%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG361-1 : 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 04:08:32 PM UTC 2026
% Result : Unsatisfiable 0.52s 1.67s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 636)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_that_0,axiom,
( v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,X1,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
cnf(cls_summable__norm_0,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_Series_Osuminf(X2,X1)),c_Series_Osuminf(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__norm_0) ).
cnf(cls_abs__setsum__abs_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__setsum__abs_0) ).
cnf(cls_LIM__o_0,axiom,
( c_Lim_OLIM(c_Fun_Ocomp(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OLIM(X4,X7,hAPP(X4,X7),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__o_0) ).
cnf(cls_LIM__compose_0,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OLIM(X4,X7,hAPP(X4,X7),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__compose_0) ).
cnf(cls_o__assoc_0,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
cnf(cls_CHAINED_1,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
cnf(cls_tendsto__minus__cancel_0,axiom,
( c_Limits_Otendsto(X2,X3,X4,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X5),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X4,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__minus__cancel_0) ).
cnf(cls_LIM__norm__zero__iff_0,axiom,
( c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm__zero__iff_0) ).
cnf(cls_setsum__abs_0,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X4),X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__abs_0) ).
cnf(cls_norm__setsum_0,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X4),X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__setsum_0) ).
cnf(cls_isCont__LIM__compose_0,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OisCont(X4,X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__LIM__compose_0) ).
cnf(cls_scaleR__right_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X6),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,X6,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIM_0) ).
cnf(cls_mult__right_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X6),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,X6,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM_0) ).
cnf(cls_scaleR__right_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X5),X6,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X3,X5,X6,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Otendsto_0) ).
cnf(cls_mult__right_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X5),X6,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_Otendsto(X3,X5,X6,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Otendsto_0) ).
cnf(cls_bounded__linear_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_RealVector_Obounded__linear(X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIM_0) ).
cnf(cls_bounded__linear_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(X3,X4,X2,X1,X5),hAPP(X3,X6),X7,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Limits_Otendsto(X4,X6,X7,X5,X2)
| ~ c_RealVector_Obounded__linear(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Otendsto_0) ).
cnf(cls_bounded__linear_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X2,X1,X3),X6,c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_RealVector_Obounded__linear(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIM__zero_0) ).
cnf(cls_scaleR__right_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIM__zero_0) ).
cnf(cls_scaleR_OLIM__right__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OLIM__right__zero_0) ).
cnf(cls_LIM__mult__right__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__right__zero_0) ).
cnf(cls_mult__right_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM__zero_0) ).
cnf(cls_LIM__of__real_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(X1),X3,tc_RealDef_Oreal,X1,X2),X4,hAPP(c_RealVector_Oof__real(X1),X5),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__of__real_0) ).
cnf(cls_LIM__minus_0,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X3,X1,X1,X2),X4,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X5),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__minus_0) ).
cnf(cls_LIM__norm_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,hAPP(c_RealVector_Onorm__class_Onorm(X1),X5),X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm_0) ).
cnf(cls_of__real_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X3),hAPP(c_RealVector_Oof__real(X1),X4),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Otendsto_0) ).
cnf(cls_tendsto__minus_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__minus_0) ).
cnf(cls_tendsto__norm_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X3),hAPP(c_RealVector_Onorm__class_Onorm(X1),X4),X5,X3,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__norm_0) ).
cnf(cls_of__real_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(X1),X3,tc_RealDef_Oreal,X1,X2),X4,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OLIM__zero_0) ).
cnf(cls_LIM__norm__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__norm__zero_0) ).
cnf(cls_Re_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_ORe,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,hAPP(c_Complex_ORe,X4),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OLIM_0) ).
cnf(cls_cnj_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_Ocnj,X2,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X1),X3,hAPP(c_Complex_Ocnj,X4),X1,tc_Complex_Ocomplex)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OLIM_0) ).
cnf(cls_Im_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_OIm,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,hAPP(c_Complex_OIm,X4),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OLIM_0) ).
cnf(cls_Re_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),hAPP(c_Complex_ORe,X3),X4,X2,tc_RealDef_Oreal)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Otendsto_0) ).
cnf(cls_cnj_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X2),hAPP(c_Complex_Ocnj,X3),X4,X2,tc_Complex_Ocomplex)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Otendsto_0) ).
cnf(cls_Im_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3),X4,X2,tc_RealDef_Oreal)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Otendsto_0) ).
cnf(cls_Re_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_ORe,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OLIM__zero_0) ).
cnf(cls_cnj_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_Ocnj,X2,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X1),X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OLIM__zero_0) ).
cnf(cls_Im_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_OIm,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OLIM__zero_0) ).
cnf(cls_setsum__abs__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__abs__ge__zero_0) ).
cnf(cls_comp__cong_0,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
| hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
cnf(cls_summable__comparison__test_1,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(X3,tc_RealDef_Oreal)
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),hAPP(X2,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1))),hAPP(X3,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1)),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__comparison__test_1) ).
cnf(cls_LIMSEQ__SEQ__conv1_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X3,X4,X2,X1,tc_nat),X5,X1)
| hAPP(X4,c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1(X4,X6,X2)) = X6
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_SEQ_OLIMSEQ(X4,X6,X2)
| ~ c_Lim_OLIM(X3,X6,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__SEQ__conv1_0) ).
cnf(cls_Zfun__norm__iff_0,axiom,
( c_Limits_OZfun(X2,X3,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X4),X3,X4,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__norm__iff_0) ).
cnf(cls_LIMSEQ__minus__cancel_0,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__minus__cancel_0) ).
cnf(cls_LIMSEQ__norm__zero_0,axiom,
( c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_0) ).
cnf(cls_o__eq__dest_0,axiom,
( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
cnf(cls_Zseq__norm__iff_0,axiom,
( c_SEQ_OZseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__norm__iff_0) ).
cnf(cls_summable__norm__cancel_0,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__norm__cancel_0) ).
cnf(cls_LIM__unique_0,axiom,
( X3 = X4
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(X5,X6,X4,X2,X1)
| ~ c_Lim_OLIM(X5,X6,X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__unique_0) ).
cnf(cls_decseq__eq__incseq_1,axiom,
( c_SEQ_Odecseq(X1)
| ~ c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_decseq__eq__incseq_1) ).
cnf(cls_isCont__o_0,axiom,
( c_Lim_OisCont(c_Fun_Ocomp(X4,X5,X3,X2,X1),X6,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OisCont(X4,hAPP(X5,X6),X3,X2)
| ~ c_Lim_OisCont(X5,X6,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__o_0) ).
cnf(cls_isCont__o2_0,axiom,
( c_Lim_OisCont(c_COMBB(X4,X5,X3,X2,X1),X6,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OisCont(X4,hAPP(X5,X6),X3,X2)
| ~ c_Lim_OisCont(X5,X6,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__o2_0) ).
cnf(cls_image__compose_0,axiom,
c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
cnf(cls_scaleR__right_Osetsum_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osetsum_0) ).
cnf(cls_setsum__right__distrib_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).
cnf(cls_mult__right_Osetsum_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osetsum_0) ).
cnf(cls_of__real_Osetsum_0,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_Finite__Set_Osetsum(X2,X3,X4,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X4),X3,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osetsum_0) ).
cnf(cls_setsum__negf_0,axiom,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__negf_0) ).
cnf(cls_Re_Osetsum_0,axiom,
hAPP(c_Complex_ORe,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X3),X2,X3,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osetsum_0) ).
cnf(cls_cnj_Osetsum_0,axiom,
hAPP(c_Complex_Ocnj,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X3),X2,X3,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Osetsum_0) ).
cnf(cls_Im_Osetsum_0,axiom,
hAPP(c_Complex_OIm,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X3),X2,X3,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osetsum_0) ).
cnf(cls_bounded__linear_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(X3,X4,X2,X1,X5),X6,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Limits_OZfun(X4,X6,X5,X2)
| ~ c_RealVector_Obounded__linear(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OZfun_0) ).
cnf(cls_scaleR_OZfun__right_0,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZfun__right_0) ).
cnf(cls_scaleR__right_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OZfun_0) ).
cnf(cls_Zfun__mult__right_0,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__right_0) ).
cnf(cls_mult__right_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZfun_0) ).
cnf(cls_isCont__minus_0,axiom,
( c_Lim_OisCont(c_COMBB(c_HOL_Ouminus__class_Ouminus(X2),X3,X2,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__minus_0) ).
cnf(cls_isCont__norm_0,axiom,
( c_Lim_OisCont(c_COMBB(c_RealVector_Onorm__class_Onorm(X2),X3,X2,tc_RealDef_Oreal,X1),X4,X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__norm_0) ).
cnf(cls_of__real_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X3),X4,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Limits_OZfun(X2,X4,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OZfun_0) ).
cnf(cls_isCont__of__real_0,axiom,
( c_Lim_OisCont(c_COMBB(c_RealVector_Oof__real(X2),X3,tc_RealDef_Oreal,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OisCont(X3,X4,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__of__real_0) ).
cnf(cls_Zfun__minus_0,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__minus_0) ).
cnf(cls_Zfun__norm__iff_1,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X3),X4,X3,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__norm__iff_1) ).
cnf(cls_Re_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),X3,X2,tc_RealDef_Oreal)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OZfun_0) ).
cnf(cls_cnj_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X2),X3,X2,tc_Complex_Ocomplex)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OZfun_0) ).
cnf(cls_Im_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),X3,X2,tc_RealDef_Oreal)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OZfun_0) ).
cnf(cls_differentiable__compose_0,axiom,
( c_Deriv_Odifferentiable(c_COMBB(X2,X3,X1,X1,X1),X4,X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| ~ c_Deriv_Odifferentiable(X2,hAPP(X3,X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__compose_0) ).
cnf(cls_scaleR__right_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osums_0) ).
cnf(cls_sums__mult_0,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__mult_0) ).
cnf(cls_mult__right_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osums_0) ).
cnf(cls_scaleR__right_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OLIMSEQ_0) ).
cnf(cls_mult__right_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIMSEQ_0) ).
cnf(cls_bounded__linear_Osums_0,axiom,
( c_Series_Osums(c_COMBB(X3,X4,X1,X2,tc_nat),hAPP(X3,X5),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osums(X4,X5,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osums_0) ).
cnf(cls_bounded__linear_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X3,X4,X1,X2,tc_nat),hAPP(X3,X5),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OLIMSEQ(X4,X5,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OLIMSEQ_0) ).
cnf(cls_of__real_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),hAPP(c_RealVector_Oof__real(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osums(X2,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osums_0) ).
cnf(cls_of__real_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),hAPP(c_RealVector_Oof__real(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OLIMSEQ_0) ).
cnf(cls_sums__minus_0,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__minus_0) ).
cnf(cls_LIMSEQ__minus_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__minus_0) ).
cnf(cls_LIMSEQ__norm_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),hAPP(c_RealVector_Onorm__class_Onorm(X1),X3),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm_0) ).
cnf(cls_bounded__linear_Osuminf_0,axiom,
( hAPP(X3,c_Series_Osuminf(X4,X1)) = c_Series_Osuminf(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osummable(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osuminf_0) ).
cnf(cls_LIMSEQ__norm__zero_1,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__norm__zero_1) ).
cnf(cls_differentiable__minus_0,axiom,
( c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X1),X3,X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__minus_0) ).
cnf(cls_suminf__mult_0,axiom,
( c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Series_Osuminf(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__mult_0) ).
cnf(cls_scaleR__right_Osuminf_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osuminf_0) ).
cnf(cls_mult__right_Osuminf_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osuminf_0) ).
cnf(cls_LIMSEQ__subseq__LIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_Fun_Ocomp(X2,X3,tc_nat,X1,tc_nat),X4,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Osubseq(X3)
| ~ c_SEQ_OLIMSEQ(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__subseq__LIMSEQ_0) ).
cnf(cls_Re_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X2),tc_RealDef_Oreal)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osums_0) ).
cnf(cls_cnj_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X2),tc_Complex_Ocomplex)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Osums_0) ).
cnf(cls_Im_Osums_0,axiom,
( c_Series_Osums(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X2),tc_RealDef_Oreal)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osums_0) ).
cnf(cls_Re_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X2),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OLIMSEQ_0) ).
cnf(cls_cnj_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X2),tc_Complex_Ocomplex)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OLIMSEQ_0) ).
cnf(cls_Im_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X2),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OLIMSEQ_0) ).
cnf(cls_isUCont__Cauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_SEQ_OCauchy(X4,X1)
| ~ c_Lim_OisUCont(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isUCont__Cauchy_0) ).
cnf(cls_bounded__linear_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OCauchy(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OCauchy_0) ).
cnf(cls_bounded__linear_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OZseq(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OZseq_0) ).
cnf(cls_bounded__linear_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osummable(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Osummable_0) ).
cnf(cls_suminf__minus_0,axiom,
( c_Series_Osuminf(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Series_Osuminf(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__minus_0) ).
cnf(cls_of__real_Osuminf_0,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_Series_Osuminf(X2,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osummable(X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osuminf_0) ).
cnf(cls_scaleR__right_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OCauchy(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OCauchy_0) ).
cnf(cls_mult__right_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OCauchy(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OCauchy_0) ).
cnf(cls_scaleR_OZseq__right_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZseq__right_0) ).
cnf(cls_scaleR__right_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OZseq_0) ).
cnf(cls_Zseq__mult__right_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__mult__right_0) ).
cnf(cls_mult__right_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZseq_0) ).
cnf(cls_scaleR__right_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Osummable_0) ).
cnf(cls_mult__right_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osummable_0) ).
cnf(cls_summable__mult_0,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__mult_0) ).
cnf(cls_Re_Osuminf_0,axiom,
( hAPP(c_Complex_ORe,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osuminf_0) ).
cnf(cls_cnj_Osuminf_0,axiom,
( hAPP(c_Complex_Ocnj,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Osuminf_0) ).
cnf(cls_Im_Osuminf_0,axiom,
( hAPP(c_Complex_OIm,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osuminf_0) ).
cnf(cls_of__real_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OCauchy(X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OCauchy_0) ).
cnf(cls_of__real_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OZseq(X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_OZseq_0) ).
cnf(cls_of__real_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osummable(X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Osummable_0) ).
cnf(cls_o__apply_0,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
cnf(cls_COMBB__def_0,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
cnf(cls_o__eq__dest__lhs_0,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
cnf(cls_Zseq__minus_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__minus_0) ).
cnf(cls_summable__minus_0,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__minus_0) ).
cnf(cls_Zseq__norm__iff_1,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__norm__iff_1) ).
cnf(cls_Cauchy__subseq__Cauchy_0,axiom,
( c_SEQ_OCauchy(c_Fun_Ocomp(X2,X3,tc_nat,X1,tc_nat),X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Osubseq(X3)
| ~ c_SEQ_OCauchy(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cauchy__subseq__Cauchy_0) ).
cnf(cls_Re_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OCauchy_0) ).
cnf(cls_cnj_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OCauchy_0) ).
cnf(cls_Im_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OCauchy_0) ).
cnf(cls_Re_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OZseq_0) ).
cnf(cls_cnj_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_OZseq_0) ).
cnf(cls_Im_OZseq_0,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OZseq_0) ).
cnf(cls_Re_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Osummable_0) ).
cnf(cls_cnj_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Osummable_0) ).
cnf(cls_Im_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Osummable_0) ).
cnf(cls_decseq__eq__incseq_0,axiom,
( c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Odecseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_decseq__eq__incseq_0) ).
cnf(cls_monoseq__minus_0,axiom,
( c_SEQ_Omonoseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Omonoseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__minus_0) ).
cnf(cls_seq__monosub_1,axiom,
c_SEQ_Omonoseq(c_COMBB(X1,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X1),tc_nat,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_seq__monosub_1) ).
cnf(cls_isCont__def_1,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_1) ).
cnf(cls_isCont__def_0,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_0) ).
cnf(cls_bounded__linear_Ocont_0,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_Ocont_0) ).
cnf(cls_scaleR__right_Ocont_0,axiom,
( c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Ocont_0) ).
cnf(cls_mult__right_Ocont_0,axiom,
( c_Lim_OLIM(c_HOL_Otimes__class_Otimes(X2,X1),X3,hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ocont_0) ).
cnf(cls_Re_Ocont_0,axiom,
c_Lim_OLIM(c_Complex_ORe,X1,hAPP(c_Complex_ORe,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Ocont_0) ).
cnf(cls_Im_Ocont_0,axiom,
c_Lim_OLIM(c_Complex_OIm,X1,hAPP(c_Complex_OIm,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Ocont_0) ).
cnf(cls_abs__mult__less_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3)),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X3),X5,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(X4,X1),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X5))
| ~ 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_summable__comparison__test_0,axiom,
( c_Series_Osummable(X2,X1)
| c_lessequals(X4,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1),tc_nat)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__comparison__test_0) ).
cnf(cls_mult__mono_H_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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__le__mult_0,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3)),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X5))
| ~ 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_class__semiring_Osemiring__rules_I14_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)))
| ~ 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__le__cancel__left__pos_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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__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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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__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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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_monoseq__le_3,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),hAPP(X1,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_OLIMSEQ(X1,X6,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__le_3) ).
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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
cnf(cls_abs__eq__mult_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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__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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__left__mono_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__right__mono_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__less__cancel__left__pos_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__left__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__right__disj_4,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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__strict__right__mono_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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__le__cancel__left__neg_1,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__left__mono__neg_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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__right__mono__neg_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_class__semiring_Osemiring__rules_I16_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1),X3)
| ~ 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_monoseq__def_0,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),hAPP(X1,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_Omonoseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__def_0) ).
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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
cnf(cls_monoseq__le_1,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),X5,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_SEQ_OLIMSEQ(X1,X5,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__le_1) ).
cnf(cls_monoseq__le_2,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X2,X4),hAPP(X2,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__le_2) ).
cnf(cls_isUCont__isCont_0,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisUCont(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isUCont__isCont_0) ).
cnf(cls_bounded__linear_OisCont_0,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OisCont_0) ).
cnf(cls_mult__le__0__iff_1,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_zero__le__mult__iff_4,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_split__mult__pos__le_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_mult__pos__pos_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_zero__le__mult__iff_5,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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__nonpos__nonpos_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_mult__neg__neg_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_abs__le__iff_2,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).
cnf(cls_abs__leI_0,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__leI_0) ).
cnf(cls_abs__less__iff_2,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
cnf(cls_mult__scaleR__left_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
cnf(cls_mult__left_OscaleR_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ 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_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ 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_Omul__a_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4)
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4)
| ~ 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_abs__mult__pos_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),X3) = hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ 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_scaleR__right_OisCont_0,axiom,
( c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OisCont_0) ).
cnf(cls_mult__right_OisCont_0,axiom,
( c_Lim_OisCont(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).
cnf(cls_neg__le__iff__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
cnf(cls_abs__mult_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
cnf(cls_bounded__linear_OscaleR_0,axiom,
( hAPP(X3,hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X1),X5)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X2),hAPP(X3,X5))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OscaleR_0) ).
cnf(cls_monoseq__le_0,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X2,X4),X1,tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoseq__le_0) ).
cnf(cls_minus__le__iff_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
cnf(cls_minus__le__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
cnf(cls_abs__le__D2_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).
cnf(cls_abs__less__iff_1,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
cnf(cls_minus__less__iff_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
cnf(cls_le__minus__iff_0,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
cnf(cls_le__minus__iff_1,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
cnf(cls_Re_OisCont_0,axiom,
c_Lim_OisCont(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OisCont_0) ).
cnf(cls_Im_OisCont_0,axiom,
c_Lim_OisCont(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OisCont_0) ).
cnf(cls_scaleR__left__commute_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
cnf(cls_scaleR__right_OscaleR_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ 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,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
cnf(cls_mult__right_OscaleR_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ 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_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__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_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_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_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
cnf(cls_le__imp__neg__le_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),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_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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).
cnf(cls_mult_Ominus__left_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
cnf(cls_minus__mult__left_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_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_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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
cnf(cls_scaleR__left_Ominus_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Ominus_0) ).
cnf(cls_scaleR__minus__left_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__left_0) ).
cnf(cls_scaleR_Ominus__left_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__left_0) ).
cnf(cls_abs__le__D1_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),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(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_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_neg__le__0__iff__le_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),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),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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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__mult__self_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
cnf(cls_square__eq__iff_1,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2)
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
cnf(cls_minus__mult__commute_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
cnf(cls_decseq__def_0,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_SEQ_Odecseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_decseq__def_0) ).
cnf(cls_incseq__def_0,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_SEQ_Oincseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_incseq__def_0) ).
cnf(cls_subseq__def_0,axiom,
( c_HOL_Oord__class_Oless(hAPP(X1,X2),hAPP(X1,X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_SEQ_Osubseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subseq__def_0) ).
cnf(cls_minus__le__self__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_nat__less__cases_0,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).
cnf(cls_complex__minus__def_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1) = c_Complex_Ocomplex_OComplex(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__minus__def_0) ).
cnf(cls_scaleR__minus__right_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
cnf(cls_scaleR_Ominus__right_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).
cnf(cls_mult_Ominus__right_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
cnf(cls_minus__mult__right_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
cnf(cls_abs__minus__le__zero_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)),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_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),hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
cnf(cls_order__antisym__conv_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
cnf(cls_order__eq__iff_2,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
cnf(cls_order__antisym_0,axiom,
( X2 = X3
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X2,X1)
| ~ c_lessequals(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
cnf(cls_LIMSEQ__unique_0,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X4,X3,X1)
| ~ c_SEQ_OLIMSEQ(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__unique_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_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_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_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_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_incseq__le_0,axiom,
( c_lessequals(hAPP(X1,X2),X3,tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X3,tc_RealDef_Oreal)
| ~ c_SEQ_Oincseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_incseq__le_0) ).
cnf(cls_decseq__le_0,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Odecseq(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_decseq__le_0) ).
cnf(cls_le__antisym_0,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_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_abs__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).
cnf(cls_mult__left__idem_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_scaleR__conv__of__real_0,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_Oof__real(X1),X2),X1),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
cnf(cls_abs__not__less__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
cnf(cls_norm__le__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),X2),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_square__eq__iff_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2) != hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_bounded__linear_OisUCont_0,axiom,
( c_Lim_OisUCont(X3,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bounded__linear_OisUCont_0) ).
cnf(cls_abs__if__lattice_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_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_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_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_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__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__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_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_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_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_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_zero__le__square_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
cnf(cls_abs__if_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
cnf(cls_nat__less__le_2,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
cnf(cls_le__neq__implies__less_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
cnf(cls_scaleR__cancel__left_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).
cnf(cls_termination__basic__simps_I5_J_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
cnf(cls_nat__less__le_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
cnf(cls_cnj__def_0,axiom,
hAPP(c_Complex_Ocnj,X1) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj__def_0) ).
cnf(cls_of__real_Ominus_0,axiom,
( hAPP(c_RealVector_Oof__real(X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_Oof__real(X1),X2))
| ~ 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__of__nonneg_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_complex__minus_0,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__minus_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_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_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__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__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_abs__le__zero__iff_1,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(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_of__real__minus_0,axiom,
( hAPP(c_RealVector_Oof__real(X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_Oof__real(X1),X2))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__minus_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_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__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_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_cnj__def__raw_0,axiom,
hAPP(c_Complex_Ocnj,v_z) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,v_z),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,v_z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj__def__raw_0) ).
cnf(cls_norm__le__zero__iff_1,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_HOL_Ozero__class_Ozero(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),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),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_sums__iff_2,axiom,
( c_Series_Osums(X2,c_Series_Osuminf(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_2) ).
cnf(cls_summable__sums_0,axiom,
( c_Series_Osums(X2,c_Series_Osuminf(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__sums_0) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
cnf(cls_sums__iff_1,axiom,
( c_Series_Osuminf(X2,X1) = X3
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_1) ).
cnf(cls_sums__unique_0,axiom,
( X2 = c_Series_Osuminf(X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__unique_0) ).
cnf(cls_LIMSEQ__imp__Cauchy_0,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).
cnf(cls_sums__iff_0,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_0) ).
cnf(cls_sums__summable_0,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__summable_0) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_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__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).
cnf(cls_norm__ge__zero_0,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(X1),X2),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).
cnf(cls_abs__ge__self_0,axiom,
( c_lessequals(X2,hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).
cnf(cls_scaleR__cancel__left_1,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X3)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).
cnf(cls_scaleR__cancel__right_1,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
cnf(cls_abs__if__lattice_1,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_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_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_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_summable__LIMSEQ__zero_0,axiom,
( c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__LIMSEQ__zero_0) ).
cnf(cls_abs__if_1,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_ATP__Linkup_Ofequal__imp__equal_0,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
cnf(cls_scaleR__right_OisUCont_0,axiom,
( c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OisUCont_0) ).
cnf(cls_mult__right_OisUCont_0,axiom,
( c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisUCont_0) ).
cnf(cls_scaleR_Obounded__linear__right_0,axiom,
( c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Obounded__linear__right_0) ).
cnf(cls_mult_Obounded__linear__right_0,axiom,
( c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded__linear__right_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)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).
cnf(cls_no__zero__divisors_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2)
| ~ 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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_seq__suble_0,axiom,
( c_lessequals(X1,hAPP(X2,X1),tc_nat)
| ~ c_SEQ_Osubseq(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_seq__suble_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)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).
cnf(cls_norm__minus__cancel_0,axiom,
( hAPP(c_RealVector_Onorm__class_Onorm(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_RealVector_Onorm__class_Onorm(X1),X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).
cnf(cls_abs__idempotent_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)) = hAPP(c_HOL_Oabs__class_Oabs(X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
cnf(cls_abs__minus__cancel_0,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Oabs__class_Oabs(X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
cnf(cls_Re_Ominus_0,axiom,
hAPP(c_Complex_ORe,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Ominus_0) ).
cnf(cls_cnj_Ominus_0,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_Complex_Ocnj,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ominus_0) ).
cnf(cls_Im_Ominus_0,axiom,
hAPP(c_Complex_OIm,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Ominus_0) ).
cnf(cls_complex__cnj_0,axiom,
hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj_0) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
cnf(cls_complex__equality_0,axiom,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__equality_0) ).
cnf(cls_complex__Im__cnj_0,axiom,
hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__Im__cnj_0) ).
cnf(cls_of__real__eq__iff_0,axiom,
( X2 = X3
| ~ class_RealVector_Oreal__algebra__1(X1)
| hAPP(c_RealVector_Oof__real(X1),X2) != hAPP(c_RealVector_Oof__real(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
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)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
cnf(cls_double__compl_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
cnf(cls_minus__minus_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
cnf(cls_minus__equation__iff_1,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = 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 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ 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 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
cnf(cls_mult__zero__left_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_mult__eq__0__iff_1,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_class__semiring_Omul__0_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_Ozero__left_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_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_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_complex__cnj__complex__of__real_0,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__complex__of__real_0) ).
cnf(cls_complex__surj_0,axiom,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__surj_0) ).
cnf(cls_scaleR__eq__0__iff_1,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = 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,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = 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_scaleR__eq__0__iff_2,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(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,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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_mult__eq__0__iff_2,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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_class__semiring_Osemiring__rules_I10_J_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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__right_Ozero_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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_ATP__Linkup_Oequal__imp__fequal_0,axiom,
c_fequal(X1,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(X1,X1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_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_complex__eq__cancel__iff2_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_1) ).
cnf(cls_complex__eq__cancel__iff2_0,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_0) ).
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) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__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)
| hAPP(c_HOL_Oabs__class_Oabs(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
cnf(cls_Re_OisUCont_0,axiom,
c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_OisUCont_0) ).
cnf(cls_Im_OisUCont_0,axiom,
c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_OisUCont_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)
| hAPP(c_RealVector_Oof__real(X1),X2) != 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)
| hAPP(c_RealVector_Onorm__class_Onorm(X1),X2) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).
cnf(cls_mult__idem_0,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_complex__Re__cnj_0,axiom,
hAPP(c_Complex_ORe,hAPP(c_Complex_Ocnj,X1)) = hAPP(c_Complex_ORe,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__Re__cnj_0) ).
cnf(cls_Im__complex__of__real_0,axiom,
hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im__complex__of__real_0) ).
cnf(cls_complex_Oinject_0,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_0) ).
cnf(cls_complex_Oinject_1,axiom,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex_Oinject_1) ).
cnf(cls_neg__equal__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
cnf(cls_Re__complex__of__real_0,axiom,
hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re__complex__of__real_0) ).
cnf(cls_of__real_Ozero_0,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = 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_complex__cnj__cancel__iff_0,axiom,
( X1 = X2
| hAPP(c_Complex_Ocnj,X1) != hAPP(c_Complex_Ocnj,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
cnf(cls_Re_0,axiom,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_0) ).
cnf(cls_Im_0,axiom,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_0) ).
cnf(cls_abs__eq__0_1,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(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_minus__zero_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(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,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(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_neg__0__equal__iff__equal_1,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).
cnf(clsarity_fun__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
cnf(clsarity_fun__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
cnf(cls_complex__cnj__cnj_0,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
cnf(cls_norm__zero_0,axiom,
( hAPP(c_RealVector_Onorm__class_Onorm(X1),c_HOL_Ozero__class_Ozero(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,
( hAPP(c_RealVector_Oof__real(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = 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(cls_complex__of__real__def_0,axiom,
hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1) = c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__of__real__def_0) ).
cnf(cls_complex__eq__cancel__iff2_2,axiom,
c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__eq__cancel__iff2_2) ).
cnf(cls_Complex__eq__0_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__eq__0_0) ).
cnf(cls_Complex__eq__0_1,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__eq__0_1) ).
cnf(cls_complex__cnj__zero__iff_0,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Complex_Ocnj,X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
cnf(cls_Complex__eq__0_2,axiom,
c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Complex__eq__0_2) ).
cnf(cls_complex__zero__def_0,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__zero__def_0) ).
cnf(cls_Re_Ozero_0,axiom,
hAPP(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Re_Ozero_0) ).
cnf(cls_cnj_Ozero_0,axiom,
hAPP(c_Complex_Ocnj,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
cnf(cls_Im_Ozero_0,axiom,
hAPP(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Im_Ozero_0) ).
cnf(cls_decseq__imp__monoseq_0,axiom,
( c_SEQ_Omonoseq(X1)
| ~ c_SEQ_Odecseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_decseq__imp__monoseq_0) ).
cnf(cls_incseq__imp__monoseq_0,axiom,
( c_SEQ_Omonoseq(X1)
| ~ c_SEQ_Oincseq(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_incseq__imp__monoseq_0) ).
cnf(cls_seq__monosub_0,axiom,
c_SEQ_Osubseq(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_seq__monosub_0) ).
cnf(cls_CHAINED_0,axiom,
c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(clsarity_bool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_bool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_bool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
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_Complex__Ocomplex__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
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_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
cnf(clsarity_Complex__Ocomplex__SEQ_Obanach,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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__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_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_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_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_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_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_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_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_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_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_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_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_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(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).
cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Ometric__space) ).
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_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_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_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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_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_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__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(cls_conjecture_0,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(i_0_595,axiom,
( v_thesis____
| ~ c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,X1,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Osubseq(X1) ),
cls_that_0,
[final] ).
cnf(i_0_596,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_Series_Osuminf(X2,X1)),c_Series_Osuminf(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
cls_summable__norm_0,
[final] ).
cnf(i_0_597,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__setsum__abs_0,
[final] ).
cnf(i_0_598,axiom,
( c_Lim_OLIM(c_Fun_Ocomp(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OLIM(X4,X7,hAPP(X4,X7),X1,X2) ),
cls_LIM__o_0,
[final] ).
cnf(i_0_599,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OLIM(X4,X7,hAPP(X4,X7),X1,X2) ),
cls_LIM__compose_0,
[final] ).
cnf(i_0_600,axiom,
c_Fun_Ocomp(X1,c_Fun_Ocomp(X2,X3,X4,X5,X6),X5,X7,X6) = c_Fun_Ocomp(c_Fun_Ocomp(X1,X2,X5,X7,X4),X3,X4,X7,X6),
cls_o__assoc_0,
[final] ).
cnf(i_0_601,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_sko__CHAINED__1(v_s),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
cls_CHAINED_1,
[final] ).
cnf(i_0_602,axiom,
( c_Limits_Otendsto(X2,X3,X4,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X5),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X4,X5,X1) ),
cls_tendsto__minus__cancel_0,
[final] ).
cnf(i_0_603,axiom,
( c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_LIM__norm__zero__iff_0,
[final] ).
cnf(i_0_604,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X4),X3,X4,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_setsum__abs_0,
[final] ).
cnf(i_0_605,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X4),X3,X4,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__setsum_0,
[final] ).
cnf(i_0_606,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_Lim_OisCont(X4,X7,X1,X2) ),
cls_isCont__LIM__compose_0,
[final] ).
cnf(i_0_607,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X6),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,X6,X2,X1) ),
cls_scaleR__right_OLIM_0,
[final] ).
cnf(i_0_608,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X6),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,X6,X2,X1) ),
cls_mult__right_OLIM_0,
[final] ).
cnf(i_0_609,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X5),X6,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X3,X5,X6,X4,X1) ),
cls_scaleR__right_Otendsto_0,
[final] ).
cnf(i_0_610,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X5),X6,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_Otendsto(X3,X5,X6,X4,X1) ),
cls_mult__right_Otendsto_0,
[final] ).
cnf(i_0_611,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X1,X2,X3),X6,hAPP(X4,X7),X3,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,X7,X3,X1)
| ~ c_RealVector_Obounded__linear(X4,X1,X2) ),
cls_bounded__linear_OLIM_0,
[final] ).
cnf(i_0_612,axiom,
( c_Limits_Otendsto(c_COMBB(X3,X4,X2,X1,X5),hAPP(X3,X6),X7,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Limits_Otendsto(X4,X6,X7,X5,X2)
| ~ c_RealVector_Obounded__linear(X3,X2,X1) ),
cls_bounded__linear_Otendsto_0,
[final] ).
cnf(i_0_613,axiom,
( c_Lim_OLIM(c_COMBB(X4,X5,X2,X1,X3),X6,c_HOL_Ozero__class_Ozero(X1),X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OLIM(X5,X6,c_HOL_Ozero__class_Ozero(X2),X3,X2)
| ~ c_RealVector_Obounded__linear(X4,X2,X1) ),
cls_bounded__linear_OLIM__zero_0,
[final] ).
cnf(i_0_614,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_scaleR__right_OLIM__zero_0,
[final] ).
cnf(i_0_615,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_scaleR_OLIM__right__zero_0,
[final] ).
cnf(i_0_616,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_LIM__mult__right__zero_0,
[final] ).
cnf(i_0_617,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Otimes__class_Otimes(X3,X1),X4,X1,X1,X2),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X4,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__right_OLIM__zero_0,
[final] ).
cnf(i_0_618,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(X1),X3,tc_RealDef_Oreal,X1,X2),X4,hAPP(c_RealVector_Oof__real(X1),X5),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,tc_RealDef_Oreal) ),
cls_LIM__of__real_0,
[final] ).
cnf(i_0_619,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X3,X1,X1,X2),X4,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X5),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
cls_LIM__minus_0,
[final] ).
cnf(i_0_620,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,hAPP(c_RealVector_Onorm__class_Onorm(X1),X5),X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
cls_LIM__norm_0,
[final] ).
cnf(i_0_621,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X3),hAPP(c_RealVector_Oof__real(X1),X4),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,tc_RealDef_Oreal) ),
cls_of__real_Otendsto_0,
[final] ).
cnf(i_0_622,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
cls_tendsto__minus_0,
[final] ).
cnf(i_0_623,axiom,
( c_Limits_Otendsto(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X3),hAPP(c_RealVector_Onorm__class_Onorm(X1),X4),X5,X3,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
cls_tendsto__norm_0,
[final] ).
cnf(i_0_624,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Oof__real(X1),X3,tc_RealDef_Oreal,X1,X2),X4,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_of__real_OLIM__zero_0,
[final] ).
cnf(i_0_625,axiom,
( c_Lim_OLIM(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X3,X1,tc_RealDef_Oreal,X2),X4,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_LIM__norm__zero_0,
[final] ).
cnf(i_0_626,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_ORe,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,hAPP(c_Complex_ORe,X4),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
cls_Re_OLIM_0,
[final] ).
cnf(i_0_627,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_Ocnj,X2,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X1),X3,hAPP(c_Complex_Ocnj,X4),X1,tc_Complex_Ocomplex)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
cls_cnj_OLIM_0,
[final] ).
cnf(i_0_628,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_OIm,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,hAPP(c_Complex_OIm,X4),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,X4,X1,tc_Complex_Ocomplex) ),
cls_Im_OLIM_0,
[final] ).
cnf(i_0_629,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),hAPP(c_Complex_ORe,X3),X4,X2,tc_RealDef_Oreal)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
cls_Re_Otendsto_0,
[final] ).
cnf(i_0_630,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X2),hAPP(c_Complex_Ocnj,X3),X4,X2,tc_Complex_Ocomplex)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
cls_cnj_Otendsto_0,
[final] ).
cnf(i_0_631,axiom,
( c_Limits_Otendsto(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),hAPP(c_Complex_OIm,X3),X4,X2,tc_RealDef_Oreal)
| ~ c_Limits_Otendsto(X1,X3,X4,X2,tc_Complex_Ocomplex) ),
cls_Im_Otendsto_0,
[final] ).
cnf(i_0_632,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_ORe,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
cls_Re_OLIM__zero_0,
[final] ).
cnf(i_0_633,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_Ocnj,X2,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X1),X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
cls_cnj_OLIM__zero_0,
[final] ).
cnf(i_0_634,axiom,
( c_Lim_OLIM(c_COMBB(c_Complex_OIm,X2,tc_Complex_Ocomplex,tc_RealDef_Oreal,X1),X3,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_Lim_OLIM(X2,X3,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
cls_Im_OLIM__zero_0,
[final] ).
cnf(i_0_635,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),c_Finite__Set_Osetsum(c_COMBB(c_HOL_Oabs__class_Oabs(X1),X2,X1,X1,X3),X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_setsum__abs__ge__zero_0,
[final] ).
cnf(i_0_636,axiom,
( hAPP(c_Fun_Ocomp(X1,X2,X7,X8,X9),X3) = hAPP(c_Fun_Ocomp(X4,X5,X10,X8,X11),X6)
| hAPP(X1,hAPP(X2,X3)) != hAPP(X4,hAPP(X5,X6)) ),
cls_comp__cong_0,
[final] ).
cnf(i_0_637,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(X3,tc_RealDef_Oreal)
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),hAPP(X2,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1))),hAPP(X3,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1)),tc_RealDef_Oreal) ),
cls_summable__comparison__test_1,
[final] ).
cnf(i_0_638,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X3,X4,X2,X1,tc_nat),X5,X1)
| hAPP(X4,c_Lim_Osko__Lim__XLIMSEQ__SEQ__conv1__1__1(X4,X6,X2)) = X6
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_SEQ_OLIMSEQ(X4,X6,X2)
| ~ c_Lim_OLIM(X3,X6,X5,X2,X1) ),
cls_LIMSEQ__SEQ__conv1_0,
[final] ).
cnf(i_0_639,axiom,
( c_Limits_OZfun(X2,X3,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X4),X3,X4,tc_RealDef_Oreal) ),
cls_Zfun__norm__iff_0,
[final] ).
cnf(i_0_640,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1) ),
cls_LIMSEQ__minus__cancel_0,
[final] ).
cnf(i_0_641,axiom,
( c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_LIMSEQ__norm__zero_0,
[final] ).
cnf(i_0_642,axiom,
( hAPP(X1,hAPP(X2,X9)) = hAPP(X6,hAPP(X7,X9))
| c_Fun_Ocomp(X1,X2,X3,X4,X5) != c_Fun_Ocomp(X6,X7,X8,X4,X5) ),
cls_o__eq__dest_0,
[final] ).
cnf(i_0_643,axiom,
( c_SEQ_OZseq(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
cls_Zseq__norm__iff_0,
[final] ).
cnf(i_0_644,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
cls_summable__norm__cancel_0,
[final] ).
cnf(i_0_645,axiom,
( X3 = X4
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(X5,X6,X4,X2,X1)
| ~ c_Lim_OLIM(X5,X6,X3,X2,X1) ),
cls_LIM__unique_0,
[final] ).
cnf(i_0_646,axiom,
( c_SEQ_Odecseq(X1)
| ~ c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat)) ),
cls_decseq__eq__incseq_1,
[final] ).
cnf(i_0_647,axiom,
( c_Lim_OisCont(c_Fun_Ocomp(X4,X5,X3,X2,X1),X6,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OisCont(X4,hAPP(X5,X6),X3,X2)
| ~ c_Lim_OisCont(X5,X6,X1,X3) ),
cls_isCont__o_0,
[final] ).
cnf(i_0_648,axiom,
( c_Lim_OisCont(c_COMBB(X4,X5,X3,X2,X1),X6,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ class_RealVector_Ometric__space(X3)
| ~ c_Lim_OisCont(X4,hAPP(X5,X6),X3,X2)
| ~ c_Lim_OisCont(X5,X6,X1,X3) ),
cls_isCont__o2_0,
[final] ).
cnf(i_0_649,axiom,
c_Set_Oimage(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6,X5,X4) = c_Set_Oimage(X1,c_Set_Oimage(X2,X6,X5,X3),X3,X4),
cls_image__compose_0,
[final] ).
cnf(i_0_650,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
cls_image__image_0,
[final] ).
cnf(i_0_651,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__right_Osetsum_0,
[final] ).
cnf(i_0_652,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__right__distrib_0,
[final] ).
cnf(i_0_653,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Osetsum_0,
[final] ).
cnf(i_0_654,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_Finite__Set_Osetsum(X2,X3,X4,tc_RealDef_Oreal)) = c_Finite__Set_Osetsum(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X4),X3,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real_Osetsum_0,
[final] ).
cnf(i_0_655,axiom,
( c_Finite__Set_Osetsum(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Finite__Set_Osetsum(X2,X4,X3,X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_setsum__negf_0,
[final] ).
cnf(i_0_656,axiom,
hAPP(c_Complex_ORe,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X3),X2,X3,tc_RealDef_Oreal),
cls_Re_Osetsum_0,
[final] ).
cnf(i_0_657,axiom,
hAPP(c_Complex_Ocnj,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X3),X2,X3,tc_Complex_Ocomplex),
cls_cnj_Osetsum_0,
[final] ).
cnf(i_0_658,axiom,
hAPP(c_Complex_OIm,c_Finite__Set_Osetsum(X1,X2,X3,tc_Complex_Ocomplex)) = c_Finite__Set_Osetsum(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X3),X2,X3,tc_RealDef_Oreal),
cls_Im_Osetsum_0,
[final] ).
cnf(i_0_659,axiom,
( c_Limits_OZfun(c_COMBB(X3,X4,X2,X1,X5),X6,X5,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Limits_OZfun(X4,X6,X5,X2)
| ~ c_RealVector_Obounded__linear(X3,X2,X1) ),
cls_bounded__linear_OZfun_0,
[final] ).
cnf(i_0_660,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
cls_scaleR_OZfun__right_0,
[final] ).
cnf(i_0_661,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
cls_scaleR__right_OZfun_0,
[final] ).
cnf(i_0_662,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
cls_Zfun__mult__right_0,
[final] ).
cnf(i_0_663,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,X4),X5,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X3,X5,X4,X1) ),
cls_mult__right_OZfun_0,
[final] ).
cnf(i_0_664,axiom,
( c_Lim_OisCont(c_COMBB(c_HOL_Ouminus__class_Ouminus(X2),X3,X2,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
cls_isCont__minus_0,
[final] ).
cnf(i_0_665,axiom,
( c_Lim_OisCont(c_COMBB(c_RealVector_Onorm__class_Onorm(X2),X3,X2,tc_RealDef_Oreal,X1),X4,X1,tc_RealDef_Oreal)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
cls_isCont__norm_0,
[final] ).
cnf(i_0_666,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,X3),X4,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Limits_OZfun(X2,X4,X3,tc_RealDef_Oreal) ),
cls_of__real_OZfun_0,
[final] ).
cnf(i_0_667,axiom,
( c_Lim_OisCont(c_COMBB(c_RealVector_Oof__real(X2),X3,tc_RealDef_Oreal,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OisCont(X3,X4,X1,tc_RealDef_Oreal) ),
cls_isCont__of__real_0,
[final] ).
cnf(i_0_668,axiom,
( c_Limits_OZfun(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X3),X4,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X4,X3,X1) ),
cls_Zfun__minus_0,
[final] ).
cnf(i_0_669,axiom,
( c_Limits_OZfun(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,X3),X4,X3,tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X4,X3,X1) ),
cls_Zfun__norm__iff_1,
[final] ).
cnf(i_0_670,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),X3,X2,tc_RealDef_Oreal)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
cls_Re_OZfun_0,
[final] ).
cnf(i_0_671,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,X2),X3,X2,tc_Complex_Ocomplex)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
cls_cnj_OZfun_0,
[final] ).
cnf(i_0_672,axiom,
( c_Limits_OZfun(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,X2),X3,X2,tc_RealDef_Oreal)
| ~ c_Limits_OZfun(X1,X3,X2,tc_Complex_Ocomplex) ),
cls_Im_OZfun_0,
[final] ).
cnf(i_0_673,axiom,
( c_Deriv_Odifferentiable(c_COMBB(X2,X3,X1,X1,X1),X4,X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| ~ c_Deriv_Odifferentiable(X2,hAPP(X3,X4),X1) ),
cls_differentiable__compose_0,
[final] ).
cnf(i_0_674,axiom,
( c_Series_Osums(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_scaleR__right_Osums_0,
[final] ).
cnf(i_0_675,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_sums__mult_0,
[final] ).
cnf(i_0_676,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_mult__right_Osums_0,
[final] ).
cnf(i_0_677,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
cls_scaleR__right_OLIMSEQ_0,
[final] ).
cnf(i_0_678,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
cls_mult__right_OLIMSEQ_0,
[final] ).
cnf(i_0_679,axiom,
( c_Series_Osums(c_COMBB(X3,X4,X1,X2,tc_nat),hAPP(X3,X5),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osums(X4,X5,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_Osums_0,
[final] ).
cnf(i_0_680,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X3,X4,X1,X2,tc_nat),hAPP(X3,X5),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OLIMSEQ(X4,X5,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OLIMSEQ_0,
[final] ).
cnf(i_0_681,axiom,
( c_Series_Osums(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),hAPP(c_RealVector_Oof__real(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osums(X2,X3,tc_RealDef_Oreal) ),
cls_of__real_Osums_0,
[final] ).
cnf(i_0_682,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),hAPP(c_RealVector_Oof__real(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,tc_RealDef_Oreal) ),
cls_of__real_OLIMSEQ_0,
[final] ).
cnf(i_0_683,axiom,
( c_Series_Osums(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
cls_sums__minus_0,
[final] ).
cnf(i_0_684,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_LIMSEQ__minus_0,
[final] ).
cnf(i_0_685,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),hAPP(c_RealVector_Onorm__class_Onorm(X1),X3),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_LIMSEQ__norm_0,
[final] ).
cnf(i_0_686,axiom,
( hAPP(X3,c_Series_Osuminf(X4,X1)) = c_Series_Osuminf(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osummable(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_Osuminf_0,
[final] ).
cnf(i_0_687,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_LIMSEQ__norm__zero_1,
[final] ).
cnf(i_0_688,axiom,
( c_Deriv_Odifferentiable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,X1),X3,X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X2,X3,X1) ),
cls_differentiable__minus_0,
[final] ).
cnf(i_0_689,axiom,
( c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Series_Osuminf(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_suminf__mult_0,
[final] ).
cnf(i_0_690,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_scaleR__right_Osuminf_0,
[final] ).
cnf(i_0_691,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_mult__right_Osuminf_0,
[final] ).
cnf(i_0_692,axiom,
( c_SEQ_OLIMSEQ(c_Fun_Ocomp(X2,X3,tc_nat,X1,tc_nat),X4,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Osubseq(X3)
| ~ c_SEQ_OLIMSEQ(X2,X4,X1) ),
cls_LIMSEQ__subseq__LIMSEQ_0,
[final] ).
cnf(i_0_693,axiom,
( c_Series_Osums(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X2),tc_RealDef_Oreal)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
cls_Re_Osums_0,
[final] ).
cnf(i_0_694,axiom,
( c_Series_Osums(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X2),tc_Complex_Ocomplex)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
cls_cnj_Osums_0,
[final] ).
cnf(i_0_695,axiom,
( c_Series_Osums(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X2),tc_RealDef_Oreal)
| ~ c_Series_Osums(X1,X2,tc_Complex_Ocomplex) ),
cls_Im_Osums_0,
[final] ).
cnf(i_0_696,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_ORe,X2),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
cls_Re_OLIMSEQ_0,
[final] ).
cnf(i_0_697,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),hAPP(c_Complex_Ocnj,X2),tc_Complex_Ocomplex)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
cls_cnj_OLIMSEQ_0,
[final] ).
cnf(i_0_698,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),hAPP(c_Complex_OIm,X2),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X2,tc_Complex_Ocomplex) ),
cls_Im_OLIMSEQ_0,
[final] ).
cnf(i_0_699,axiom,
( c_SEQ_OCauchy(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_SEQ_OCauchy(X4,X1)
| ~ c_Lim_OisUCont(X3,X1,X2) ),
cls_isUCont__Cauchy_0,
[final] ).
cnf(i_0_700,axiom,
( c_SEQ_OCauchy(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OCauchy(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OCauchy_0,
[final] ).
cnf(i_0_701,axiom,
( c_SEQ_OZseq(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_SEQ_OZseq(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OZseq_0,
[final] ).
cnf(i_0_702,axiom,
( c_Series_Osummable(c_COMBB(X3,X4,X1,X2,tc_nat),X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Series_Osummable(X4,X1)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_Osummable_0,
[final] ).
cnf(i_0_703,axiom,
( c_Series_Osuminf(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_Series_Osuminf(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_suminf__minus_0,
[final] ).
cnf(i_0_704,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_Series_Osuminf(X2,tc_RealDef_Oreal)) = c_Series_Osuminf(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osummable(X2,tc_RealDef_Oreal) ),
cls_of__real_Osuminf_0,
[final] ).
cnf(i_0_705,axiom,
( c_SEQ_OCauchy(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OCauchy(X3,X1) ),
cls_scaleR__right_OCauchy_0,
[final] ).
cnf(i_0_706,axiom,
( c_SEQ_OCauchy(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OCauchy(X3,X1) ),
cls_mult__right_OCauchy_0,
[final] ).
cnf(i_0_707,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
cls_scaleR_OZseq__right_0,
[final] ).
cnf(i_0_708,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
cls_scaleR__right_OZseq_0,
[final] ).
cnf(i_0_709,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
cls_Zseq__mult__right_0,
[final] ).
cnf(i_0_710,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OZseq(X3,X1) ),
cls_mult__right_OZseq_0,
[final] ).
cnf(i_0_711,axiom,
( c_Series_Osummable(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_scaleR__right_Osummable_0,
[final] ).
cnf(i_0_712,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_mult__right_Osummable_0,
[final] ).
cnf(i_0_713,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_summable__mult_0,
[final] ).
cnf(i_0_714,axiom,
( hAPP(c_Complex_ORe,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_Re_Osuminf_0,
[final] ).
cnf(i_0_715,axiom,
( hAPP(c_Complex_Ocnj,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_cnj_Osuminf_0,
[final] ).
cnf(i_0_716,axiom,
( hAPP(c_Complex_OIm,c_Series_Osuminf(X1,tc_Complex_Ocomplex)) = c_Series_Osuminf(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_Im_Osuminf_0,
[final] ).
cnf(i_0_717,axiom,
( c_SEQ_OCauchy(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OCauchy(X2,tc_RealDef_Oreal) ),
cls_of__real_OCauchy_0,
[final] ).
cnf(i_0_718,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_SEQ_OZseq(X2,tc_RealDef_Oreal) ),
cls_of__real_OZseq_0,
[final] ).
cnf(i_0_719,axiom,
( c_Series_Osummable(c_COMBB(c_RealVector_Oof__real(X1),X2,tc_RealDef_Oreal,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1)
| ~ c_Series_Osummable(X2,tc_RealDef_Oreal) ),
cls_of__real_Osummable_0,
[final] ).
cnf(i_0_720,axiom,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_o__apply_0,
[final] ).
cnf(i_0_721,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0,
[final] ).
cnf(i_0_722,axiom,
hAPP(X1,hAPP(X2,X3)) = hAPP(c_Fun_Ocomp(X1,X2,X4,X5,X6),X3),
cls_o__eq__dest__lhs_0,
[final] ).
cnf(i_0_723,axiom,
( c_SEQ_OZseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X2,X1) ),
cls_Zseq__minus_0,
[final] ).
cnf(i_0_724,axiom,
( c_Series_Osummable(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_summable__minus_0,
[final] ).
cnf(i_0_725,axiom,
( c_SEQ_OZseq(c_COMBB(c_RealVector_Onorm__class_Onorm(X1),X2,X1,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(X2,X1) ),
cls_Zseq__norm__iff_1,
[final] ).
cnf(i_0_726,axiom,
( c_SEQ_OCauchy(c_Fun_Ocomp(X2,X3,tc_nat,X1,tc_nat),X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Osubseq(X3)
| ~ c_SEQ_OCauchy(X2,X1) ),
cls_Cauchy__subseq__Cauchy_0,
[final] ).
cnf(i_0_727,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
cls_Re_OCauchy_0,
[final] ).
cnf(i_0_728,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
cls_cnj_OCauchy_0,
[final] ).
cnf(i_0_729,axiom,
( c_SEQ_OCauchy(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_Complex_Ocomplex) ),
cls_Im_OCauchy_0,
[final] ).
cnf(i_0_730,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
cls_Re_OZseq_0,
[final] ).
cnf(i_0_731,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
cls_cnj_OZseq_0,
[final] ).
cnf(i_0_732,axiom,
( c_SEQ_OZseq(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_SEQ_OZseq(X1,tc_Complex_Ocomplex) ),
cls_Im_OZseq_0,
[final] ).
cnf(i_0_733,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_Re_Osummable_0,
[final] ).
cnf(i_0_734,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_Ocnj,X1,tc_Complex_Ocomplex,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_cnj_Osummable_0,
[final] ).
cnf(i_0_735,axiom,
( c_Series_Osummable(c_COMBB(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
| ~ c_Series_Osummable(X1,tc_Complex_Ocomplex) ),
cls_Im_Osummable_0,
[final] ).
cnf(i_0_736,axiom,
( c_SEQ_Oincseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Odecseq(X1) ),
cls_decseq__eq__incseq_0,
[final] ).
cnf(i_0_737,axiom,
( c_SEQ_Omonoseq(c_COMBB(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1,tc_RealDef_Oreal,tc_RealDef_Oreal,tc_nat))
| ~ c_SEQ_Omonoseq(X1) ),
cls_monoseq__minus_0,
[final] ).
cnf(i_0_738,axiom,
c_SEQ_Omonoseq(c_COMBB(X1,c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X1),tc_nat,tc_RealDef_Oreal,tc_nat)),
cls_seq__monosub_1,
[final] ).
cnf(i_0_739,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2) ),
cls_isCont__def_1,
[final] ).
cnf(i_0_740,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
cls_isCont__def_0,
[final] ).
cnf(i_0_741,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_Ocont_0,
[final] ).
cnf(i_0_742,axiom,
( c_Lim_OLIM(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Ocont_0,
[final] ).
cnf(i_0_743,axiom,
( c_Lim_OLIM(c_HOL_Otimes__class_Otimes(X2,X1),X3,hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ocont_0,
[final] ).
cnf(i_0_744,axiom,
c_Lim_OLIM(c_Complex_ORe,X1,hAPP(c_Complex_ORe,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Re_Ocont_0,
[final] ).
cnf(i_0_745,axiom,
c_Lim_OLIM(c_Complex_OIm,X1,hAPP(c_Complex_OIm,X1),tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Im_Ocont_0,
[final] ).
cnf(i_0_746,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3)),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X3),X5,X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X4,X1) ),
cls_abs__mult__less_0,
[final] ).
cnf(i_0_747,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(X4,X1),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_748,axiom,
( c_Series_Osummable(X2,X1)
| c_lessequals(X4,c_Series_Osko__Series__Xsummable__comparison__test__1__1(X2,X3,X4,X1),tc_nat)
| ~ class_SEQ_Obanach(X1)
| ~ c_Series_Osummable(X3,tc_RealDef_Oreal) ),
cls_summable__comparison__test_0,
[final] ).
cnf(i_0_749,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_750,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_751,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_752,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_753,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_754,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5),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_755,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)),hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3)),X1)
| ~ class_Ring__and__Field_Olordered__ring(X1) ),
cls_abs__le__mult_0,
[final] ).
cnf(i_0_756,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_757,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_758,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_759,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),X1) ),
cls_mult__right__le__imp__le_0,
[final] ).
cnf(i_0_760,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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
cls_mult__left__le__imp__le_0,
[final] ).
cnf(i_0_761,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),X1) ),
cls_mult__right__less__imp__less_0,
[final] ).
cnf(i_0_762,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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
cls_mult__left__less__imp__less_0,
[final] ).
cnf(i_0_763,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_764,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),X1) ),
cls_mult__less__imp__less__right_0,
[final] ).
cnf(i_0_765,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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),X1) ),
cls_mult__less__imp__less__left_0,
[final] ).
cnf(i_0_766,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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_767,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),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_768,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),hAPP(X1,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_OLIMSEQ(X1,X6,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X1) ),
cls_monoseq__le_3,
[final] ).
cnf(i_0_769,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1) ),
cls_mult__less__cancel__left__disj_0,
[final] ).
cnf(i_0_770,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
cls_mult__less__cancel__right__disj_0,
[final] ).
cnf(i_0_771,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1) ),
cls_mult__less__cancel__right__disj_1,
[final] ).
cnf(i_0_772,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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
cls_mult__less__cancel__left__disj_1,
[final] ).
cnf(i_0_773,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1) ),
cls_mult__less__cancel__left__disj_2,
[final] ).
cnf(i_0_774,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
cls_mult__less__cancel__right__disj_2,
[final] ).
cnf(i_0_775,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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_776,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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_777,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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_778,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ 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_779,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1) ),
cls_mult__less__cancel__right__disj_3,
[final] ).
cnf(i_0_780,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(hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X2),X1) ),
cls_mult__less__cancel__left__disj_3,
[final] ).
cnf(i_0_781,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_782,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_783,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_784,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_785,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_786,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_787,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_788,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_789,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_790,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_791,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_792,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_793,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_794,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_795,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_796,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),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_797,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_798,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),hAPP(c_HOL_Otimes__class_Otimes(X4,X1),X3),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_799,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4),X1),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_800,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),hAPP(X1,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_Omonoseq(X1) ),
cls_monoseq__def_0,
[final] ).
cnf(i_0_801,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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1) ),
cls_zero__less__mult__pos2_0,
[final] ).
cnf(i_0_802,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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),X1) ),
cls_zero__less__mult__pos_0,
[final] ).
cnf(i_0_803,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X1,X4),X5,tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_SEQ_OLIMSEQ(X1,X5,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X1) ),
cls_monoseq__le_1,
[final] ).
cnf(i_0_804,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X2,X4),hAPP(X2,X5),tc_RealDef_Oreal)
| ~ c_lessequals(X4,X5,tc_nat)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X2) ),
cls_monoseq__le_2,
[final] ).
cnf(i_0_805,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisUCont(X3,X1,X2) ),
cls_isUCont__isCont_0,
[final] ).
cnf(i_0_806,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OisCont_0,
[final] ).
cnf(i_0_807,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_1,
[final] ).
cnf(i_0_808,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_0,
[final] ).
cnf(i_0_809,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(hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_3,
[final] ).
cnf(i_0_810,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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1) ),
cls_zero__le__mult__iff_0,
[final] ).
cnf(i_0_811,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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),X1) ),
cls_zero__le__mult__iff_3,
[final] ).
cnf(i_0_812,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),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1) ),
cls_zero__le__mult__iff_2,
[final] ).
cnf(i_0_813,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),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2),X1) ),
cls_zero__le__mult__iff_1,
[final] ).
cnf(i_0_814,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(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_mult__le__0__iff_2,
[final] ).
cnf(i_0_815,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_816,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_817,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_818,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_819,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_820,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_821,axiom,
( c_lessequals(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_822,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_823,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_824,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_825,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_826,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_827,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_828,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_829,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_830,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_831,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_832,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),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_833,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__le__iff_2,
[final] ).
cnf(i_0_834,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_lessequals(X2,X3,X1) ),
cls_abs__leI_0,
[final] ).
cnf(i_0_835,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ c_HOL_Oord__class_Oless(X2,X3,X1) ),
cls_abs__less__iff_2,
[final] ).
cnf(i_0_836,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__left_0,
[final] ).
cnf(i_0_837,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_OscaleR_0,
[final] ).
cnf(i_0_838,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3),X1),X4) = hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__left_0,
[final] ).
cnf(i_0_839,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_840,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_841,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_842,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3),X1),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_843,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),X3) = hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ 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_844,axiom,
( c_Lim_OisCont(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OisCont_0,
[final] ).
cnf(i_0_845,axiom,
( c_Lim_OisCont(c_HOL_Otimes__class_Otimes(X2,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OisCont_0,
[final] ).
cnf(i_0_846,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__le__iff__le_0,
[final] ).
cnf(i_0_847,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__less__iff__less_0,
[final] ).
cnf(i_0_848,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X3))
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult_0,
[final] ).
cnf(i_0_849,axiom,
( hAPP(X3,hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X1),X5)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X2),hAPP(X3,X5))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OscaleR_0,
[final] ).
cnf(i_0_850,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| c_lessequals(hAPP(X2,X4),X1,tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Omonoseq(X2) ),
cls_monoseq__le_0,
[final] ).
cnf(i_0_851,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__le__iff_0,
[final] ).
cnf(i_0_852,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__le__iff_1,
[final] ).
cnf(i_0_853,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
cls_abs__le__D2_0,
[final] ).
cnf(i_0_854,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
cls_abs__less__iff_1,
[final] ).
cnf(i_0_855,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__less__iff_0,
[final] ).
cnf(i_0_856,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X2,X1) ),
cls_minus__less__iff_1,
[final] ).
cnf(i_0_857,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__iff_0,
[final] ).
cnf(i_0_858,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__iff_1,
[final] ).
cnf(i_0_859,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_less__minus__iff_0,
[final] ).
cnf(i_0_860,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(X3,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_less__minus__iff_1,
[final] ).
cnf(i_0_861,axiom,
c_Lim_OisCont(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Re_OisCont_0,
[final] ).
cnf(i_0_862,axiom,
c_Lim_OisCont(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Im_OisCont_0,
[final] ).
cnf(i_0_863,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left__commute_0,
[final] ).
cnf(i_0_864,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OscaleR_0,
[final] ).
cnf(i_0_865,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_OscaleR__right_0,
[final] ).
cnf(i_0_866,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__right_0,
[final] ).
cnf(i_0_867,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OscaleR_0,
[final] ).
cnf(i_0_868,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),X4)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__right_0,
[final] ).
cnf(i_0_869,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X4)) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_870,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_871,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_872,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_873,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_874,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_875,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_876,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_877,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_878,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_not__square__less__zero_0,
[final] ).
cnf(i_0_879,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X3,X2,X1) ),
cls_le__imp__neg__le_0,
[final] ).
cnf(i_0_880,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3),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_881,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__le__0__iff__le_0,
[final] ).
cnf(i_0_882,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(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_neg__less__0__iff__less_0,
[final] ).
cnf(i_0_883,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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__0__le__iff__le_0,
[final] ).
cnf(i_0_884,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),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_neg__0__less__iff__less_0,
[final] ).
cnf(i_0_885,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ominus_0,
[final] ).
cnf(i_0_886,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__left_0,
[final] ).
cnf(i_0_887,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_888,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_lessequals(X1,X3,tc_nat) ),
cls_le__trans_0,
[final] ).
cnf(i_0_889,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_890,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
cls_minus__le__self__iff_0,
[final] ).
cnf(i_0_891,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X2,X1) ),
cls_neg__less__eq__nonneg_0,
[final] ).
cnf(i_0_892,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_le__minus__self__iff_0,
[final] ).
cnf(i_0_893,axiom,
( c_lessequals(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| ~ c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_less__eq__neg__nonpos_0,
[final] ).
cnf(i_0_894,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,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1) ),
cls_less__minus__self__iff_0,
[final] ).
cnf(i_0_895,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left_Ominus_0,
[final] ).
cnf(i_0_896,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__minus__left_0,
[final] ).
cnf(i_0_897,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2),X1),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ominus__left_0,
[final] ).
cnf(i_0_898,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
cls_abs__le__D1_0,
[final] ).
cnf(i_0_899,axiom,
( c_HOL_Oord__class_Oless(X2,X3,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X3,X1) ),
cls_abs__less__iff_0,
[final] ).
cnf(i_0_900,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_901,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_902,axiom,
( c_HOL_Oord__class_Oless(hAPP(c_HOL_Ouminus__class_Ouminus(X1),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),X2,X1) ),
cls_neg__less__0__iff__less_1,
[final] ).
cnf(i_0_903,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_904,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_905,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_abs__mult__self_0,
[final] ).
cnf(i_0_906,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_907,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_908,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_909,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(X3,X2,tc_nat)
| ~ c_SEQ_Odecseq(X1) ),
cls_decseq__def_0,
[final] ).
cnf(i_0_910,axiom,
( c_lessequals(hAPP(X1,X2),hAPP(X1,X3),tc_RealDef_Oreal)
| ~ c_lessequals(X2,X3,tc_nat)
| ~ c_SEQ_Oincseq(X1) ),
cls_incseq__def_0,
[final] ).
cnf(i_0_911,axiom,
( c_HOL_Oord__class_Oless(hAPP(X1,X2),hAPP(X1,X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| ~ c_SEQ_Osubseq(X1) ),
cls_subseq__def_0,
[final] ).
cnf(i_0_912,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_913,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_914,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_915,axiom,
( c_lessequals(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_916,axiom,
( c_HOL_Oord__class_Oless(X2,hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),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_917,axiom,
( hBOOL(hAPP(hAPP(X1,X2),X3))
| c_HOL_Oord__class_Oless(X2,X3,tc_nat)
| X3 = X2
| c_HOL_Oord__class_Oless(X3,X2,tc_nat) ),
cls_nat__less__cases_0,
[final] ).
cnf(i_0_918,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1) = c_Complex_Ocomplex_OComplex(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1))),
cls_complex__minus__def_0,
[final] ).
cnf(i_0_919,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__minus__right_0,
[final] ).
cnf(i_0_920,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ominus__right_0,
[final] ).
cnf(i_0_921,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ominus_0,
[final] ).
cnf(i_0_922,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__right_0,
[final] ).
cnf(i_0_923,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_924,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)),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_925,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(X1)),X1) ),
cls_zero__less__abs__iff_0,
[final] ).
cnf(i_0_926,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_927,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_928,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_929,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X4,X3,X1)
| ~ c_SEQ_OLIMSEQ(X4,X2,X1) ),
cls_LIMSEQ__unique_0,
[final] ).
cnf(i_0_930,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_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,axiom,
( c_lessequals(hAPP(X1,X2),X3,tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X1,X3,tc_RealDef_Oreal)
| ~ c_SEQ_Oincseq(X1) ),
cls_incseq__le_0,
[final] ).
cnf(i_0_939,axiom,
( c_lessequals(X1,hAPP(X2,X3),tc_RealDef_Oreal)
| ~ c_SEQ_OLIMSEQ(X2,X1,tc_RealDef_Oreal)
| ~ c_SEQ_Odecseq(X2) ),
cls_decseq__le_0,
[final] ).
cnf(i_0_940,axiom,
( X1 = X2
| ~ c_lessequals(X2,X1,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__antisym_0,
[final] ).
cnf(i_0_941,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_942,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__le__zero__iff_0,
[final] ).
cnf(i_0_943,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)) = hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_944,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(hAPP(c_RealVector_Oof__real(X1),X2),X1),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_scaleR__conv__of__real_0,
[final] ).
cnf(i_0_945,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| ~ c_HOL_Oord__class_Oless(hAPP(c_HOL_Oabs__class_Oabs(X1),X2),c_HOL_Ozero__class_Ozero(X1),X1) ),
cls_abs__not__less__zero_0,
[final] ).
cnf(i_0_946,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),X2),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
cls_norm__le__zero__iff_0,
[final] ).
cnf(i_0_947,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2) != hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X3) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_948,axiom,
( c_Lim_OisUCont(X3,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_RealVector_Obounded__linear(X3,X1,X2) ),
cls_bounded__linear_OisUCont_0,
[final] ).
cnf(i_0_949,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_zero__le__square_0,
[final] ).
cnf(i_0_961,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_962,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_963,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)
| ~ 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_964,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != hAPP(c_RealVector_OscaleR__class_OscaleR(X4,X1),X3) ),
cls_scaleR__cancel__right_0,
[final] ).
cnf(i_0_965,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_nat__less__le_2,
[final] ).
cnf(i_0_966,axiom,
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__eq__less__or__eq_0,
[final] ).
cnf(i_0_967,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2
| ~ c_lessequals(X1,X2,tc_nat) ),
cls_le__neq__implies__less_0,
[final] ).
cnf(i_0_968,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X4) ),
cls_scaleR__cancel__left_0,
[final] ).
cnf(i_0_969,axiom,
( c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__minus__self_0,
[final] ).
cnf(i_0_970,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_termination__basic__simps_I5_J_0,
[final] ).
cnf(i_0_971,axiom,
( c_lessequals(X1,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ),
cls_nat__less__le_0,
[final] ).
cnf(i_0_972,axiom,
hAPP(c_Complex_Ocnj,X1) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1))),
cls_cnj__def_0,
[final] ).
cnf(i_0_973,axiom,
( hAPP(c_RealVector_Oof__real(X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_Oof__real(X1),X2))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real_Ominus_0,
[final] ).
cnf(i_0_974,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_975,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_976,axiom,
hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)),
cls_complex__minus_0,
[final] ).
cnf(i_0_977,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_978,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_979,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_980,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_981,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_982,axiom,
( c_lessequals(hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(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_983,axiom,
( hAPP(c_RealVector_Oof__real(X1),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_RealVector_Oof__real(X1),X2))
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__minus_0,
[final] ).
cnf(i_0_984,axiom,
( c_lessequals(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_linorder__linear_0,
[final] ).
cnf(i_0_985,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_986,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_987,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_988,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_989,axiom,
hAPP(c_Complex_Ocnj,v_z) = c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,v_z),hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,v_z))),
cls_cnj__def__raw_0,
[final] ).
cnf(i_0_990,axiom,
( c_lessequals(hAPP(c_RealVector_Onorm__class_Onorm(X1),c_HOL_Ozero__class_Ozero(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_991,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),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_992,axiom,
( c_Series_Osums(X2,c_Series_Osuminf(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_sums__iff_2,
[final] ).
cnf(i_0_993,axiom,
( c_Series_Osums(X2,c_Series_Osuminf(X2,X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_summable__sums_0,
[final] ).
cnf(i_0_994,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_nat__neq__iff_0,
[final] ).
cnf(i_0_995,axiom,
( c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| X2 = X1 ),
cls_linorder__neqE__nat_0,
[final] ).
cnf(i_0_996,axiom,
( c_Series_Osuminf(X2,X1) = X3
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
cls_sums__iff_1,
[final] ).
cnf(i_0_997,axiom,
( X2 = c_Series_Osuminf(X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X3,X2,X1) ),
cls_sums__unique_0,
[final] ).
cnf(i_0_998,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_LIMSEQ__imp__Cauchy_0,
[final] ).
cnf(i_0_999,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
cls_sums__iff_0,
[final] ).
cnf(i_0_1000,axiom,
( c_Series_Osummable(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X2,X3,X1) ),
cls_sums__summable_0,
[final] ).
cnf(i_0_1001,axiom,
( c_lessequals(X1,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ),
cls_nat__le__linear_0,
[final] ).
cnf(i_0_1002,axiom,
( c_lessequals(X1,X2,tc_RealDef_Oreal)
| c_lessequals(X2,X1,tc_RealDef_Oreal) ),
cls_real__le__linear_0,
[final] ).
cnf(i_0_1003,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__zero_0,
[final] ).
cnf(i_0_1004,axiom,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealVector_Onorm__class_Onorm(X1),X2),tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__ge__zero_0,
[final] ).
cnf(i_0_1005,axiom,
( c_lessequals(X2,hAPP(c_HOL_Oabs__class_Oabs(X1),X2),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__ge__self_0,
[final] ).
cnf(i_0_1006,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X3)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__left_1,
[final] ).
cnf(i_0_1007,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = hAPP(c_RealVector_OscaleR__class_OscaleR(X3,X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__right_1,
[final] ).
cnf(i_0_1008,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_1009,axiom,
( ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__le_1,
[final] ).
cnf(i_0_1010,axiom,
( ~ class_Orderings_Opreorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_order__less__irrefl_0,
[final] ).
cnf(i_0_1011,axiom,
( ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ),
cls_linorder__neq__iff_1,
[final] ).
cnf(i_0_1012,axiom,
( c_SEQ_OLIMSEQ(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_summable__LIMSEQ__zero_0,
[final] ).
cnf(i_0_1013,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),X2) = 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_1014,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_1015,axiom,
( c_Lim_OisUCont(c_RealVector_OscaleR__class_OscaleR(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OisUCont_0,
[final] ).
cnf(i_0_1016,axiom,
( c_Lim_OisUCont(c_HOL_Otimes__class_Otimes(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OisUCont_0,
[final] ).
cnf(i_0_1017,axiom,
( c_RealVector_Obounded__linear(c_RealVector_OscaleR__class_OscaleR(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Obounded__linear__right_0,
[final] ).
cnf(i_0_1018,axiom,
( c_RealVector_Obounded__linear(c_HOL_Otimes__class_Otimes(X2,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Obounded__linear__right_0,
[final] ).
cnf(i_0_1019,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_1020,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_1021,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_1022,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_1023,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X3) = hAPP(c_HOL_Otimes__class_Otimes(X3,X1),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_1024,axiom,
( c_lessequals(X1,hAPP(X2,X1),tc_nat)
| ~ c_SEQ_Osubseq(X2) ),
cls_seq__suble_0,
[final] ).
cnf(i_0_1025,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_scaleR__eq__0__iff_0,
[final] ).
cnf(i_0_1026,axiom,
( hAPP(c_RealVector_Onorm__class_Onorm(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_RealVector_Onorm__class_Onorm(X1),X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__minus__cancel_0,
[final] ).
cnf(i_0_1027,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Oabs__class_Oabs(X1),X2)) = hAPP(c_HOL_Oabs__class_Oabs(X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__idempotent_0,
[final] ).
cnf(i_0_1028,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Oabs__class_Oabs(X1),X2)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__minus__cancel_0,
[final] ).
cnf(i_0_1029,axiom,
hAPP(c_Complex_ORe,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_ORe,X1)),
cls_Re_Ominus_0,
[final] ).
cnf(i_0_1030,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),hAPP(c_Complex_Ocnj,X1)),
cls_cnj_Ominus_0,
[final] ).
cnf(i_0_1031,axiom,
hAPP(c_Complex_OIm,hAPP(c_HOL_Ouminus__class_Ouminus(tc_Complex_Ocomplex),X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),
cls_Im_Ominus_0,
[final] ).
cnf(i_0_1032,axiom,
hAPP(c_Complex_Ocnj,c_Complex_Ocomplex_OComplex(X1,X2)) = c_Complex_Ocomplex_OComplex(X1,hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),X2)),
cls_complex__cnj_0,
[final] ).
cnf(i_0_1033,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_nat__less__le_1,
[final] ).
cnf(i_0_1034,axiom,
~ c_HOL_Oord__class_Oless(X1,X1,tc_nat),
cls_less__not__refl_0,
[final] ).
cnf(i_0_1035,axiom,
( X1 = X2
| hAPP(c_Complex_OIm,X1) != hAPP(c_Complex_OIm,X2)
| hAPP(c_Complex_ORe,X1) != hAPP(c_Complex_ORe,X2) ),
cls_complex__equality_0,
[final] ).
cnf(i_0_1036,axiom,
hAPP(c_Complex_OIm,hAPP(c_Complex_Ocnj,X1)) = hAPP(c_HOL_Ouminus__class_Ouminus(tc_RealDef_Oreal),hAPP(c_Complex_OIm,X1)),
cls_complex__Im__cnj_0,
[final] ).
cnf(i_0_1037,axiom,
( X2 = X3
| ~ class_RealVector_Oreal__algebra__1(X1)
| hAPP(c_RealVector_Oof__real(X1),X2) != hAPP(c_RealVector_Oof__real(X1),X3) ),
cls_of__real__eq__iff_0,
[final] ).
cnf(i_0_1038,axiom,
( X2 = X3
| ~ class_Lattices_Oboolean__algebra(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_compl__eq__compl__iff_0,
[final] ).
cnf(i_0_1039,axiom,
( X2 = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3) ),
cls_neg__equal__iff__equal_0,
[final] ).
cnf(i_0_1040,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_Lattices_Oboolean__algebra(X1) ),
cls_double__compl_0,
[final] ).
cnf(i_0_1041,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__minus_0,
[final] ).
cnf(i_0_1042,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = X2
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__equation__iff_1,
[final] ).
cnf(i_0_1043,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_0,
[final] ).
cnf(i_0_1044,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_equation__minus__iff_1,
[final] ).
cnf(i_0_1045,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_1046,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_1047,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__0_0,
[final] ).
cnf(i_0_1048,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = 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_1049,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__left_0,
[final] ).
cnf(i_0_1050,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X1),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ozero_0,
[final] ).
cnf(i_0_1051,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_order__eq__iff_0,
[final] ).
cnf(i_0_1052,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Opreorder(X1) ),
cls_order__eq__refl_0,
[final] ).
cnf(i_0_1053,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1),
cls_complex__cnj__complex__of__real_0,
[final] ).
cnf(i_0_1054,axiom,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
cls_complex__surj_0,
[final] ).
cnf(i_0_1055,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__eq__0__iff_1,
[final] ).
cnf(i_0_1056,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ozero__left_0,
[final] ).
cnf(i_0_1057,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__eq__0__iff_2,
[final] ).
cnf(i_0_1058,axiom,
( hAPP(c_RealVector_OscaleR__class_OscaleR(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ozero__right_0,
[final] ).
cnf(i_0_1059,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__right_0,
[final] ).
cnf(i_0_1060,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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_1061,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(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_1062,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ozero_0,
[final] ).
cnf(i_0_1063,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__right_0,
[final] ).
cnf(i_0_1064,axiom,
c_fequal(X1,X1,X2),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_1065,axiom,
c_lessequals(X1,X1,tc_nat),
cls_le__refl_0,
[final] ).
cnf(i_0_1066,axiom,
c_lessequals(X1,X1,tc_nat),
cls_eq__imp__le_0,
[final] ).
cnf(i_0_1067,axiom,
c_lessequals(X1,X1,tc_RealDef_Oreal),
cls_real__le__refl_0,
[final] ).
cnf(i_0_1068,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X3) ),
cls_complex__eq__cancel__iff2_1,
[final] ).
cnf(i_0_1069,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X3) ),
cls_complex__eq__cancel__iff2_0,
[final] ).
cnf(i_0_1070,axiom,
( c_HOL_Ozero__class_Ozero(X1) = X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| c_HOL_Ozero__class_Ozero(X1) != hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) ),
cls_neg__0__equal__iff__equal_0,
[final] ).
cnf(i_0_1071,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| hAPP(c_HOL_Oabs__class_Oabs(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_abs__eq__0_0,
[final] ).
cnf(i_0_1072,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_neg__equal__0__iff__equal_0,
[final] ).
cnf(i_0_1073,axiom,
c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Re_OisUCont_0,
[final] ).
cnf(i_0_1074,axiom,
c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Im_OisUCont_0,
[final] ).
cnf(i_0_1075,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__algebra__1(X1)
| hAPP(c_RealVector_Oof__real(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_of__real__eq__0__iff_0,
[final] ).
cnf(i_0_1076,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| hAPP(c_RealVector_Onorm__class_Onorm(X1),X2) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
cls_norm__eq__zero_0,
[final] ).
cnf(i_0_1077,axiom,
( hAPP(c_HOL_Otimes__class_Otimes(X2,X1),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_1078,axiom,
hAPP(c_Complex_ORe,hAPP(c_Complex_Ocnj,X1)) = hAPP(c_Complex_ORe,X1),
cls_complex__Re__cnj_0,
[final] ).
cnf(i_0_1079,axiom,
hAPP(c_Complex_OIm,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_Im__complex__of__real_0,
[final] ).
cnf(i_0_1080,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
cls_complex_Oinject_0,
[final] ).
cnf(i_0_1081,axiom,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
cls_complex_Oinject_1,
[final] ).
cnf(i_0_1082,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) != X2 ),
cls_neg__equal__zero_0,
[final] ).
cnf(i_0_1083,axiom,
hAPP(c_Complex_ORe,hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1)) = X1,
cls_Re__complex__of__real_0,
[final] ).
cnf(i_0_1084,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = 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_1085,axiom,
( X1 = X2
| hAPP(c_Complex_Ocnj,X1) != hAPP(c_Complex_Ocnj,X2) ),
cls_complex__cnj__cancel__iff_0,
[final] ).
cnf(i_0_1086,axiom,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
cls_Re_0,
[final] ).
cnf(i_0_1087,axiom,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
cls_Im_0,
[final] ).
cnf(i_0_1088,axiom,
( hAPP(c_HOL_Oabs__class_Oabs(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ),
cls_abs__eq__0_1,
[final] ).
cnf(i_0_1089,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__zero_0,
[final] ).
cnf(i_0_1090,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oordered__ab__group__add(X1) ),
cls_neg__equal__zero_1,
[final] ).
cnf(i_0_1091,axiom,
( c_HOL_Ozero__class_Ozero(X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_HOL_Ozero__class_Ozero(X1))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_neg__0__equal__iff__equal_1,
[final] ).
cnf(i_0_1092,axiom,
( class_Orderings_Oorder(tc_fun(X1,X2))
| ~ class_Orderings_Oorder(X2) ),
clsarity_fun__Orderings_Oorder,
[final] ).
cnf(i_0_1093,axiom,
( class_Orderings_Opreorder(tc_fun(X1,X2))
| ~ class_Orderings_Opreorder(X2) ),
clsarity_fun__Orderings_Opreorder,
[final] ).
cnf(i_0_1094,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
clsarity_fun__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_1095,axiom,
hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,X1)) = X1,
cls_complex__cnj__cnj_0,
[final] ).
cnf(i_0_1096,axiom,
( hAPP(c_RealVector_Onorm__class_Onorm(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_norm__zero_0,
[final] ).
cnf(i_0_1097,axiom,
( hAPP(c_RealVector_Oof__real(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_of__real__0_0,
[final] ).
cnf(i_0_1098,axiom,
hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1) = c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
cls_complex__of__real__def_0,
[final] ).
cnf(i_0_1099,axiom,
c_Complex_Ocomplex_OComplex(X1,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = hAPP(c_RealVector_Oof__real(tc_Complex_Ocomplex),X1),
cls_complex__eq__cancel__iff2_2,
[final] ).
cnf(i_0_1100,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_Complex__eq__0_0,
[final] ).
cnf(i_0_1101,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Complex_Ocomplex_OComplex(X1,X2) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_Complex__eq__0_1,
[final] ).
cnf(i_0_1102,axiom,
( X1 = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| hAPP(c_Complex_Ocnj,X1) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
cls_complex__cnj__zero__iff_0,
[final] ).
cnf(i_0_1103,axiom,
c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_Complex__eq__0_2,
[final] ).
cnf(i_0_1104,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
cls_complex__zero__def_0,
[final] ).
cnf(i_0_1105,axiom,
hAPP(c_Complex_ORe,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_Re_Ozero_0,
[final] ).
cnf(i_0_1106,axiom,
hAPP(c_Complex_Ocnj,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
cls_cnj_Ozero_0,
[final] ).
cnf(i_0_1107,axiom,
hAPP(c_Complex_OIm,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),
cls_Im_Ozero_0,
[final] ).
cnf(i_0_1108,axiom,
( c_SEQ_Omonoseq(X1)
| ~ c_SEQ_Odecseq(X1) ),
cls_decseq__imp__monoseq_0,
[final] ).
cnf(i_0_1109,axiom,
( c_SEQ_Omonoseq(X1)
| ~ c_SEQ_Oincseq(X1) ),
cls_incseq__imp__monoseq_0,
[final] ).
cnf(i_0_1110,axiom,
c_SEQ_Osubseq(c_SEQ_Osko__SEQ__Xseq__monosub__1__1(X1)),
cls_seq__monosub_0,
[final] ).
cnf(i_0_1111,axiom,
c_SEQ_Osubseq(v_sko__CHAINED__1(v_s)),
cls_CHAINED_0,
[final] ).
cnf(i_0_1112,axiom,
class_Orderings_Oorder(tc_bool),
clsarity_bool__Orderings_Oorder,
[final] ).
cnf(i_0_1113,axiom,
class_Orderings_Oorder(tc_nat),
clsarity_nat__Orderings_Oorder,
[final] ).
cnf(i_0_1114,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Oorder,
[final] ).
cnf(i_0_1115,axiom,
class_Orderings_Opreorder(tc_bool),
clsarity_bool__Orderings_Opreorder,
[final] ).
cnf(i_0_1116,axiom,
class_Orderings_Opreorder(tc_nat),
clsarity_nat__Orderings_Opreorder,
[final] ).
cnf(i_0_1117,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Opreorder,
[final] ).
cnf(i_0_1118,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_1119,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1120,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_1121,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_1122,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_1123,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_1124,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_1125,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_1126,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_1127,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_1128,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__SEQ_Obanach,
[final] ).
cnf(i_0_1129,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__SEQ_Obanach,
[final] ).
cnf(i_0_1130,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
clsarity_nat__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1131,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1132,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_1133,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,
[final] ).
cnf(i_0_1134,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_1135,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,
[final] ).
cnf(i_0_1136,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_1137,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,
[final] ).
cnf(i_0_1138,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,
[final] ).
cnf(i_0_1139,axiom,
class_Orderings_Olinorder(tc_nat),
clsarity_nat__Orderings_Olinorder,
[final] ).
cnf(i_0_1140,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Orderings_Olinorder,
[final] ).
cnf(i_0_1141,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,
[final] ).
cnf(i_0_1142,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
clsarity_nat__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1143,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1144,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_1145,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_1146,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_1147,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1148,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_1149,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,
[final] ).
cnf(i_0_1150,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,
[final] ).
cnf(i_0_1151,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_1152,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_1153,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_1154,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__vector,
[final] ).
cnf(i_0_1155,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__vector,
[final] ).
cnf(i_0_1156,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,
[final] ).
cnf(i_0_1157,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_1158,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,
[final] ).
cnf(i_0_1159,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1160,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring,
[final] ).
cnf(i_0_1161,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1162,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_1163,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_1164,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1165,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1166,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_1167,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1168,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1169,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_1170,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_1171,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,
[final] ).
cnf(i_0_1172,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_1173,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_1174,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_1175,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Ometric__space,
[final] ).
cnf(i_0_1176,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Ometric__space,
[final] ).
cnf(i_0_1177,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_1178,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_1179,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_1180,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_1181,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,
[final] ).
cnf(i_0_1182,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_1183,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,
[final] ).
cnf(i_0_1184,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
clsarity_nat__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_1185,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,
[final] ).
cnf(i_0_1186,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,
[final] ).
cnf(i_0_1187,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
clsarity_nat__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_1188,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,
[final] ).
cnf(i_0_1189,negated_conjecture,
~ v_thesis____,
cls_conjecture_0,
[final] ).
cnf(i_0_1190,axiom,
X1 = X1 ).
cnf(i_0_1191,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1192,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1193,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1194,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1195,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1196,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1197,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1198,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X1,X3) = c_Complex_Ocomplex_OComplex(X2,X3) ) ).
cnf(i_0_1199,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X3,X1) = c_Complex_Ocomplex_OComplex(X3,X2) ) ).
cnf(i_0_1200,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1201,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1202,axiom,
( X1 != X2
| c_Series_Osuminf(X1,X3) = c_Series_Osuminf(X2,X3) ) ).
cnf(i_0_1203,axiom,
( X1 != X2
| c_Series_Osuminf(X3,X1) = c_Series_Osuminf(X3,X2) ) ).
cnf(i_0_1204,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1205,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1206,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1207,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1208,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1209,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1210,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1211,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1212,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1213,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X1,X3,X4,X5,X6)
| c_Limits_Otendsto(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1214,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X1,X4,X5,X6)
| c_Limits_Otendsto(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1215,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X1,X5,X6)
| c_Limits_Otendsto(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1216,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X1,X6)
| c_Limits_Otendsto(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1217,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X6,X1)
| c_Limits_Otendsto(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1218,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1219,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X1,X3,X4,X5)
| c_Lim_OisCont(X2,X3,X4,X5) ) ).
cnf(i_0_1220,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X1,X4,X5)
| c_Lim_OisCont(X3,X2,X4,X5) ) ).
cnf(i_0_1221,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X1,X5)
| c_Lim_OisCont(X3,X4,X2,X5) ) ).
cnf(i_0_1222,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X5,X1)
| c_Lim_OisCont(X3,X4,X5,X2) ) ).
cnf(i_0_1223,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1224,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X1,X3,X4)
| c_RealVector_Obounded__linear(X2,X3,X4) ) ).
cnf(i_0_1225,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X1,X4)
| c_RealVector_Obounded__linear(X3,X2,X4) ) ).
cnf(i_0_1226,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X4,X1)
| c_RealVector_Obounded__linear(X3,X4,X2) ) ).
cnf(i_0_1227,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1228,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X1,X3,X4)
| c_SEQ_OLIMSEQ(X2,X3,X4) ) ).
cnf(i_0_1229,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X1,X4)
| c_SEQ_OLIMSEQ(X3,X2,X4) ) ).
cnf(i_0_1230,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X4,X1)
| c_SEQ_OLIMSEQ(X3,X4,X2) ) ).
cnf(i_0_1231,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X1,X3,X4,X5)
| c_Limits_OZfun(X2,X3,X4,X5) ) ).
cnf(i_0_1232,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X1,X4,X5)
| c_Limits_OZfun(X3,X2,X4,X5) ) ).
cnf(i_0_1233,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X1,X5)
| c_Limits_OZfun(X3,X4,X2,X5) ) ).
cnf(i_0_1234,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X5,X1)
| c_Limits_OZfun(X3,X4,X5,X2) ) ).
cnf(i_0_1235,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X1,X3)
| c_SEQ_OZseq(X2,X3) ) ).
cnf(i_0_1236,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X3,X1)
| c_SEQ_OZseq(X3,X2) ) ).
cnf(i_0_1237,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1238,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(X2) ) ).
cnf(i_0_1239,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1)
| c_SEQ_Odecseq(X2) ) ).
cnf(i_0_1240,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1)
| c_SEQ_Oincseq(X2) ) ).
cnf(i_0_1241,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_1242,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_1243,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1244,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X1,X3,X4)
| c_Deriv_Odifferentiable(X2,X3,X4) ) ).
cnf(i_0_1245,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X1,X4)
| c_Deriv_Odifferentiable(X3,X2,X4) ) ).
cnf(i_0_1246,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| c_Deriv_Odifferentiable(X3,X4,X2) ) ).
cnf(i_0_1247,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1248,axiom,
( X1 != X2
| ~ c_Series_Osums(X1,X3,X4)
| c_Series_Osums(X2,X3,X4) ) ).
cnf(i_0_1249,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X1,X4)
| c_Series_Osums(X3,X2,X4) ) ).
cnf(i_0_1250,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X4,X1)
| c_Series_Osums(X3,X4,X2) ) ).
cnf(i_0_1251,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X1,X3)
| c_SEQ_OCauchy(X2,X3) ) ).
cnf(i_0_1252,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X3,X1)
| c_SEQ_OCauchy(X3,X2) ) ).
cnf(i_0_1253,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X1,X3,X4)
| c_Lim_OisUCont(X2,X3,X4) ) ).
cnf(i_0_1254,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X1,X4)
| c_Lim_OisUCont(X3,X2,X4) ) ).
cnf(i_0_1255,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X4,X1)
| c_Lim_OisUCont(X3,X4,X2) ) ).
cnf(i_0_1256,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_1257,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1258,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1259,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1260,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1261,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1262,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1263,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1264,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_1265,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1266,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_1267,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1268,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_1269,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1270,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1271,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1272,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1273,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1274,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1275,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1276,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1277,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1278,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1279,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1280,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1281,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1282,axiom,
( X1 != X2
| ~ class_SEQ_Obanach(X1)
| class_SEQ_Obanach(X2) ) ).
cnf(i_0_1283,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1284,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1285,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1286,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1287,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1288,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1289,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1290,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1291,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1292,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1293,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1294,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1295,axiom,
( X1 != X2
| ~ c_Series_Osummable(X1,X3)
| c_Series_Osummable(X2,X3) ) ).
cnf(i_0_1296,axiom,
( X1 != X2
| ~ c_Series_Osummable(X3,X1)
| c_Series_Osummable(X3,X2) ) ).
cnf(i_0_1297,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1298,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1299,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1300,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1301,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1302,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X1,X3,X4,X5,X6)
| c_Lim_OLIM(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1303,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X1,X4,X5,X6)
| c_Lim_OLIM(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1304,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X1,X5,X6)
| c_Lim_OLIM(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1305,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X1,X6)
| c_Lim_OLIM(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1306,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X6,X1)
| c_Lim_OLIM(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1307,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1190_001,axiom,
X1 = X1 ).
cnf(i_0_1191_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_1192_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_1193_004,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_1194_005,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_1195_006,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_1196_007,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_1197_008,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_1198_009,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X1,X3) = c_Complex_Ocomplex_OComplex(X2,X3) ) ).
cnf(i_0_1199_010,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X3,X1) = c_Complex_Ocomplex_OComplex(X3,X2) ) ).
cnf(i_0_1200_011,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_1201_012,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_1202_013,axiom,
( X1 != X2
| c_Series_Osuminf(X1,X3) = c_Series_Osuminf(X2,X3) ) ).
cnf(i_0_1203_014,axiom,
( X1 != X2
| c_Series_Osuminf(X3,X1) = c_Series_Osuminf(X3,X2) ) ).
cnf(i_0_1204_015,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_1205_016,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_1206_017,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_1207_018,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_1208_019,axiom,
( X1 != X2
| c_Fun_Ocomp(X1,X3,X4,X5,X6) = c_Fun_Ocomp(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1209_020,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X1,X4,X5,X6) = c_Fun_Ocomp(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1210_021,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X1,X5,X6) = c_Fun_Ocomp(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1211_022,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X1,X6) = c_Fun_Ocomp(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1212_023,axiom,
( X1 != X2
| c_Fun_Ocomp(X3,X4,X5,X6,X1) = c_Fun_Ocomp(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1213_024,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X1,X3,X4,X5,X6)
| c_Limits_Otendsto(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1214_025,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X1,X4,X5,X6)
| c_Limits_Otendsto(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1215_026,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X1,X5,X6)
| c_Limits_Otendsto(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1216_027,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X1,X6)
| c_Limits_Otendsto(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1217_028,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X6,X1)
| c_Limits_Otendsto(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1218_029,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1219_030,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X1,X3,X4,X5)
| c_Lim_OisCont(X2,X3,X4,X5) ) ).
cnf(i_0_1220_031,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X1,X4,X5)
| c_Lim_OisCont(X3,X2,X4,X5) ) ).
cnf(i_0_1221_032,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X1,X5)
| c_Lim_OisCont(X3,X4,X2,X5) ) ).
cnf(i_0_1222_033,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X5,X1)
| c_Lim_OisCont(X3,X4,X5,X2) ) ).
cnf(i_0_1223_034,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1224_035,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X1,X3,X4)
| c_RealVector_Obounded__linear(X2,X3,X4) ) ).
cnf(i_0_1225_036,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X1,X4)
| c_RealVector_Obounded__linear(X3,X2,X4) ) ).
cnf(i_0_1226_037,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X4,X1)
| c_RealVector_Obounded__linear(X3,X4,X2) ) ).
cnf(i_0_1227_038,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_1228_039,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X1,X3,X4)
| c_SEQ_OLIMSEQ(X2,X3,X4) ) ).
cnf(i_0_1229_040,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X1,X4)
| c_SEQ_OLIMSEQ(X3,X2,X4) ) ).
cnf(i_0_1230_041,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X4,X1)
| c_SEQ_OLIMSEQ(X3,X4,X2) ) ).
cnf(i_0_1231_042,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X1,X3,X4,X5)
| c_Limits_OZfun(X2,X3,X4,X5) ) ).
cnf(i_0_1232_043,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X1,X4,X5)
| c_Limits_OZfun(X3,X2,X4,X5) ) ).
cnf(i_0_1233_044,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X1,X5)
| c_Limits_OZfun(X3,X4,X2,X5) ) ).
cnf(i_0_1234_045,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X5,X1)
| c_Limits_OZfun(X3,X4,X5,X2) ) ).
cnf(i_0_1235_046,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X1,X3)
| c_SEQ_OZseq(X2,X3) ) ).
cnf(i_0_1236_047,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X3,X1)
| c_SEQ_OZseq(X3,X2) ) ).
cnf(i_0_1237_048,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_1238_049,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(X2) ) ).
cnf(i_0_1239_050,axiom,
( X1 != X2
| ~ c_SEQ_Odecseq(X1)
| c_SEQ_Odecseq(X2) ) ).
cnf(i_0_1240_051,axiom,
( X1 != X2
| ~ c_SEQ_Oincseq(X1)
| c_SEQ_Oincseq(X2) ) ).
cnf(i_0_1241_052,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_1242_053,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_1243_054,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_1244_055,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X1,X3,X4)
| c_Deriv_Odifferentiable(X2,X3,X4) ) ).
cnf(i_0_1245_056,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X1,X4)
| c_Deriv_Odifferentiable(X3,X2,X4) ) ).
cnf(i_0_1246_057,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| c_Deriv_Odifferentiable(X3,X4,X2) ) ).
cnf(i_0_1247_058,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1248_059,axiom,
( X1 != X2
| ~ c_Series_Osums(X1,X3,X4)
| c_Series_Osums(X2,X3,X4) ) ).
cnf(i_0_1249_060,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X1,X4)
| c_Series_Osums(X3,X2,X4) ) ).
cnf(i_0_1250_061,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X4,X1)
| c_Series_Osums(X3,X4,X2) ) ).
cnf(i_0_1251_062,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X1,X3)
| c_SEQ_OCauchy(X2,X3) ) ).
cnf(i_0_1252_063,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X3,X1)
| c_SEQ_OCauchy(X3,X2) ) ).
cnf(i_0_1253_064,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X1,X3,X4)
| c_Lim_OisUCont(X2,X3,X4) ) ).
cnf(i_0_1254_065,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X1,X4)
| c_Lim_OisUCont(X3,X2,X4) ) ).
cnf(i_0_1255_066,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X4,X1)
| c_Lim_OisUCont(X3,X4,X2) ) ).
cnf(i_0_1256_067,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_1257_068,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X1,X3,X4)
| c_HOL_Oord__class_Oless(X2,X3,X4) ) ).
cnf(i_0_1258_069,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X1,X4)
| c_HOL_Oord__class_Oless(X3,X2,X4) ) ).
cnf(i_0_1259_070,axiom,
( X1 != X2
| ~ c_HOL_Oord__class_Oless(X3,X4,X1)
| c_HOL_Oord__class_Oless(X3,X4,X2) ) ).
cnf(i_0_1260_071,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Ring__and__Field_Oordered__idom(X2) ) ).
cnf(i_0_1261_072,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1262_073,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| class_Ring__and__Field_Opordered__semiring(X2) ) ).
cnf(i_0_1263_074,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| class_Ring__and__Field_Oordered__semiring__strict(X2) ) ).
cnf(i_0_1264_075,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Olordered__ring(X1)
| class_Ring__and__Field_Olordered__ring(X2) ) ).
cnf(i_0_1265_076,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1266_077,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__semiring(X1)
| class_Ring__and__Field_Oordered__semiring(X2) ) ).
cnf(i_0_1267_078,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring__abs(X1)
| class_Ring__and__Field_Opordered__ring__abs(X2) ) ).
cnf(i_0_1268_079,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono(X1)
| class_Ring__and__Field_Omult__mono(X2) ) ).
cnf(i_0_1269_080,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_1270_081,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_1271_082,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_1272_083,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__mono1(X1)
| class_Ring__and__Field_Omult__mono1(X2) ) ).
cnf(i_0_1273_084,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X1)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X2) ) ).
cnf(i_0_1274_085,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__ring(X1)
| class_Ring__and__Field_Opordered__ring(X2) ) ).
cnf(i_0_1275_086,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| class_Ring__and__Field_Opordered__cancel__semiring(X2) ) ).
cnf(i_0_1276_087,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1277_088,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1278_089,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| class_OrderedGroup_Opordered__ab__group__add(X2) ) ).
cnf(i_0_1279_090,axiom,
( X1 != X2
| ~ class_Orderings_Oorder(X1)
| class_Orderings_Oorder(X2) ) ).
cnf(i_0_1280_091,axiom,
( X1 != X2
| ~ class_Orderings_Opreorder(X1)
| class_Orderings_Opreorder(X2) ) ).
cnf(i_0_1281_092,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1282_093,axiom,
( X1 != X2
| ~ class_SEQ_Obanach(X1)
| class_SEQ_Obanach(X2) ) ).
cnf(i_0_1283_094,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1284_095,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1285_096,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1286_097,axiom,
( X1 != X2
| ~ hBOOL(X1)
| hBOOL(X2) ) ).
cnf(i_0_1287_098,axiom,
( X1 != X2
| ~ class_Orderings_Olinorder(X1)
| class_Orderings_Olinorder(X2) ) ).
cnf(i_0_1288_099,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1289_100,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X1)
| class_OrderedGroup_Olordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1290_101,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oabs__if(X1)
| class_Ring__and__Field_Oabs__if(X2) ) ).
cnf(i_0_1291_102,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1292_103,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1293_104,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1294_105,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1295_106,axiom,
( X1 != X2
| ~ c_Series_Osummable(X1,X3)
| c_Series_Osummable(X2,X3) ) ).
cnf(i_0_1296_107,axiom,
( X1 != X2
| ~ c_Series_Osummable(X3,X1)
| c_Series_Osummable(X3,X2) ) ).
cnf(i_0_1297_108,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1298_109,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1299_110,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1300_111,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1301_112,axiom,
( X1 != X2
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| class_OrderedGroup_Opordered__ab__group__add__abs(X2) ) ).
cnf(i_0_1302_113,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X1,X3,X4,X5,X6)
| c_Lim_OLIM(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1303_114,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X1,X4,X5,X6)
| c_Lim_OLIM(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1304_115,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X1,X5,X6)
| c_Lim_OLIM(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1305_116,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X1,X6)
| c_Lim_OLIM(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1306_117,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X6,X1)
| c_Lim_OLIM(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1307_118,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1308,plain,
hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X6) = hAPP(c_Fun_Ocomp(X1,X2,X7,X4,X8),X6),
inference(equality_inference,[],[636]) ).
cnf(i_0_1309,plain,
hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
inference(equality_inference,[],[642]) ).
cnf(i_0_1310,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1) ),
inference(equality_inference,[],[947]) ).
cnf(i_0_1311,plain,
( ~ class_RealVector_Oreal__vector(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[964]) ).
cnf(i_0_1312,plain,
( X1 = X1
| ~ class_RealVector_Oreal__vector(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[968]) ).
cnf(i_0_1313,plain,
( X1 = X1
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(equality_inference,[],[1037]) ).
cnf(i_0_1314,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[1038]) ).
cnf(i_0_1315,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[1039]) ).
cnf(i_0_1316,plain,
X1 = X1,
inference(equality_inference,[],[1080]) ).
cnf(i_0_1317,plain,
X1 = X1,
inference(equality_inference,[],[1081]) ).
cnf(i_0_1318,plain,
X1 = X1,
inference(equality_inference,[],[1085]) ).
cnf(i_0_1319,plain,
$false,
inference(scs_inference,[],[i_0_1189,i_0_601,i_0_1111,i_0_595]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG361-1 : 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
% 0.15/0.33 % Computer : n004.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 10:32:47 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.52/1.67 % Version : CSE_E---1.7
% 0.52/1.67 % Problem : theBenchmark.p
% 0.52/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 0.52/1.67 % SZS output start CNFRefutation
% See solution above
% 0.57/1.73 % Total time : 1.328s
%------------------------------------------------------------------------------