%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG365-1 : 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 : n001.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 0.39s 1.67s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 651)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
( v_thesis____
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_that_0,axiom,
( v_thesis____
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
cnf(cls_CHAINED_0,axiom,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
cnf(cls_conv2_0,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conv2_0) ).
cnf(cls_g_I2_J_0,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_g_I2_J_0) ).
cnf(cls_LIMSEQ__offset_0,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X4,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__offset_0) ).
cnf(cls_mult__left_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X6),X4),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,X6,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM_0) ).
cnf(cls_mult__left_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4),X6,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_Otendsto(X2,X5,X6,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Otendsto_0) ).
cnf(cls_scaleR__left_OLIM_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X6),X4),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,X6,X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OLIM_0) ).
cnf(cls_scaleR__left_Otendsto_0,axiom,
( c_Limits_Otendsto(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X5),X4),X6,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X5,X6,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Otendsto_0) ).
cnf(cls_LIM__mult__left__zero_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__left__zero_0) ).
cnf(cls_mult__left_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM__zero_0) ).
cnf(cls_scaleR__left_OLIM__zero_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OLIM__zero_0) ).
cnf(cls_scaleR_OLIM__left__zero_0,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OLIM__left__zero_0) ).
cnf(cls_setsum__left__distrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).
cnf(cls_mult__left_Osetsum_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osetsum_0) ).
cnf(cls_scaleR__left_Osetsum_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_Finite__Set_Osetsum(X2,X3,X4,tc_RealDef_Oreal)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_Osetsum_0) ).
cnf(cls_Zfun__mult__left_0,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X2,X5,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__left_0) ).
cnf(cls_mult__left_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X2,X5,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OZfun_0) ).
cnf(cls_scaleR_OZfun__left_0,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X5,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OZfun__left_0) ).
cnf(cls_scaleR__left_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X5,X3,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left_OZfun_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_LIMSEQ__ignore__initial__segment_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X3,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X4,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__ignore__initial__segment_0) ).
cnf(cls_summable__ignore__initial__segment_0,axiom,
( c_Series_Osummable(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X3,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__ignore__initial__segment_0) ).
cnf(cls_conv1_0,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conv1_0) ).
cnf(cls_f_I2_J_0,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f_I2_J_0) ).
cnf(cls_LIM__isCont__iff_1,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_1) ).
cnf(cls_LIM__offset__zero__cancel_0,axiom,
( c_Lim_OLIM(X3,X4,X5,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X2,X1,X2),c_HOL_Ozero__class_Ozero(X2),X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero__cancel_0) ).
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_isCont__iff_1,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__iff_1) ).
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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4,X1,X1,X2),X5,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4,X1,X1,X2),X5,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,X4),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_LIM__isCont__iff_0,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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__offset__zero_0,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X2,X1,X2),c_HOL_Ozero__class_Ozero(X2),X5,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero_0) ).
cnf(cls_LIM__inverse_0,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X3,X1,X1,X2),X4,hAPP(c_HOL_Oinverse__class_Oinverse(X1),X5),X2,X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse_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_tendsto__inverse_0,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,X3),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X4),X5,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__inverse_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_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_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_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_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_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_isCont__iff_0,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__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_LIMSEQ__Suc__iff_0,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(X2,c_Suc,tc_nat,X1,tc_nat),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc__iff_0) ).
cnf(cls_convergent__minus__iff_1,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__minus__iff_1) ).
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_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_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_mult__left_Ocont_0,axiom,
( c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ocont_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__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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_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_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_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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_mult__right_OZfun_0,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_Zfun__mult__right_0,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_isCont__inverse_0,axiom,
( c_Lim_OisCont(c_COMBB(c_HOL_Oinverse__class_Oinverse(X2),X3,X2,X2,X1),X4,X1,X2)
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__inverse_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_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_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_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_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_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_scaleR__right_OLIMSEQ_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_scaleR__right_Osums_0,axiom,
( c_Series_Osums(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_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_mult__left_OisCont_0,axiom,
( c_Lim_OisCont(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OisCont_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_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_LIMSEQ__inverse_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__inverse_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_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_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_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_suminf__mult_0,axiom,
( c_Series_Osuminf(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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__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_differentiable__inverse_0,axiom,
( c_Deriv_Odifferentiable(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,X1),X3,X1)
| hAPP(X2,X3) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__inverse_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_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_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_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_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_LIMSEQ__Suc_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X2,c_Suc,tc_nat,X1,tc_nat),X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc_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_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_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_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_scaleR__right_Osummable_0,axiom,
( c_Series_Osummable(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_scaleR_OZseq__right_0,axiom,
( c_SEQ_OZseq(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_OCauchy_0,axiom,
( c_SEQ_OCauchy(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_lim__uminus_0,axiom,
( c_SEQ_Olim(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_SEQ_Olim(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lim__uminus_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_mult_Obounded__linear__left_0,axiom,
( c_RealVector_Obounded__linear(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded__linear__left_0) ).
cnf(cls_mult__left_OisUCont_0,axiom,
( c_Lim_OisUCont(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OisUCont_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_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_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_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_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_ATP__Linkup_OCOMBC__def_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).
cnf(cls_COMBC__def_0,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
cnf(cls_ATP__Linkup_OCOMBB__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_ATP__Linkup_OCOMBB__def_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_convergent__minus__iff_0,axiom,
( c_SEQ_Oconvergent(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__minus__iff_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__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_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_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_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_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_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_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_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_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_LIM__not__zero_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_HOL_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__not__zero_0) ).
cnf(cls_LIM__const__eq_0,axiom,
( X3 = X4
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X5,X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const__eq_0) ).
cnf(cls_LIM__const__not__eq_0,axiom,
( X3 = X5
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,X5,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const__not__eq_0) ).
cnf(cls_combine__common__factor_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
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_inverse__add_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).
cnf(cls_scaleR__right_Ocont_0,axiom,
( c_Lim_OLIM(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ocont_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_LIM__const_0,axiom,
( c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,X3,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__const_0) ).
cnf(cls_tendsto__const_0,axiom,
( c_Limits_Otendsto(c_COMBK(X2,X1,X3),X2,X4,X3,X1)
| ~ class_RealVector_Otopological__space(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__const_0) ).
cnf(cls_LIM__inverse__fun_0,axiom,
( c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(X1),X2,hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2),X1,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse__fun_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_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_division__ring__inverse__add_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),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_class__ringb_Onoteq__reduce_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),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_class__semiring_Osemiring__rules_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
cnf(cls_mult_Oadd__left_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
cnf(cls_mult__left_Oadd_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
cnf(cls_scaleR_Oadd__right_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
cnf(cls_scaleR__right_Oadd_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
cnf(cls_mult_Oadd__right_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
cnf(cls_mult__right_Oadd_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),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_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
cnf(cls_mult__scaleR__left_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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_Osemiring__rules_I17_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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_class__semiring_Osemiring__rules_I25_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),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_add__cancel__21_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
cnf(cls_setsum__0_0,axiom,
( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__0_0) ).
cnf(cls_Zfun__zero_0,axiom,
( c_Limits_OZfun(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__zero_0) ).
cnf(cls_isCont__const_0,axiom,
( c_Lim_OisCont(c_COMBK(X3,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__const_0) ).
cnf(cls_nat__add__assoc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_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_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_add__cancel__21_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
cnf(cls_scaleR__right_OscaleR_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).
cnf(cls_scaleR__left__commute_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
cnf(cls_mult__scaleR__right_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_add__minus__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
cnf(cls_nonzero__inverse__mult__distrib_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
cnf(cls_inverse__mult__distrib_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
cnf(cls_minus__add__distrib_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
cnf(cls_minus__add_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
cnf(cls_bounded__linear_OscaleR_0,axiom,
( hAPP(X3,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X4),X5)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X2),X4),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_scaleR__right_OisCont_0,axiom,
( c_Lim_OisCont(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).
cnf(cls_add__cancel__end_0,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
cnf(cls_nat__add__left__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
cnf(cls_LIMSEQ__const__iff_0,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_0) ).
cnf(cls_mult__left_Ominus_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_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_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_minus__add__cancel_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
cnf(cls_add__cancel__end_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
cnf(cls_square__eq__iff_1,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_scaleR_Ominus__right_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
cnf(cls_scaleR__minus__right_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
cnf(cls_mult__right_Ominus_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_mult__left__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).
cnf(cls_Zseq__const__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(c_COMBK(X2,X1,tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__const__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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
cnf(cls_add__Suc_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
cnf(cls_scaleR__conv__of__real_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_RealVector_Oof__real(X1),X2)),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).
cnf(cls_sums__zero_0,axiom,
( c_Series_Osums(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__zero_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_class__ringb_Oadd__cancel_0,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
cnf(cls_scaleR__cancel__right_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).
cnf(cls_add__right__cancel_0,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
cnf(cls_add__left__cancel_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
cnf(cls_add__imp__eq_0,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
cnf(cls_add__Suc__right_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
cnf(cls_differentiable__const_0,axiom,
( c_Deriv_Odifferentiable(c_COMBK(X2,X1,X1),X3,X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__const_0) ).
cnf(cls_LIMSEQ__const__iff_1,axiom,
( c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const__iff_1) ).
cnf(cls_LIMSEQ__const_0,axiom,
( c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__const_0) ).
cnf(cls_add__Suc__shift_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_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_convergent__LIMSEQ__iff_1,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,c_SEQ_Olim(X2,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_1) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
cnf(cls_suminf__zero_0,axiom,
( c_Series_Osuminf(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__zero_0) ).
cnf(cls_ab__left__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
cnf(cls_left__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).
cnf(cls_summable__zero_0,axiom,
( c_Series_Osummable(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__zero_0) ).
cnf(cls_Zseq__zero_0,axiom,
( c_SEQ_OZseq(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__zero_0) ).
cnf(cls_inverse__minus__eq_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
cnf(cls_nonzero__inverse__minus__eq_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
cnf(cls_scaleR__cancel__left_1,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),X2) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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_COMBK__def_0,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
cnf(cls_minus__unique_0,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
cnf(cls_convergent__LIMSEQ__iff_0,axiom,
( c_SEQ_OLIMSEQ(X2,c_SEQ_Olim(X2,X1),X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__LIMSEQ__iff_0) ).
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_limI_0,axiom,
( c_SEQ_Olim(X2,X1) = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_limI_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_convergent__def_1,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__def_1) ).
cnf(cls_convergentI_0,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergentI_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_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_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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_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(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
cnf(cls_right__minus_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
cnf(cls_double__eq__0__iff_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
cnf(cls_scaleR_Obounded__linear__right_0,axiom,
( c_RealVector_Obounded__linear(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded__linear__right_0) ).
cnf(cls_scaleR__right_OisUCont_0,axiom,
( c_Lim_OisUCont(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisUCont_0) ).
cnf(cls_nat__add__commute_0,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
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_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_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_nonzero__inverse__eq__imp__eq_0,axiom,
( X2 = X3
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
cnf(cls_double__eq__0__iff_1,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
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_inverse__eq__iff__eq_0,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
cnf(cls_mult__zero__left_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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_inverse__inverse__eq_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
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_add__0__left_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
cnf(cls_nonzero__inverse__inverse__eq_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)) = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
cnf(cls_scaleR_Ozero__left_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),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_1,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),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__right_0,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_scaleR__eq__0__iff_2,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_mult__zero__right_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_monoid__add__class_Oadd__0__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_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_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_mult__idem_0,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).
cnf(cls_inverse__nonzero__iff__nonzero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_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_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_inverse__zero__imp__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_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_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_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_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_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_inverse__nonzero__iff__nonzero_1,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).
cnf(cls_Cauchy__convergent__iff_0,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_SEQ_Ocomplete__space(X1)
| ~ c_SEQ_OCauchy(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_0) ).
cnf(cls_Cauchy__convergent__iff_1,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_SEQ_Ocomplete__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cauchy__convergent__iff_1) ).
cnf(cls_convergent__Cauchy_0,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_convergent__Cauchy_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_Suc__inject_0,axiom,
( X1 = X2
| hAPP(c_Suc,X1) != hAPP(c_Suc,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
cnf(cls_nat_Oinject_0,axiom,
( X1 = X2
| hAPP(c_Suc,X1) != hAPP(c_Suc,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_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_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_inverse__zero_0,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__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_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__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__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_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_real__Cauchy__convergent_0,axiom,
( c_SEQ_Oconvergent(X1,tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__Cauchy__convergent_0) ).
cnf(cls_Suc__n__not__n_0,axiom,
hAPP(c_Suc,X1) != X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
cnf(cls_n__not__Suc__n_0,axiom,
X1 != hAPP(c_Suc,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
cnf(cls_g_I1_J_0,axiom,
c_SEQ_Osubseq(v_ga____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_g_I1_J_0) ).
cnf(cls_f_I1_J_0,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f_I1_J_0) ).
cnf(clsarity_Complex__Ocomplex__SEQ_Ocomplete__space,axiom,
class_SEQ_Ocomplete__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Ocomplete__space) ).
cnf(clsarity_RealDef__Oreal__SEQ_Ocomplete__space,axiom,
class_SEQ_Ocomplete__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Ocomplete__space) ).
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_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_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Otopological__space,axiom,
class_RealVector_Otopological__space(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Otopological__space) ).
cnf(clsarity_RealDef__Oreal__RealVector_Otopological__space,axiom,
class_RealVector_Otopological__space(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Otopological__space) ).
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__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
cnf(clsarity_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_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_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_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
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_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
cnf(clsarity_nat__HOL_Ozero,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
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_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_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_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
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__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
cnf(clsarity_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_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__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_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__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__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
cnf(clsarity_Complex__Ocomplex__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_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_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_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_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__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_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__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_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_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_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__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__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(cls_conjecture_0,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(i_0_477,negated_conjecture,
( v_thesis____
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X1,tc_RealDef_Oreal) ),
cls_conjecture_1,
[final] ).
cnf(i_0_478,axiom,
( v_thesis____
| ~ c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),X1,tc_RealDef_Oreal) ),
cls_that_0,
[final] ).
cnf(i_0_479,axiom,
c_SEQ_OLIMSEQ(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),v_sko__CHAINED__1(v_f____,v_ga____,v_s),tc_RealDef_Oreal),
cls_CHAINED_0,
[final] ).
cnf(i_0_480,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
cls_conv2_0,
[final] ).
cnf(i_0_481,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_OIm,c_COMBB(v_s,c_COMBB(v_f____,v_ga____,tc_nat,tc_nat,tc_nat),tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
cls_g_I2_J_0,
[final] ).
cnf(i_0_482,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X4,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X3,X1) ),
cls_LIMSEQ__offset_0,
[final] ).
cnf(i_0_483,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X6),X4),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,X6,X2,X1) ),
cls_mult__left_OLIM_0,
[final] ).
cnf(i_0_484,axiom,
( c_Limits_Otendsto(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X5),X4),X6,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_Otendsto(X2,X5,X6,X3,X1) ),
cls_mult__left_Otendsto_0,
[final] ).
cnf(i_0_485,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X6),X4),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,X6,X2,tc_RealDef_Oreal) ),
cls_scaleR__left_OLIM_0,
[final] ).
cnf(i_0_486,axiom,
( c_Limits_Otendsto(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X5),X4),X6,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_Otendsto(X2,X5,X6,X3,tc_RealDef_Oreal) ),
cls_scaleR__left_Otendsto_0,
[final] ).
cnf(i_0_487,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_LIM__mult__left__zero_0,
[final] ).
cnf(i_0_488,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X3,X1,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_mult__left_OLIM__zero_0,
[final] ).
cnf(i_0_489,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_scaleR__left_OLIM__zero_0,
[final] ).
cnf(i_0_490,axiom,
( c_Lim_OLIM(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X3,tc_RealDef_Oreal,tc_fun(X1,X1),X2),X4,X2,X1,X1),X5,c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X5,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
cls_scaleR_OLIM__left__zero_0,
[final] ).
cnf(i_0_491,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__left__distrib_0,
[final] ).
cnf(i_0_492,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_Finite__Set_Osetsum(X2,X3,X4,X1)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Osetsum_0,
[final] ).
cnf(i_0_493,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_Finite__Set_Osetsum(X2,X3,X4,tc_RealDef_Oreal)),X5) = c_Finite__Set_Osetsum(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X4),X5,X4,X1,X1),X3,X4,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left_Osetsum_0,
[final] ).
cnf(i_0_494,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X2,X5,X3,X1) ),
cls_Zfun__mult__left_0,
[final] ).
cnf(i_0_495,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_HOL_Otimes__class_Otimes(X1),X2,X1,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Limits_OZfun(X2,X5,X3,X1) ),
cls_mult__left_OZfun_0,
[final] ).
cnf(i_0_496,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X5,X3,tc_RealDef_Oreal) ),
cls_scaleR_OZfun__left_0,
[final] ).
cnf(i_0_497,axiom,
( c_Limits_OZfun(c_COMBC(c_COMBB(c_RealVector_OscaleR__class_OscaleR(X1),X2,tc_RealDef_Oreal,tc_fun(X1,X1),X3),X4,X3,X1,X1),X5,X3,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Limits_OZfun(X2,X5,X3,tc_RealDef_Oreal) ),
cls_scaleR__left_OZfun_0,
[final] ).
cnf(i_0_498,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_499,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X3,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X4,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X4,X1) ),
cls_LIMSEQ__ignore__initial__segment_0,
[final] ).
cnf(i_0_500,axiom,
( c_Series_Osummable(c_COMBB(X2,c_COMBC(c_HOL_Oplus__class_Oplus(tc_nat),X3,tc_nat,tc_nat,tc_nat),tc_nat,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osummable(X2,X1) ),
cls_summable__ignore__initial__segment_0,
[final] ).
cnf(i_0_501,axiom,
c_SEQ_Oconvergent(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal),
cls_conv1_0,
[final] ).
cnf(i_0_502,axiom,
c_SEQ_Omonoseq(c_COMBB(c_Complex_ORe,c_COMBB(v_s,v_f____,tc_nat,tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex,tc_RealDef_Oreal,tc_nat)),
cls_f_I2_J_0,
[final] ).
cnf(i_0_503,axiom,
( c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2) ),
cls_LIM__isCont__iff_1,
[final] ).
cnf(i_0_504,axiom,
( c_Lim_OLIM(X3,X4,X5,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X2,X1,X2),c_HOL_Ozero__class_Ozero(X2),X5,X2,X1) ),
cls_LIM__offset__zero__cancel_0,
[final] ).
cnf(i_0_505,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_506,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_507,axiom,
( c_Lim_OisCont(X3,X4,X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2) ),
cls_isCont__iff_1,
[final] ).
cnf(i_0_508,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_509,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4,X1,X1,X2),X5,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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_510,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4,X1,X1,X2),X5,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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_511,axiom,
( c_Limits_Otendsto(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,X4),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_512,axiom,
( c_Limits_Otendsto(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_513,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,hAPP(X3,X4),X1,X2) ),
cls_LIM__isCont__iff_0,
[final] ).
cnf(i_0_514,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_515,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_516,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_517,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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_518,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),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_519,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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_520,axiom,
( c_Lim_OLIM(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),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_521,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X2),X4),X2,X1,X2),c_HOL_Ozero__class_Ozero(X2),X5,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__vector(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
cls_LIM__offset__zero_0,
[final] ).
cnf(i_0_522,axiom,
( c_Lim_OLIM(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X3,X1,X1,X2),X4,hAPP(c_HOL_Oinverse__class_Oinverse(X1),X5),X2,X1)
| X5 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OLIM(X3,X4,X5,X2,X1) ),
cls_LIM__inverse_0,
[final] ).
cnf(i_0_523,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_524,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_525,axiom,
( c_Limits_Otendsto(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,X3),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X4),X5,X3,X1)
| X4 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ c_Limits_Otendsto(X2,X4,X5,X3,X1) ),
cls_tendsto__inverse_0,
[final] ).
cnf(i_0_526,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_527,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_528,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_529,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_530,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_531,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_532,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_533,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_534,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_535,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_536,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_537,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_538,axiom,
( c_Lim_OLIM(c_COMBB(X3,hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X1,X2,X1),c_HOL_Ozero__class_Ozero(X1),hAPP(X3,X4),X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ class_RealVector_Ometric__space(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
cls_isCont__iff_0,
[final] ).
cnf(i_0_539,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_540,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_541,axiom,
( c_SEQ_OLIMSEQ(X2,X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBB(X2,c_Suc,tc_nat,X1,tc_nat),X3,X1) ),
cls_LIMSEQ__Suc__iff_0,
[final] ).
cnf(i_0_542,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) ),
cls_convergent__minus__iff_1,
[final] ).
cnf(i_0_543,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_544,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_545,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_546,axiom,
( c_Lim_OLIM(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ocont_0,
[final] ).
cnf(i_0_547,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_548,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_549,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__right_Osetsum_0,
[final] ).
cnf(i_0_550,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X5),X4,X5,X1)
| ~ class_Ring__and__Field_Osemiring__0(X1) ),
cls_setsum__right__distrib_0,
[final] ).
cnf(i_0_551,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Finite__Set_Osetsum(X3,X4,X5,X1)) = c_Finite__Set_Osetsum(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,X5),X4,X5,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Osetsum_0,
[final] ).
cnf(i_0_552,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_553,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_554,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_555,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_556,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_557,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_558,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_559,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_560,axiom,
( c_Limits_OZfun(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_561,axiom,
( c_Lim_OisCont(c_COMBB(c_HOL_Oinverse__class_Oinverse(X2),X3,X2,X2,X1),X4,X1,X2)
| hAPP(X3,X4) = c_HOL_Ozero__class_Ozero(X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X2)
| ~ c_Lim_OisCont(X3,X4,X1,X2) ),
cls_isCont__inverse_0,
[final] ).
cnf(i_0_562,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_563,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_564,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_565,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_566,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_567,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_568,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_569,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_570,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
cls_scaleR__right_OLIMSEQ_0,
[final] ).
cnf(i_0_571,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_SEQ_OLIMSEQ(X3,X4,X1) ),
cls_mult__right_OLIMSEQ_0,
[final] ).
cnf(i_0_572,axiom,
( c_Series_Osums(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_scaleR__right_Osums_0,
[final] ).
cnf(i_0_573,axiom,
( c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_sums__mult_0,
[final] ).
cnf(i_0_574,axiom,
( c_Series_Osums(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4),X1)
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osums(X3,X4,X1) ),
cls_mult__right_Osums_0,
[final] ).
cnf(i_0_575,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_576,axiom,
( c_Lim_OisCont(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_OisCont_0,
[final] ).
cnf(i_0_577,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_578,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_579,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,tc_nat),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_LIMSEQ__inverse_0,
[final] ).
cnf(i_0_580,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_581,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_582,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_583,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_584,axiom,
( c_Series_Osuminf(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1,tc_nat),X1) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Series_Osuminf(X3,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1)
| ~ c_Series_Osummable(X3,X1) ),
cls_suminf__mult_0,
[final] ).
cnf(i_0_585,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_586,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),c_Series_Osuminf(X3,X1)) = c_Series_Osuminf(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_587,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_588,axiom,
( c_Deriv_Odifferentiable(c_COMBB(c_HOL_Oinverse__class_Oinverse(X1),X2,X1,X1,X1),X3,X1)
| hAPP(X2,X3) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__field(X1)
| ~ c_Deriv_Odifferentiable(X2,X3,X1) ),
cls_differentiable__inverse_0,
[final] ).
cnf(i_0_589,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_590,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_591,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_592,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_593,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_594,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_595,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_596,axiom,
( c_SEQ_OLIMSEQ(c_COMBB(X2,c_Suc,tc_nat,X1,tc_nat),X3,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_LIMSEQ__Suc_0,
[final] ).
cnf(i_0_597,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_598,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_599,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_600,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_601,axiom,
( c_Series_Osummable(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_602,axiom,
( c_Series_Osummable(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_603,axiom,
( c_Series_Osummable(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_604,axiom,
( c_SEQ_OZseq(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_605,axiom,
( c_SEQ_OZseq(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_606,axiom,
( c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_607,axiom,
( c_SEQ_OZseq(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_608,axiom,
( c_SEQ_OCauchy(c_COMBB(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_609,axiom,
( c_SEQ_OCauchy(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_610,axiom,
( c_SEQ_Olim(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),c_SEQ_Olim(X2,X1))
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
cls_lim__uminus_0,
[final] ).
cnf(i_0_611,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_612,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_613,axiom,
( c_RealVector_Obounded__linear(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Obounded__linear__left_0,
[final] ).
cnf(i_0_614,axiom,
( c_Lim_OisUCont(c_COMBC(c_HOL_Otimes__class_Otimes(X1),X2,X1,X1,X1),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_OisUCont_0,
[final] ).
cnf(i_0_615,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_616,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_617,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_618,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_619,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_620,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
cls_ATP__Linkup_OCOMBC__def_0,
[final] ).
cnf(i_0_621,axiom,
hAPP(c_COMBC(X1,X2,X3,X4,X5),X6) = hAPP(hAPP(X1,X6),X2),
cls_COMBC__def_0,
[final] ).
cnf(i_0_622,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_ATP__Linkup_OCOMBB__def_0,
[final] ).
cnf(i_0_623,axiom,
hAPP(c_COMBB(X1,X2,X3,X4,X5),X6) = hAPP(X1,hAPP(X2,X6)),
cls_COMBB__def_0,
[final] ).
cnf(i_0_624,axiom,
( c_SEQ_Oconvergent(c_COMBB(c_HOL_Ouminus__class_Ouminus(X1),X2,X1,X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
cls_convergent__minus__iff_0,
[final] ).
cnf(i_0_625,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_626,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_627,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_628,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_629,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_630,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_631,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_632,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_633,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_634,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_635,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_HOL_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,c_HOL_Ozero__class_Ozero(X1),X2,X1) ),
cls_LIM__not__zero_0,
[final] ).
cnf(i_0_636,axiom,
( X3 = X4
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X5,X4,X2,X1) ),
cls_LIM__const__eq_0,
[final] ).
cnf(i_0_637,axiom,
( X3 = X5
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Oreal__normed__algebra__1(X2)
| ~ c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,X5,X2,X1) ),
cls_LIM__const__not__eq_0,
[final] ).
cnf(i_0_638,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)),X5)
| ~ class_Ring__and__Field_Osemiring(X1) ),
cls_combine__common__factor_0,
[final] ).
cnf(i_0_639,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_640,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_inverse__add_0,
[final] ).
cnf(i_0_641,axiom,
( c_Lim_OLIM(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_Ocont_0,
[final] ).
cnf(i_0_642,axiom,
( c_Lim_OLIM(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ocont_0,
[final] ).
cnf(i_0_643,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_644,axiom,
( c_Lim_OLIM(c_COMBK(X3,X1,X2),X4,X3,X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2) ),
cls_LIM__const_0,
[final] ).
cnf(i_0_645,axiom,
( c_Limits_Otendsto(c_COMBK(X2,X1,X3),X2,X4,X3,X1)
| ~ class_RealVector_Otopological__space(X1) ),
cls_tendsto__const_0,
[final] ).
cnf(i_0_646,axiom,
( c_Lim_OLIM(c_HOL_Oinverse__class_Oinverse(X1),X2,hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2),X1,X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__div__algebra(X1) ),
cls_LIM__inverse__fun_0,
[final] ).
cnf(i_0_647,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_648,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_649,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3))),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_division__ring__inverse__add_0,
[final] ).
cnf(i_0_650,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Oadd__mul__solve_0,
[final] ).
cnf(i_0_651,axiom,
( X3 = X5
| X2 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X5)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) ),
cls_class__ringb_Onoteq__reduce_0,
[final] ).
cnf(i_0_652,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I15_J_0,
[final] ).
cnf(i_0_653,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Onoteq__reduce_1,
[final] ).
cnf(i_0_654,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__mul__solve_1,
[final] ).
cnf(i_0_655,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X5)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I20_J_0,
[final] ).
cnf(i_0_656,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I13_J_0,
[final] ).
cnf(i_0_657,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X5)))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I14_J_0,
[final] ).
cnf(i_0_658,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I1_J_0,
[final] ).
cnf(i_0_659,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring(X1) ),
cls_comm__semiring__class_Odistrib_0,
[final] ).
cnf(i_0_660,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I8_J_0,
[final] ).
cnf(i_0_661,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__left_0,
[final] ).
cnf(i_0_662,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Oadd_0,
[final] ).
cnf(i_0_663,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_0,
[final] ).
cnf(i_0_664,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3)) != c_HOL_Ozero__class_Ozero(X1) ),
cls_sum__squares__eq__zero__iff_1,
[final] ).
cnf(i_0_665,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Oadd__right_0,
[final] ).
cnf(i_0_666,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__right_Oadd_0,
[final] ).
cnf(i_0_667,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__d_0,
[final] ).
cnf(i_0_668,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Oadd__right_0,
[final] ).
cnf(i_0_669,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Oadd_0,
[final] ).
cnf(i_0_670,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I23_J_0,
[final] ).
cnf(i_0_671,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4)),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I16_J_0,
[final] ).
cnf(i_0_672,axiom,
( X4 = X5
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X5)) ),
cls_class__ringb_Oadd__scale__eq__noteq_0,
[final] ).
cnf(i_0_673,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1))) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ),
cls_sum__squares__eq__zero__iff_2,
[final] ).
cnf(i_0_674,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__add(X1) ),
cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,
[final] ).
cnf(i_0_675,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__assoc_0,
[final] ).
cnf(i_0_676,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I21_J_0,
[final] ).
cnf(i_0_677,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__left_0,
[final] ).
cnf(i_0_678,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_OscaleR_0,
[final] ).
cnf(i_0_679,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3)),X4) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__left_0,
[final] ).
cnf(i_0_680,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,
[final] ).
cnf(i_0_681,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I17_J_0,
[final] ).
cnf(i_0_682,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I25_J_0,
[final] ).
cnf(i_0_683,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__a_0,
[final] ).
cnf(i_0_684,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__a_0,
[final] ).
cnf(i_0_685,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)),X4)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I18_J_0,
[final] ).
cnf(i_0_686,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) = X5
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X5) ),
cls_add__cancel__21_0,
[final] ).
cnf(i_0_687,axiom,
( c_Finite__Set_Osetsum(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_setsum__0_0,
[final] ).
cnf(i_0_688,axiom,
( c_Limits_OZfun(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,X2),X3,X2,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_Zfun__zero_0,
[final] ).
cnf(i_0_689,axiom,
( c_Lim_OisCont(c_COMBK(X3,X2,X1),X4,X1,X2)
| ~ class_RealVector_Ometric__space(X1)
| ~ class_RealVector_Ometric__space(X2) ),
cls_isCont__const_0,
[final] ).
cnf(i_0_690,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)),
cls_nat__add__assoc_0,
[final] ).
cnf(i_0_691,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_692,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_693,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__21_1,
[final] ).
cnf(i_0_694,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__left__commute_0,
[final] ).
cnf(i_0_695,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I22_J_0,
[final] ).
cnf(i_0_696,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OscaleR_0,
[final] ).
cnf(i_0_697,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_OscaleR__right_0,
[final] ).
cnf(i_0_698,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__left__commute_0,
[final] ).
cnf(i_0_699,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__algebra(X1) ),
cls_mult__scaleR__right_0,
[final] ).
cnf(i_0_700,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OscaleR_0,
[final] ).
cnf(i_0_701,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),X4)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_OscaleR__right_0,
[final] ).
cnf(i_0_702,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X4)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X4))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I19_J_0,
[final] ).
cnf(i_0_703,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_add__minus__cancel_0,
[final] ).
cnf(i_0_704,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__mult__distrib_0,
[final] ).
cnf(i_0_705,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3))
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__mult__distrib_0,
[final] ).
cnf(i_0_706,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_minus__add__distrib_0,
[final] ).
cnf(i_0_707,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2))
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add_0,
[final] ).
cnf(i_0_708,axiom,
( hAPP(X3,hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X4),X5)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X2),X4),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_709,axiom,
( c_Lim_OisCont(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OisCont_0,
[final] ).
cnf(i_0_710,axiom,
( c_Lim_OisCont(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3,X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OisCont_0,
[final] ).
cnf(i_0_711,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X4)
| ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X4)) != X3 ),
cls_add__cancel__end_0,
[final] ).
cnf(i_0_712,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X3)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3)),
cls_nat__add__left__commute_0,
[final] ).
cnf(i_0_713,axiom,
( X2 = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X3,X1) ),
cls_LIMSEQ__const__iff_0,
[final] ).
cnf(i_0_714,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ominus_0,
[final] ).
cnf(i_0_715,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__left_0,
[final] ).
cnf(i_0_716,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__left_0,
[final] ).
cnf(i_0_717,axiom,
c_Lim_OisCont(c_Complex_OIm,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Im_OisCont_0,
[final] ).
cnf(i_0_718,axiom,
c_Lim_OisCont(c_Complex_ORe,X1,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Re_OisCont_0,
[final] ).
cnf(i_0_719,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3)) = X3
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_minus__add__cancel_0,
[final] ).
cnf(i_0_720,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)) = X3
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_add__cancel__end_1,
[final] ).
cnf(i_0_721,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2)
| ~ class_Ring__and__Field_Oidom(X1) ),
cls_square__eq__iff_1,
[final] ).
cnf(i_0_722,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__minus_0,
[final] ).
cnf(i_0_723,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__commute_0,
[final] ).
cnf(i_0_724,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ominus__right_0,
[final] ).
cnf(i_0_725,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__minus__right_0,
[final] ).
cnf(i_0_726,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_Ominus_0,
[final] ).
cnf(i_0_727,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ominus__right_0,
[final] ).
cnf(i_0_728,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3))
| ~ class_Ring__and__Field_Oring(X1) ),
cls_minus__mult__right_0,
[final] ).
cnf(i_0_729,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3)
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__left__idem_0,
[final] ).
cnf(i_0_730,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1)
| ~ c_SEQ_OZseq(c_COMBK(X2,X1,tc_nat),X1) ),
cls_Zseq__const__iff_0,
[final] ).
cnf(i_0_731,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| X2 = X3
| ~ class_Ring__and__Field_Oidom(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) != hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X3) ),
cls_square__eq__iff_0,
[final] ).
cnf(i_0_732,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc_0,
[final] ).
cnf(i_0_733,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),hAPP(c_RealVector_Oof__real(X1),X2)),X3)
| ~ class_RealVector_Oreal__algebra__1(X1) ),
cls_scaleR__conv__of__real_0,
[final] ).
cnf(i_0_734,axiom,
( c_Series_Osums(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_sums__zero_0,
[final] ).
cnf(i_0_735,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_736,axiom,
( X3 = X4
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_class__ringb_Oadd__cancel_0,
[final] ).
cnf(i_0_737,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X4),X3) ),
cls_scaleR__cancel__right_0,
[final] ).
cnf(i_0_738,axiom,
( X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| X3 = X4
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X4) ),
cls_scaleR__cancel__left_0,
[final] ).
cnf(i_0_739,axiom,
( X2 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X4),X3) ),
cls_add__right__cancel_0,
[final] ).
cnf(i_0_740,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__left__cancel_0,
[final] ).
cnf(i_0_741,axiom,
( X3 = X4
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X4) ),
cls_add__imp__eq_0,
[final] ).
cnf(i_0_742,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)) = hAPP(c_Suc,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2)),
cls_add__Suc__right_0,
[final] ).
cnf(i_0_743,axiom,
( c_Deriv_Odifferentiable(c_COMBK(X2,X1,X1),X3,X1)
| ~ class_RealVector_Oreal__normed__field(X1) ),
cls_differentiable__const_0,
[final] ).
cnf(i_0_744,axiom,
( c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
cls_LIMSEQ__const__iff_1,
[final] ).
cnf(i_0_745,axiom,
( c_SEQ_OLIMSEQ(c_COMBK(X2,X1,tc_nat),X2,X1)
| ~ class_RealVector_Ometric__space(X1) ),
cls_LIMSEQ__const_0,
[final] ).
cnf(i_0_746,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(c_Suc,X1)),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),hAPP(c_Suc,X2)),
cls_add__Suc__shift_0,
[final] ).
cnf(i_0_747,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_748,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,c_SEQ_Olim(X2,X1),X1) ),
cls_convergent__LIMSEQ__iff_1,
[final] ).
cnf(i_0_749,axiom,
( X1 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X2) ),
cls_nat__add__right__cancel_0,
[final] ).
cnf(i_0_750,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_natgb_Oadd__cancel_0,
[final] ).
cnf(i_0_751,axiom,
( X2 = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X3) ),
cls_nat__add__left__cancel_0,
[final] ).
cnf(i_0_752,axiom,
( c_Series_Osuminf(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_suminf__zero_0,
[final] ).
cnf(i_0_753,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Oab__group__add(X1) ),
cls_ab__left__minus_0,
[final] ).
cnf(i_0_754,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_left__minus_0,
[final] ).
cnf(i_0_755,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_eq__neg__iff__add__eq__0_0,
[final] ).
cnf(i_0_756,axiom,
( c_Series_Osummable(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_summable__zero_0,
[final] ).
cnf(i_0_757,axiom,
( c_SEQ_OZseq(c_COMBK(c_HOL_Ozero__class_Ozero(X1),X1,tc_nat),X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_Zseq__zero_0,
[final] ).
cnf(i_0_758,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__minus__eq_0,
[final] ).
cnf(i_0_759,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_HOL_Ouminus__class_Ouminus(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2))
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__minus__eq_0,
[final] ).
cnf(i_0_760,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),X2) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),X3)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__left_1,
[final] ).
cnf(i_0_761,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X3),c_HOL_Ozero__class_Ozero(X1))
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__cancel__right_1,
[final] ).
cnf(i_0_762,axiom,
hAPP(c_COMBK(X1,X2,X3),X4) = X1,
cls_COMBK__def_0,
[final] ).
cnf(i_0_763,axiom,
( hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2) = X3
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_minus__unique_0,
[final] ).
cnf(i_0_764,axiom,
( X2 = hAPP(c_HOL_Ouminus__class_Ouminus(X1),X3)
| ~ class_OrderedGroup_Ogroup__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_eq__neg__iff__add__eq__0_1,
[final] ).
cnf(i_0_765,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0,
[final] ).
cnf(i_0_766,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__c_0,
[final] ).
cnf(i_0_767,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I24_J_0,
[final] ).
cnf(i_0_768,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I7_J_0,
[final] ).
cnf(i_0_769,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X3),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Omul__c_0,
[final] ).
cnf(i_0_770,axiom,
( c_SEQ_OLIMSEQ(X2,c_SEQ_Olim(X2,X1),X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
cls_convergent__LIMSEQ__iff_0,
[final] ).
cnf(i_0_771,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_772,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_773,axiom,
( c_SEQ_Olim(X2,X1) = X3
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_limI_0,
[final] ).
cnf(i_0_774,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_775,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_776,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_convergent__def_1,
[final] ).
cnf(i_0_777,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_OLIMSEQ(X2,X3,X1) ),
cls_convergentI_0,
[final] ).
cnf(i_0_778,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_779,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_780,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_781,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divirors__neq0_0,
[final] ).
cnf(i_0_782,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_no__zero__divisors_0,
[final] ).
cnf(i_0_783,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(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_mult__eq__0__iff_0,
[final] ).
cnf(i_0_784,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__vector(X1)
| hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X3) != c_HOL_Ozero__class_Ozero(X1) ),
cls_scaleR__eq__0__iff_0,
[final] ).
cnf(i_0_785,axiom,
( X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
cls_class__ringb_Oadd__r0__iff_0,
[final] ).
cnf(i_0_786,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),hAPP(c_HOL_Ouminus__class_Ouminus(X1),X2)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Ogroup__add(X1) ),
cls_right__minus_0,
[final] ).
cnf(i_0_787,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_double__eq__0__iff_0,
[final] ).
cnf(i_0_788,axiom,
( c_RealVector_Obounded__linear(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Obounded__linear__right_0,
[final] ).
cnf(i_0_789,axiom,
( c_RealVector_Obounded__linear(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Obounded__linear__right_0,
[final] ).
cnf(i_0_790,axiom,
( c_Lim_OisUCont(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR__right_OisUCont_0,
[final] ).
cnf(i_0_791,axiom,
( c_Lim_OisUCont(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X1,X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__right_OisUCont_0,
[final] ).
cnf(i_0_792,axiom,
hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X2) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X2),X1),
cls_nat__add__commute_0,
[final] ).
cnf(i_0_793,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_794,axiom,
( X1 = X2
| ~ c_fequal(X1,X2,X3) ),
cls_ATP__Linkup_Ofequal__imp__equal_0,
[final] ).
cnf(i_0_795,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_796,axiom,
( X2 = X3
| X3 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3) ),
cls_nonzero__inverse__eq__imp__eq_0,
[final] ).
cnf(i_0_797,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1) ),
cls_double__eq__0__iff_1,
[final] ).
cnf(i_0_798,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_799,axiom,
( X2 = X3
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != hAPP(c_HOL_Oinverse__class_Oinverse(X1),X3) ),
cls_inverse__eq__iff__eq_0,
[final] ).
cnf(i_0_800,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Omult__zero(X1) ),
cls_mult__zero__left_0,
[final] ).
cnf(i_0_801,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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_802,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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_803,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(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_804,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult_Ozero__left_0,
[final] ).
cnf(i_0_805,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
cls_mult__left_Ozero_0,
[final] ).
cnf(i_0_806,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)) = X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__inverse__eq_0,
[final] ).
cnf(i_0_807,axiom,
( X2 = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1))
| ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_class__ringb_Oadd__r0__iff_1,
[final] ).
cnf(i_0_808,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_809,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_810,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_811,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_add__0__left_0,
[final] ).
cnf(i_0_812,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1_0,
[final] ).
cnf(i_0_813,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I5_J_0,
[final] ).
cnf(i_0_814,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),c_HOL_Ozero__class_Ozero(X1)),X2) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Oadd__0_0,
[final] ).
cnf(i_0_815,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2)) = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
cls_nonzero__inverse__inverse__eq_0,
[final] ).
cnf(i_0_816,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
cls_scaleR_Ozero__left_0,
[final] ).
cnf(i_0_817,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),X2) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_RealVector_Oreal__vector(X1) ),
cls_scaleR__eq__0__iff_1,
[final] ).
cnf(i_0_818,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_819,axiom,
( hAPP(hAPP(c_RealVector_OscaleR__class_OscaleR(X1),X2),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_820,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_821,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_822,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_823,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_824,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),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_825,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Omonoid__add(X1) ),
cls_monoid__add__class_Oadd__0__right_0,
[final] ).
cnf(i_0_826,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__1__right_0,
[final] ).
cnf(i_0_827,axiom,
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),c_HOL_Ozero__class_Ozero(X1)) = X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I6_J_0,
[final] ).
cnf(i_0_828,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_829,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_830,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_831,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_832,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_833,axiom,
c_Complex_Ocomplex_OComplex(hAPP(c_Complex_ORe,X1),hAPP(c_Complex_OIm,X1)) = X1,
cls_complex__surj_0,
[final] ).
cnf(i_0_834,axiom,
( hAPP(hAPP(c_HOL_Otimes__class_Otimes(X1),X2),X2) = X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1) ),
cls_mult__idem_0,
[final] ).
cnf(i_0_835,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inverse__nonzero__iff__nonzero_0,
[final] ).
cnf(i_0_836,axiom,
c_fequal(X1,X1,X2),
cls_ATP__Linkup_Oequal__imp__fequal_0,
[final] ).
cnf(i_0_837,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_838,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| hAPP(c_HOL_Oinverse__class_Oinverse(X1),X2) != c_HOL_Ozero__class_Ozero(X1) ),
cls_inverse__zero__imp__zero_0,
[final] ).
cnf(i_0_839,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_840,axiom,
c_Lim_OisUCont(c_Complex_OIm,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Im_OisUCont_0,
[final] ).
cnf(i_0_841,axiom,
c_Lim_OisUCont(c_Complex_ORe,tc_Complex_Ocomplex,tc_RealDef_Oreal),
cls_Re_OisUCont_0,
[final] ).
cnf(i_0_842,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_843,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_844,axiom,
( X1 = X3
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
cls_complex_Oinject_0,
[final] ).
cnf(i_0_845,axiom,
( X2 = X4
| c_Complex_Ocomplex_OComplex(X1,X2) != c_Complex_Ocomplex_OComplex(X3,X4) ),
cls_complex_Oinject_1,
[final] ).
cnf(i_0_846,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_847,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__ring(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__nonzero__iff__nonzero_1,
[final] ).
cnf(i_0_848,axiom,
( c_SEQ_Oconvergent(X2,X1)
| ~ class_SEQ_Ocomplete__space(X1)
| ~ c_SEQ_OCauchy(X2,X1) ),
cls_Cauchy__convergent__iff_0,
[final] ).
cnf(i_0_849,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_SEQ_Ocomplete__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
cls_Cauchy__convergent__iff_1,
[final] ).
cnf(i_0_850,axiom,
( c_SEQ_OCauchy(X2,X1)
| ~ class_RealVector_Ometric__space(X1)
| ~ c_SEQ_Oconvergent(X2,X1) ),
cls_convergent__Cauchy_0,
[final] ).
cnf(i_0_851,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_852,axiom,
( X1 = X2
| hAPP(c_Suc,X1) != hAPP(c_Suc,X2) ),
cls_Suc__inject_0,
[final] ).
cnf(i_0_853,axiom,
( X1 = X2
| hAPP(c_Suc,X1) != hAPP(c_Suc,X2) ),
cls_nat_Oinject_0,
[final] ).
cnf(i_0_854,axiom,
hAPP(c_Complex_OIm,c_Complex_Ocomplex_OComplex(X1,X2)) = X2,
cls_Im_0,
[final] ).
cnf(i_0_855,axiom,
hAPP(c_Complex_ORe,c_Complex_Ocomplex_OComplex(X1,X2)) = X1,
cls_Re_0,
[final] ).
cnf(i_0_856,axiom,
( hAPP(c_HOL_Oinverse__class_Oinverse(X1),c_HOL_Ozero__class_Ozero(X1)) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1) ),
cls_inverse__zero_0,
[final] ).
cnf(i_0_857,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_858,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_859,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_860,axiom,
( class_Lattices_Oboolean__algebra(tc_fun(X1,X2))
| ~ class_Lattices_Oboolean__algebra(X2) ),
clsarity_fun__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_861,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_862,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_863,axiom,
( c_SEQ_Oconvergent(X1,tc_RealDef_Oreal)
| ~ c_SEQ_OCauchy(X1,tc_RealDef_Oreal) ),
cls_real__Cauchy__convergent_0,
[final] ).
cnf(i_0_864,axiom,
hAPP(c_Suc,X1) != X1,
cls_Suc__n__not__n_0,
[final] ).
cnf(i_0_865,axiom,
X1 != hAPP(c_Suc,X1),
cls_n__not__Suc__n_0,
[final] ).
cnf(i_0_866,axiom,
c_SEQ_Osubseq(v_ga____),
cls_g_I1_J_0,
[final] ).
cnf(i_0_867,axiom,
c_SEQ_Osubseq(v_f____),
cls_f_I1_J_0,
[final] ).
cnf(i_0_868,axiom,
class_SEQ_Ocomplete__space(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__SEQ_Ocomplete__space,
[final] ).
cnf(i_0_869,axiom,
class_SEQ_Ocomplete__space(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__SEQ_Ocomplete__space,
[final] ).
cnf(i_0_870,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_871,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
clsarity_nat__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_872,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,
[final] ).
cnf(i_0_873,axiom,
class_RealVector_Otopological__space(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Otopological__space,
[final] ).
cnf(i_0_874,axiom,
class_RealVector_Otopological__space(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Otopological__space,
[final] ).
cnf(i_0_875,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_876,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra,
[final] ).
cnf(i_0_877,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_878,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
clsarity_nat__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_879,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,
[final] ).
cnf(i_0_880,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_881,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_882,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,
[final] ).
cnf(i_0_883,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_884,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_885,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,
[final] ).
cnf(i_0_886,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_887,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,
[final] ).
cnf(i_0_888,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_889,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
clsarity_nat__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_890,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,
[final] ).
cnf(i_0_891,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,
[final] ).
cnf(i_0_892,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_893,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
clsarity_nat__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_894,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,
[final] ).
cnf(i_0_895,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_896,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_897,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_898,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_899,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,
[final] ).
cnf(i_0_900,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_901,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_902,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,
[final] ).
cnf(i_0_903,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,
[final] ).
cnf(i_0_904,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ofield,
[final] ).
cnf(i_0_905,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,
[final] ).
cnf(i_0_906,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__HOL_Ozero,
[final] ).
cnf(i_0_907,axiom,
class_HOL_Ozero(tc_nat),
clsarity_nat__HOL_Ozero,
[final] ).
cnf(i_0_908,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__HOL_Ozero,
[final] ).
cnf(i_0_909,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_910,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_911,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,
[final] ).
cnf(i_0_912,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_913,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
clsarity_nat__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_914,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,
[final] ).
cnf(i_0_915,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,
[final] ).
cnf(i_0_916,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,
[final] ).
cnf(i_0_917,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,
[final] ).
cnf(i_0_918,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring,
[final] ).
cnf(i_0_919,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,
[final] ).
cnf(i_0_920,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Int_Onumber__ring,
[final] ).
cnf(i_0_921,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring,
[final] ).
cnf(i_0_922,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_923,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oidom,
[final] ).
cnf(i_0_924,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Oring,
[final] ).
cnf(i_0_925,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Oring,
[final] ).
cnf(i_0_926,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_927,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,
[final] ).
cnf(i_0_928,axiom,
class_Lattices_Oboolean__algebra(tc_bool),
clsarity_bool__Lattices_Oboolean__algebra,
[final] ).
cnf(i_0_929,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_930,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,
[final] ).
cnf(i_0_931,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_932,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,
[final] ).
cnf(i_0_933,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__SEQ_Obanach,
[final] ).
cnf(i_0_934,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__SEQ_Obanach,
[final] ).
cnf(i_0_935,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_936,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
clsarity_nat__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_937,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,
[final] ).
cnf(i_0_938,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_939,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,
[final] ).
cnf(i_0_940,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_941,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,
[final] ).
cnf(i_0_942,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_943,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,
[final] ).
cnf(i_0_944,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__vector,
[final] ).
cnf(i_0_945,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__vector,
[final] ).
cnf(i_0_946,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_947,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
clsarity_nat__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_948,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,
[final] ).
cnf(i_0_949,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Ometric__space,
[final] ).
cnf(i_0_950,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Ometric__space,
[final] ).
cnf(i_0_951,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_952,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,
[final] ).
cnf(i_0_953,negated_conjecture,
~ v_thesis____,
cls_conjecture_0,
[final] ).
cnf(i_0_954,axiom,
X1 = X1 ).
cnf(i_0_955,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_956,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_957,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_958,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_959,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_960,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_961,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_962,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_963,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_964,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_965,axiom,
( X1 != X2
| c_Series_Osuminf(X1,X3) = c_Series_Osuminf(X2,X3) ) ).
cnf(i_0_966,axiom,
( X1 != X2
| c_Series_Osuminf(X3,X1) = c_Series_Osuminf(X3,X2) ) ).
cnf(i_0_967,axiom,
( X1 != X2
| c_SEQ_Olim(X1,X3) = c_SEQ_Olim(X2,X3) ) ).
cnf(i_0_968,axiom,
( X1 != X2
| c_SEQ_Olim(X3,X1) = c_SEQ_Olim(X3,X2) ) ).
cnf(i_0_969,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X1,X3) = c_Complex_Ocomplex_OComplex(X2,X3) ) ).
cnf(i_0_970,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X3,X1) = c_Complex_Ocomplex_OComplex(X3,X2) ) ).
cnf(i_0_971,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_972,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_973,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_974,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_975,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_976,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X1,X3,X4,X5)
| c_Limits_OZfun(X2,X3,X4,X5) ) ).
cnf(i_0_977,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X1,X4,X5)
| c_Limits_OZfun(X3,X2,X4,X5) ) ).
cnf(i_0_978,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X1,X5)
| c_Limits_OZfun(X3,X4,X2,X5) ) ).
cnf(i_0_979,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X5,X1)
| c_Limits_OZfun(X3,X4,X5,X2) ) ).
cnf(i_0_980,axiom,
( X1 != X2
| ~ c_Series_Osummable(X1,X3)
| c_Series_Osummable(X2,X3) ) ).
cnf(i_0_981,axiom,
( X1 != X2
| ~ c_Series_Osummable(X3,X1)
| c_Series_Osummable(X3,X2) ) ).
cnf(i_0_982,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X1,X3,X4,X5)
| c_Lim_OisCont(X2,X3,X4,X5) ) ).
cnf(i_0_983,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X1,X4,X5)
| c_Lim_OisCont(X3,X2,X4,X5) ) ).
cnf(i_0_984,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X1,X5)
| c_Lim_OisCont(X3,X4,X2,X5) ) ).
cnf(i_0_985,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X5,X1)
| c_Lim_OisCont(X3,X4,X5,X2) ) ).
cnf(i_0_986,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X1,X3,X4)
| c_RealVector_Obounded__linear(X2,X3,X4) ) ).
cnf(i_0_987,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X1,X4)
| c_RealVector_Obounded__linear(X3,X2,X4) ) ).
cnf(i_0_988,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X4,X1)
| c_RealVector_Obounded__linear(X3,X4,X2) ) ).
cnf(i_0_989,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_990,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_991,axiom,
( X1 != X2
| ~ class_SEQ_Obanach(X1)
| class_SEQ_Obanach(X2) ) ).
cnf(i_0_992,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X1,X3)
| c_SEQ_OZseq(X2,X3) ) ).
cnf(i_0_993,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X3,X1)
| c_SEQ_OZseq(X3,X2) ) ).
cnf(i_0_994,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X1,X3,X4)
| c_SEQ_OLIMSEQ(X2,X3,X4) ) ).
cnf(i_0_995,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X1,X4)
| c_SEQ_OLIMSEQ(X3,X2,X4) ) ).
cnf(i_0_996,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X4,X1)
| c_SEQ_OLIMSEQ(X3,X4,X2) ) ).
cnf(i_0_997,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_998,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_999,axiom,
( X1 != X2
| ~ c_Series_Osums(X1,X3,X4)
| c_Series_Osums(X2,X3,X4) ) ).
cnf(i_0_1000,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X1,X4)
| c_Series_Osums(X3,X2,X4) ) ).
cnf(i_0_1001,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X4,X1)
| c_Series_Osums(X3,X4,X2) ) ).
cnf(i_0_1002,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X1,X3,X4)
| c_Deriv_Odifferentiable(X2,X3,X4) ) ).
cnf(i_0_1003,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X1,X4)
| c_Deriv_Odifferentiable(X3,X2,X4) ) ).
cnf(i_0_1004,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| c_Deriv_Odifferentiable(X3,X4,X2) ) ).
cnf(i_0_1005,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1006,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X1,X3)
| c_SEQ_OCauchy(X2,X3) ) ).
cnf(i_0_1007,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X3,X1)
| c_SEQ_OCauchy(X3,X2) ) ).
cnf(i_0_1008,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X1,X3,X4)
| c_Lim_OisUCont(X2,X3,X4) ) ).
cnf(i_0_1009,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X1,X4)
| c_Lim_OisUCont(X3,X2,X4) ) ).
cnf(i_0_1010,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X4,X1)
| c_Lim_OisUCont(X3,X4,X2) ) ).
cnf(i_0_1011,axiom,
( X1 != X2
| ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(X2) ) ).
cnf(i_0_1012,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_1013,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_1014,axiom,
( X1 != X2
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X2,X3) ) ).
cnf(i_0_1015,axiom,
( X1 != X2
| ~ c_SEQ_Oconvergent(X3,X1)
| c_SEQ_Oconvergent(X3,X2) ) ).
cnf(i_0_1016,axiom,
( X1 != X2
| ~ class_RealVector_Otopological__space(X1)
| class_RealVector_Otopological__space(X2) ) ).
cnf(i_0_1017,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| class_Ring__and__Field_Odivision__ring(X2) ) ).
cnf(i_0_1018,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1019,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1020,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1021,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_1022,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1023,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1024,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1025,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1026,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(X2) ) ).
cnf(i_0_1027,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1028,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1029,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_1030,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1031,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1032,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1033,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1034,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1035,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1036,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1037,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1038,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1039,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1040,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1041,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1042,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1043,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1044,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1045,axiom,
( X1 != X2
| ~ class_SEQ_Ocomplete__space(X1)
| class_SEQ_Ocomplete__space(X2) ) ).
cnf(i_0_1046,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_1047,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X1,X3,X4,X5,X6)
| c_Lim_OLIM(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1048,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X1,X4,X5,X6)
| c_Lim_OLIM(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1049,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X1,X5,X6)
| c_Lim_OLIM(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1050,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X1,X6)
| c_Lim_OLIM(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1051,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X6,X1)
| c_Lim_OLIM(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1052,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1053,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X1,X3,X4,X5,X6)
| c_Limits_Otendsto(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1054,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X1,X4,X5,X6)
| c_Limits_Otendsto(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1055,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X1,X5,X6)
| c_Limits_Otendsto(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1056,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X1,X6)
| c_Limits_Otendsto(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1057,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X6,X1)
| c_Limits_Otendsto(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1058,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_954_001,axiom,
X1 = X1 ).
cnf(i_0_955_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_956_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_957_004,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X1,X3,X4,X5) = c_Finite__Set_Osetsum(X2,X3,X4,X5) ) ).
cnf(i_0_958_005,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X1,X4,X5) = c_Finite__Set_Osetsum(X3,X2,X4,X5) ) ).
cnf(i_0_959_006,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X1,X5) = c_Finite__Set_Osetsum(X3,X4,X2,X5) ) ).
cnf(i_0_960_007,axiom,
( X1 != X2
| c_Finite__Set_Osetsum(X3,X4,X5,X1) = c_Finite__Set_Osetsum(X3,X4,X5,X2) ) ).
cnf(i_0_961_008,axiom,
( X1 != X2
| c_Set_Oimage(X1,X3,X4,X5) = c_Set_Oimage(X2,X3,X4,X5) ) ).
cnf(i_0_962_009,axiom,
( X1 != X2
| c_Set_Oimage(X3,X1,X4,X5) = c_Set_Oimage(X3,X2,X4,X5) ) ).
cnf(i_0_963_010,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X1,X5) = c_Set_Oimage(X3,X4,X2,X5) ) ).
cnf(i_0_964_011,axiom,
( X1 != X2
| c_Set_Oimage(X3,X4,X5,X1) = c_Set_Oimage(X3,X4,X5,X2) ) ).
cnf(i_0_965_012,axiom,
( X1 != X2
| c_Series_Osuminf(X1,X3) = c_Series_Osuminf(X2,X3) ) ).
cnf(i_0_966_013,axiom,
( X1 != X2
| c_Series_Osuminf(X3,X1) = c_Series_Osuminf(X3,X2) ) ).
cnf(i_0_967_014,axiom,
( X1 != X2
| c_SEQ_Olim(X1,X3) = c_SEQ_Olim(X2,X3) ) ).
cnf(i_0_968_015,axiom,
( X1 != X2
| c_SEQ_Olim(X3,X1) = c_SEQ_Olim(X3,X2) ) ).
cnf(i_0_969_016,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X1,X3) = c_Complex_Ocomplex_OComplex(X2,X3) ) ).
cnf(i_0_970_017,axiom,
( X1 != X2
| c_Complex_Ocomplex_OComplex(X3,X1) = c_Complex_Ocomplex_OComplex(X3,X2) ) ).
cnf(i_0_971_018,axiom,
( X1 != X2
| hAPP(X1,X3) = hAPP(X2,X3) ) ).
cnf(i_0_972_019,axiom,
( X1 != X2
| hAPP(X3,X1) = hAPP(X3,X2) ) ).
cnf(i_0_973_020,axiom,
( X1 != X2
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Ozero__class_Ozero(X2) ) ).
cnf(i_0_974_021,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring__0(X1)
| class_Ring__and__Field_Osemiring__0(X2) ) ).
cnf(i_0_975_022,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__vector(X1)
| class_RealVector_Oreal__vector(X2) ) ).
cnf(i_0_976_023,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X1,X3,X4,X5)
| c_Limits_OZfun(X2,X3,X4,X5) ) ).
cnf(i_0_977_024,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X1,X4,X5)
| c_Limits_OZfun(X3,X2,X4,X5) ) ).
cnf(i_0_978_025,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X1,X5)
| c_Limits_OZfun(X3,X4,X2,X5) ) ).
cnf(i_0_979_026,axiom,
( X1 != X2
| ~ c_Limits_OZfun(X3,X4,X5,X1)
| c_Limits_OZfun(X3,X4,X5,X2) ) ).
cnf(i_0_980_027,axiom,
( X1 != X2
| ~ c_Series_Osummable(X1,X3)
| c_Series_Osummable(X2,X3) ) ).
cnf(i_0_981_028,axiom,
( X1 != X2
| ~ c_Series_Osummable(X3,X1)
| c_Series_Osummable(X3,X2) ) ).
cnf(i_0_982_029,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X1,X3,X4,X5)
| c_Lim_OisCont(X2,X3,X4,X5) ) ).
cnf(i_0_983_030,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X1,X4,X5)
| c_Lim_OisCont(X3,X2,X4,X5) ) ).
cnf(i_0_984_031,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X1,X5)
| c_Lim_OisCont(X3,X4,X2,X5) ) ).
cnf(i_0_985_032,axiom,
( X1 != X2
| ~ c_Lim_OisCont(X3,X4,X5,X1)
| c_Lim_OisCont(X3,X4,X5,X2) ) ).
cnf(i_0_986_033,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X1,X3,X4)
| c_RealVector_Obounded__linear(X2,X3,X4) ) ).
cnf(i_0_987_034,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X1,X4)
| c_RealVector_Obounded__linear(X3,X2,X4) ) ).
cnf(i_0_988_035,axiom,
( X1 != X2
| ~ c_RealVector_Obounded__linear(X3,X4,X1)
| c_RealVector_Obounded__linear(X3,X4,X2) ) ).
cnf(i_0_989_036,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__div__algebra(X1)
| class_RealVector_Oreal__normed__div__algebra(X2) ) ).
cnf(i_0_990_037,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra__1(X1)
| class_RealVector_Oreal__algebra__1(X2) ) ).
cnf(i_0_991_038,axiom,
( X1 != X2
| ~ class_SEQ_Obanach(X1)
| class_SEQ_Obanach(X2) ) ).
cnf(i_0_992_039,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X1,X3)
| c_SEQ_OZseq(X2,X3) ) ).
cnf(i_0_993_040,axiom,
( X1 != X2
| ~ c_SEQ_OZseq(X3,X1)
| c_SEQ_OZseq(X3,X2) ) ).
cnf(i_0_994_041,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X1,X3,X4)
| c_SEQ_OLIMSEQ(X2,X3,X4) ) ).
cnf(i_0_995_042,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X1,X4)
| c_SEQ_OLIMSEQ(X3,X2,X4) ) ).
cnf(i_0_996_043,axiom,
( X1 != X2
| ~ c_SEQ_OLIMSEQ(X3,X4,X1)
| c_SEQ_OLIMSEQ(X3,X4,X2) ) ).
cnf(i_0_997_044,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra__1(X1)
| class_RealVector_Oreal__normed__algebra__1(X2) ) ).
cnf(i_0_998_045,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__group__add(X1)
| class_OrderedGroup_Oab__group__add(X2) ) ).
cnf(i_0_999_046,axiom,
( X1 != X2
| ~ c_Series_Osums(X1,X3,X4)
| c_Series_Osums(X2,X3,X4) ) ).
cnf(i_0_1000_047,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X1,X4)
| c_Series_Osums(X3,X2,X4) ) ).
cnf(i_0_1001_048,axiom,
( X1 != X2
| ~ c_Series_Osums(X3,X4,X1)
| c_Series_Osums(X3,X4,X2) ) ).
cnf(i_0_1002_049,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X1,X3,X4)
| c_Deriv_Odifferentiable(X2,X3,X4) ) ).
cnf(i_0_1003_050,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X1,X4)
| c_Deriv_Odifferentiable(X3,X2,X4) ) ).
cnf(i_0_1004_051,axiom,
( X1 != X2
| ~ c_Deriv_Odifferentiable(X3,X4,X1)
| c_Deriv_Odifferentiable(X3,X4,X2) ) ).
cnf(i_0_1005_052,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__field(X1)
| class_RealVector_Oreal__normed__field(X2) ) ).
cnf(i_0_1006_053,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X1,X3)
| c_SEQ_OCauchy(X2,X3) ) ).
cnf(i_0_1007_054,axiom,
( X1 != X2
| ~ c_SEQ_OCauchy(X3,X1)
| c_SEQ_OCauchy(X3,X2) ) ).
cnf(i_0_1008_055,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X1,X3,X4)
| c_Lim_OisUCont(X2,X3,X4) ) ).
cnf(i_0_1009_056,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X1,X4)
| c_Lim_OisUCont(X3,X2,X4) ) ).
cnf(i_0_1010_057,axiom,
( X1 != X2
| ~ c_Lim_OisUCont(X3,X4,X1)
| c_Lim_OisUCont(X3,X4,X2) ) ).
cnf(i_0_1011_058,axiom,
( X1 != X2
| ~ class_HOL_Ozero(X1)
| class_HOL_Ozero(X2) ) ).
cnf(i_0_1012_059,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Osemiring(X1)
| class_Ring__and__Field_Osemiring(X2) ) ).
cnf(i_0_1013_060,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ofield(X1)
| class_Ring__and__Field_Ofield(X2) ) ).
cnf(i_0_1014_061,axiom,
( X1 != X2
| ~ c_SEQ_Oconvergent(X1,X3)
| c_SEQ_Oconvergent(X2,X3) ) ).
cnf(i_0_1015_062,axiom,
( X1 != X2
| ~ c_SEQ_Oconvergent(X3,X1)
| c_SEQ_Oconvergent(X3,X2) ) ).
cnf(i_0_1016_063,axiom,
( X1 != X2
| ~ class_RealVector_Otopological__space(X1)
| class_RealVector_Otopological__space(X2) ) ).
cnf(i_0_1017_064,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__ring(X1)
| class_Ring__and__Field_Odivision__ring(X2) ) ).
cnf(i_0_1018_065,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oidom(X1)
| class_Ring__and__Field_Oidom(X2) ) ).
cnf(i_0_1019_066,axiom,
( X1 != X2
| ~ class_Int_Onumber__ring(X1)
| class_Int_Onumber__ring(X2) ) ).
cnf(i_0_1020_067,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| class_Ring__and__Field_Ocomm__semiring__1(X2) ) ).
cnf(i_0_1021_068,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ocomm__semiring(X1)
| class_Ring__and__Field_Ocomm__semiring(X2) ) ).
cnf(i_0_1022_069,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| class_Ring__and__Field_Oordered__ring__strict(X2) ) ).
cnf(i_0_1023_070,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__add(X1)
| class_OrderedGroup_Oab__semigroup__add(X2) ) ).
cnf(i_0_1024_071,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| class_OrderedGroup_Ocomm__monoid__add(X2) ) ).
cnf(i_0_1025_072,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__algebra(X1)
| class_RealVector_Oreal__algebra(X2) ) ).
cnf(i_0_1026_073,axiom,
( X1 != X2
| ~ c_SEQ_Omonoseq(X1)
| c_SEQ_Omonoseq(X2) ) ).
cnf(i_0_1027_074,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__mult(X1)
| class_OrderedGroup_Oab__semigroup__mult(X2) ) ).
cnf(i_0_1028_075,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ogroup__add(X1)
| class_OrderedGroup_Ogroup__add(X2) ) ).
cnf(i_0_1029_076,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| class_Ring__and__Field_Odivision__by__zero(X2) ) ).
cnf(i_0_1030_077,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring(X1)
| class_Ring__and__Field_Oring(X2) ) ).
cnf(i_0_1031_078,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oab__semigroup__idem__mult(X1)
| class_OrderedGroup_Oab__semigroup__idem__mult(X2) ) ).
cnf(i_0_1032_079,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| class_OrderedGroup_Ocancel__semigroup__add(X2) ) ).
cnf(i_0_1033_080,axiom,
( X1 != X2
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X1)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ) ).
cnf(i_0_1034_081,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Ono__zero__divisors(X1)
| class_Ring__and__Field_Ono__zero__divisors(X2) ) ).
cnf(i_0_1035_082,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Oring__no__zero__divisors(X1)
| class_Ring__and__Field_Oring__no__zero__divisors(X2) ) ).
cnf(i_0_1036_083,axiom,
( X1 != X2
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| class_OrderedGroup_Olordered__ab__group__add(X2) ) ).
cnf(i_0_1037_084,axiom,
( X1 != X2
| ~ class_RealVector_Ometric__space(X1)
| class_RealVector_Ometric__space(X2) ) ).
cnf(i_0_1038_085,axiom,
( X1 != X2
| ~ c_fequal(X1,X3,X4)
| c_fequal(X2,X3,X4) ) ).
cnf(i_0_1039_086,axiom,
( X1 != X2
| ~ c_fequal(X3,X1,X4)
| c_fequal(X3,X2,X4) ) ).
cnf(i_0_1040_087,axiom,
( X1 != X2
| ~ c_fequal(X3,X4,X1)
| c_fequal(X3,X4,X2) ) ).
cnf(i_0_1041_088,axiom,
( X1 != X2
| ~ class_Ring__and__Field_Omult__zero(X1)
| class_Ring__and__Field_Omult__zero(X2) ) ).
cnf(i_0_1042_089,axiom,
( X1 != X2
| ~ class_Lattices_Oboolean__algebra(X1)
| class_Lattices_Oboolean__algebra(X2) ) ).
cnf(i_0_1043_090,axiom,
( X1 != X2
| ~ class_OrderedGroup_Omonoid__add(X1)
| class_OrderedGroup_Omonoid__add(X2) ) ).
cnf(i_0_1044_091,axiom,
( X1 != X2
| ~ class_OrderedGroup_Oordered__ab__group__add(X1)
| class_OrderedGroup_Oordered__ab__group__add(X2) ) ).
cnf(i_0_1045_092,axiom,
( X1 != X2
| ~ class_SEQ_Ocomplete__space(X1)
| class_SEQ_Ocomplete__space(X2) ) ).
cnf(i_0_1046_093,axiom,
( X1 != X2
| ~ c_SEQ_Osubseq(X1)
| c_SEQ_Osubseq(X2) ) ).
cnf(i_0_1047_094,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X1,X3,X4,X5,X6)
| c_Lim_OLIM(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1048_095,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X1,X4,X5,X6)
| c_Lim_OLIM(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1049_096,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X1,X5,X6)
| c_Lim_OLIM(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1050_097,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X1,X6)
| c_Lim_OLIM(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1051_098,axiom,
( X1 != X2
| ~ c_Lim_OLIM(X3,X4,X5,X6,X1)
| c_Lim_OLIM(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1052_099,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__algebra(X1)
| class_RealVector_Oreal__normed__algebra(X2) ) ).
cnf(i_0_1053_100,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X1,X3,X4,X5,X6)
| c_Limits_Otendsto(X2,X3,X4,X5,X6) ) ).
cnf(i_0_1054_101,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X1,X4,X5,X6)
| c_Limits_Otendsto(X3,X2,X4,X5,X6) ) ).
cnf(i_0_1055_102,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X1,X5,X6)
| c_Limits_Otendsto(X3,X4,X2,X5,X6) ) ).
cnf(i_0_1056_103,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X1,X6)
| c_Limits_Otendsto(X3,X4,X5,X2,X6) ) ).
cnf(i_0_1057_104,axiom,
( X1 != X2
| ~ c_Limits_Otendsto(X3,X4,X5,X6,X1)
| c_Limits_Otendsto(X3,X4,X5,X6,X2) ) ).
cnf(i_0_1058_105,axiom,
( X1 != X2
| ~ class_RealVector_Oreal__normed__vector(X1)
| class_RealVector_Oreal__normed__vector(X2) ) ).
cnf(i_0_1059,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = X4
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[651]) ).
cnf(i_0_1060,plain,
( ~ class_Ring__and__Field_Oidom(X1)
| ~ class_Int_Onumber__ring(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[672]) ).
cnf(i_0_1061,plain,
( ~ class_OrderedGroup_Oab__group__add(X1)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X1),X2),X3) ),
inference(equality_inference,[],[686]) ).
cnf(i_0_1062,plain,
( X1 = X1
| ~ class_Ring__and__Field_Oidom(X2)
| X1 = hAPP(c_HOL_Ouminus__class_Ouminus(X2),X1) ),
inference(equality_inference,[],[731]) ).
cnf(i_0_1063,plain,
( ~ class_Int_Onumber__ring(X1)
| X2 = X2
| ~ class_Ring__and__Field_Oidom(X1) ),
inference(equality_inference,[],[736]) ).
cnf(i_0_1064,plain,
( ~ class_RealVector_Oreal__vector(X1)
| X2 = X2
| X3 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[737]) ).
cnf(i_0_1065,plain,
( X1 = X1
| ~ class_RealVector_Oreal__vector(X2)
| X3 = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(equality_inference,[],[738]) ).
cnf(i_0_1066,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[739]) ).
cnf(i_0_1067,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__semigroup__add(X2) ),
inference(equality_inference,[],[740]) ).
cnf(i_0_1068,plain,
( X1 = X1
| ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X2) ),
inference(equality_inference,[],[741]) ).
cnf(i_0_1069,plain,
X1 = X1,
inference(equality_inference,[],[749]) ).
cnf(i_0_1070,plain,
X1 = X1,
inference(equality_inference,[],[751]) ).
cnf(i_0_1071,plain,
( ~ class_Ring__and__Field_Odivision__ring(X1)
| X2 = X2
| X2 = c_HOL_Ozero__class_Ozero(X1)
| X2 = c_HOL_Ozero__class_Ozero(X1) ),
inference(equality_inference,[],[796]) ).
cnf(i_0_1072,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| X2 = X2
| ~ class_Ring__and__Field_Odivision__ring(X1) ),
inference(equality_inference,[],[799]) ).
cnf(i_0_1073,plain,
( X1 = X1
| ~ class_RealVector_Oreal__algebra__1(X2) ),
inference(equality_inference,[],[808]) ).
cnf(i_0_1074,plain,
( X1 = X1
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(equality_inference,[],[809]) ).
cnf(i_0_1075,plain,
( X1 = X1
| ~ class_OrderedGroup_Ogroup__add(X2) ),
inference(equality_inference,[],[810]) ).
cnf(i_0_1076,plain,
X1 = X1,
inference(equality_inference,[],[844]) ).
cnf(i_0_1077,plain,
X1 = X1,
inference(equality_inference,[],[845]) ).
cnf(i_0_1078,plain,
X1 = X1,
inference(equality_inference,[],[853]) ).
cnf(i_0_1079,plain,
$false,
inference(scs_inference,[],[i_0_953,i_0_479,i_0_478]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG365-1 : 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
% 0.14/0.33 % Computer : n001.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 10:34:03 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.39/1.67 % Version : CSE_E---1.7
% 0.39/1.67 % Problem : theBenchmark.p
% 0.39/1.67 % SZS status Unsatisfiable for theBenchmark.p
% 0.39/1.67 % SZS output start CNFRefutation
% See solution above
% 0.44/1.72 % Total time : 1.324s
%------------------------------------------------------------------------------