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_986,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_987,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_988,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_989,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_990,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X1,X3,X4) = c_RealVector_OscaleR__class_OscaleR(X2,X3,X4) ) ).
cnf(i_0_991,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X3,X1,X4) = c_RealVector_OscaleR__class_OscaleR(X3,X2,X4) ) ).
cnf(i_0_992,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X3,X4,X1) = c_RealVector_OscaleR__class_OscaleR(X3,X4,X2) ) ).
cnf(i_0_993,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_994,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_995,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_996,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_997,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_998,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_999,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1000,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1001,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1002,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1003,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1004,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1005,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_1006,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1007,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1008,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1009,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_1010,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1011,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1012,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1013,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_1014,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1015,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1016,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1017,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1018,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1019,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_1020,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1021,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1022,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1023,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1024,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1025,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1026,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1027,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1028,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1029,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1030,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1031,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1032,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1033,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1034,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1035,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1036,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_1037,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1038,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_1039,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1040,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1041,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1042,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1043,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_970_001,axiom,
X1 = X1 ).
cnf(i_0_971_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_972_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_973_004,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X1,X3) = c_RealVector_Onorm__class_Onorm(X2,X3) ) ).
cnf(i_0_974_005,axiom,
( X1 != X2
| c_RealVector_Onorm__class_Onorm(X3,X1) = c_RealVector_Onorm__class_Onorm(X3,X2) ) ).
cnf(i_0_975_006,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X1,X3) = c_HOL_Oabs__class_Oabs(X2,X3) ) ).
cnf(i_0_976_007,axiom,
( X1 != X2
| c_HOL_Oabs__class_Oabs(X3,X1) = c_HOL_Oabs__class_Oabs(X3,X2) ) ).
cnf(i_0_977_008,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X1,X3,X4) = c_HOL_Otimes__class_Otimes(X2,X3,X4) ) ).
cnf(i_0_978_009,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X1,X4) = c_HOL_Otimes__class_Otimes(X3,X2,X4) ) ).
cnf(i_0_979_010,axiom,
( X1 != X2
| c_HOL_Otimes__class_Otimes(X3,X4,X1) = c_HOL_Otimes__class_Otimes(X3,X4,X2) ) ).
cnf(i_0_980_011,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X1,X3) = c_HOL_Ouminus__class_Ouminus(X2,X3) ) ).
cnf(i_0_981_012,axiom,
( X1 != X2
| c_HOL_Ouminus__class_Ouminus(X3,X1) = c_HOL_Ouminus__class_Ouminus(X3,X2) ) ).
cnf(i_0_982_013,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X1,X3) = c_Int_Onumber__class_Onumber__of(X2,X3) ) ).
cnf(i_0_983_014,axiom,
( X1 != X2
| c_Int_Onumber__class_Onumber__of(X3,X1) = c_Int_Onumber__class_Onumber__of(X3,X2) ) ).
cnf(i_0_984_015,axiom,
( X1 != X2
| c_RealVector_Oof__real(X1,X3) = c_RealVector_Oof__real(X2,X3) ) ).
cnf(i_0_985_016,axiom,
( X1 != X2
| c_RealVector_Oof__real(X3,X1) = c_RealVector_Oof__real(X3,X2) ) ).
cnf(i_0_986_017,axiom,
( X1 != X2
| c_Polynomial_Opoly(X1,X3,X4) = c_Polynomial_Opoly(X2,X3,X4) ) ).
cnf(i_0_987_018,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X1,X4) = c_Polynomial_Opoly(X3,X2,X4) ) ).
cnf(i_0_988_019,axiom,
( X1 != X2
| c_Polynomial_Opoly(X3,X4,X1) = c_Polynomial_Opoly(X3,X4,X2) ) ).
cnf(i_0_989_020,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_990_021,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X1,X3,X4) = c_RealVector_OscaleR__class_OscaleR(X2,X3,X4) ) ).
cnf(i_0_991_022,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X3,X1,X4) = c_RealVector_OscaleR__class_OscaleR(X3,X2,X4) ) ).
cnf(i_0_992_023,axiom,
( X1 != X2
| c_RealVector_OscaleR__class_OscaleR(X3,X4,X1) = c_RealVector_OscaleR__class_OscaleR(X3,X4,X2) ) ).
cnf(i_0_993_024,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_994_025,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_995_026,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_996_027,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_997_028,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_998_029,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_999_030,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1000_031,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1001_032,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1002_033,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1003_034,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1004_035,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1005_036,axiom,
( X1 != X2
| ~ class_Int_Onumber(X1)
| class_Int_Onumber(X2) ) ).
cnf(i_0_1006_037,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1007_038,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1008_039,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1009_040,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_1010_041,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1011_042,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1012_043,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1013_044,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_1014_045,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1015_046,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1016_047,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1017_048,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1018_049,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1019_050,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring(X1)
| class_Ring__and__Field_Ocomm__ring(X2) ) ).
cnf(i_0_1020_051,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1021_052,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1022_053,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1023_054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1024_055,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1025_056,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1026_057,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1027_058,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1028_059,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1029_060,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1030_061,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1031_062,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1032_063,axiom,
( X1 != X2
| ~ class_Int_Oring__char__0(X1)
| class_Int_Oring__char__0(X2) ) ).
cnf(i_0_1033_064,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1034_065,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1035_066,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1036_067,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| class_Ring__and__Field_Ocomm__ring__1(X2) ) ).
cnf(i_0_1037_068,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1038_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__0(X1)
| class_Ring__and__Field_Ocomm__semiring__0(X2) ) ).
cnf(i_0_1039_070,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1040_071,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1041_072,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1042_073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1043_074,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1044,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = c_HOL_Ouminus__class_Ouminus(X1,X2) ),
inference(equality_inference,[],[666]) ).
cnf(i_0_1045,plain,
( ~ class_RealVector_Oreal__vector(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[679]) ).
cnf(i_0_1046,plain,
( X1 = X1
| ~ class_RealVector_Oreal__vector(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[681]) ).
cnf(i_0_1047,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[700]) ).
cnf(i_0_1048,plain,
( X1 = X1
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[701]) ).
cnf(i_0_1049,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Int_Oring__char__0(X1) ),
inference(equality_inference,[],[810]) ).
cnf(i_0_1050,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[814]) ).
cnf(i_0_1051,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[815]) ).
cnf(i_0_1052,plain,
( X1 = X1
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(equality_inference,[],[816]) ).
cnf(i_0_1053,plain,
$false,
inference(scs_inference,[],[i_0_771,i_0_726,i_0_782,i_0_572]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG373-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 10:33:02 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 0.94/1.68 % Version : CSE_E---1.7
% 0.94/1.68 % Problem : theBenchmark.p
% 0.94/1.68 % SZS status Unsatisfiable for theBenchmark.p
% 0.94/1.68 % SZS output start CNFRefutation
% See solution above
% 0.98/1.72 % Total time : 1.327s
%------------------------------------------------------------------------------