TSTP Solution File: ALG337-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG337-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 18:03:23 EDT 2022
% Result : Unsatisfiable 137.74s 137.98s
% Output : Refutation 141.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 92
% Syntax : Number of clauses : 143 ( 108 unt; 0 nHn; 143 RR)
% Number of literals : 180 ( 0 equ; 43 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 71 ( 70 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(210,axiom,
equal(c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(u,c_Transcendental_Opi,tc_RealDef_Oreal)),c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(u),tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(330,axiom,
equal(c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(382,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(442,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v) ),
file('ALG337-1.p',unknown),
[] ).
cnf(506,axiom,
( ~ equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(636,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Oplus__class_Oplus(w,v,u),u),w) ),
file('ALG337-1.p',unknown),
[] ).
cnf(654,axiom,
( ~ class_OrderedGroup_Omonoid__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(u),v,u),v) ),
file('ALG337-1.p',unknown),
[] ).
cnf(681,axiom,
equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi)),
file('ALG337-1.p',unknown),
[] ).
cnf(908,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Oplus__class_Oplus(v,v,u),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(u),c_HOL_Oone__class_Oone(u),u),v,u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(965,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,u),u),c_HOL_Ominus__class_Ominus(w,v,u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1074,axiom,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oinverse__class_Oinverse(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(u,v,tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1081,axiom,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1148,axiom,
( ~ class_Int_Onumber__ring(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(u),c_HOL_Oone__class_Oone(u),u),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1187,axiom,
equal(c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
file('ALG337-1.p',unknown),
[] ).
cnf(1201,axiom,
equal(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(u,c_HOL_Otimes__class_Otimes(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1228,axiom,
equal(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v,u,tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1234,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(v,w,u),x,u),c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(w,x,u),u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1247,axiom,
( ~ class_RealVector_Oreal__normed__algebra(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(v,w,u),c_HOL_Otimes__class_Otimes(x,w,u),u),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(v,x,u),w,u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1251,axiom,
( ~ class_Int_Onumber__ring(u)
| equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),u),v,u),c_HOL_Oplus__class_Oplus(v,v,u)) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1255,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v,w,u),w,u),v) ),
file('ALG337-1.p',unknown),
[] ).
cnf(1258,axiom,
equal(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1259,axiom,
equal(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('ALG337-1.p',unknown),
[] ).
cnf(1348,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1349,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1350,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1351,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1352,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1353,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1354,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1355,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1356,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1357,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1358,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1359,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1360,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1361,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1362,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1363,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1364,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1365,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1366,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1367,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1368,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1369,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1370,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1371,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1372,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1373,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1374,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1375,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1376,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1377,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1378,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1379,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1380,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1381,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1382,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1383,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1384,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1385,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1386,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1387,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1388,axiom,
class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1389,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1390,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1391,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1392,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1393,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1394,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1395,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1396,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1397,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1398,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1399,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1400,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1401,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1402,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1403,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1404,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1405,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1406,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1407,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1408,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1409,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1410,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1411,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1412,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1413,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1414,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1415,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1416,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('ALG337-1.p',unknown),
[] ).
cnf(1417,axiom,
~ equal(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),c_NthRoot_Osqrt(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),v_x____),
file('ALG337-1.p',unknown),
[] ).
cnf(1426,plain,
equal(c_Transcendental_Ocos(c_Transcendental_Otan(c_Transcendental_Opi)),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rew,[status(thm),theory(equality)],[681,330]),
[iquote('0:Rew:681.0,330.0')] ).
cnf(1485,plain,
( ~ equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi))
| equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[681,506]),
[iquote('0:Rew:681.0,506.0')] ).
cnf(1665,plain,
~ equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),v_x____),
inference(rew,[status(thm),theory(equality)],[1259,1417,1258]),
[iquote('0:Rew:1259.0,1417.0,1258.0,1417.0')] ).
cnf(2161,plain,
( ~ class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)) ),
inference(spr,[status(thm),theory(equality)],[654,210]),
[iquote('0:SpR:654.1,210.0')] ).
cnf(2171,plain,
( ~ class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)) ),
inference(rew,[status(thm),theory(equality)],[1426,2161,681]),
[iquote('0:Rew:1426.0,2161.1,681.0,2161.1')] ).
cnf(2172,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi)),
inference(ssi,[status(thm)],[2171,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:2171.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(2583,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[2172,442]),
[iquote('0:SpR:2172.0,442.1')] ).
cnf(2588,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[2583,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:2583.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(3122,plain,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal)),
inference(spr,[status(thm),theory(equality)],[2588,1081]),
[iquote('0:SpR:2588.0,1081.0')] ).
cnf(15473,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ equal(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Otan(c_Transcendental_Opi))
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(spl,[status(thm),theory(equality)],[382,1485]),
[iquote('0:SpL:382.1,1485.0')] ).
cnf(15583,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ equal(c_Transcendental_Otan(c_Transcendental_Opi),c_Transcendental_Otan(c_Transcendental_Opi))
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(rew,[status(thm),theory(equality)],[681,15473]),
[iquote('0:Rew:681.0,15473.1')] ).
cnf(15584,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(obv,[status(thm),theory(equality)],[15583]),
[iquote('0:Obv:15583.1')] ).
cnf(15585,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(ssi,[status(thm)],[15584,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:15584.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(15680,plain,
equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal)),
inference(spr,[status(thm),theory(equality)],[15585,1081]),
[iquote('0:SpR:15585.0,1081.0')] ).
cnf(20559,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(v,c_HOL_Ouminus__class_Ouminus(u,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),v) ),
inference(spr,[status(thm),theory(equality)],[15585,636]),
[iquote('0:SpR:15585.0,636.1')] ).
cnf(20588,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),v) ),
inference(rew,[status(thm),theory(equality)],[1081,20559]),
[iquote('0:Rew:1081.0,20559.1')] ).
cnf(20589,plain,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,u,tc_RealDef_Oreal),tc_RealDef_Oreal),v),
inference(ssi,[status(thm)],[20588,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:20588.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(20634,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal),tc_RealDef_Oreal),v) ),
inference(spr,[status(thm),theory(equality)],[20589,1255]),
[iquote('0:SpR:20589.0,1255.1')] ).
cnf(20643,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[1255,20589]),
[iquote('0:SpR:1255.1,20589.0')] ).
cnf(20654,plain,
equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal),tc_RealDef_Oreal),v),
inference(ssi,[status(thm)],[20634,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:20634.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(20656,plain,
equal(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v,u,tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[20643,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:20643.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(20688,plain,
~ equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),v_x____),
inference(rew,[status(thm),theory(equality)],[20656,1665]),
[iquote('0:Rew:20656.0,1665.0')] ).
cnf(20704,plain,
~ equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),v_x____),
inference(rew,[status(thm),theory(equality)],[20656,20688]),
[iquote('0:Rew:20656.0,20688.0')] ).
cnf(20736,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal),v) ),
inference(spr,[status(thm),theory(equality)],[1255,20654]),
[iquote('0:SpR:1255.1,20654.0')] ).
cnf(20752,plain,
equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal),v),
inference(ssi,[status(thm)],[20736,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:20736.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(20871,plain,
equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_RealDef_Oreal),u,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(v,tc_RealDef_Oreal)),
inference(spr,[status(thm),theory(equality)],[1081,20752]),
[iquote('0:SpR:1081.0,20752.0')] ).
cnf(22470,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[965,1081]),
[iquote('0:SpR:965.1,1081.0')] ).
cnf(22591,plain,
equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[22470,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:22470.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(27491,plain,
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[1148,3122]),
[iquote('0:SpR:1148.1,3122.0')] ).
cnf(27532,plain,
equal(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[27491,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:27491.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(28264,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Otimes__class_Otimes(v,c_HOL_Oinverse__class_Oinverse(w,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal)),
inference(spr,[status(thm),theory(equality)],[1201,1074]),
[iquote('0:SpR:1201.0,1074.0')] ).
cnf(28358,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oinverse__class_Odivide(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal)),
inference(rew,[status(thm),theory(equality)],[1074,28264]),
[iquote('0:Rew:1074.0,28264.0')] ).
cnf(56068,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[908,1228]),
[iquote('0:SpR:908.1,1228.0')] ).
cnf(56179,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Ocos(c_Transcendental_Opi),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[3122,56068]),
[iquote('0:Rew:3122.0,56068.1')] ).
cnf(56180,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| equal(c_HOL_Otimes__class_Otimes(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[27532,56179]),
[iquote('0:Rew:27532.0,56179.1')] ).
cnf(56181,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[56180,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:56180.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(56204,plain,
equal(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(rew,[status(thm),theory(equality)],[56181,1187]),
[iquote('0:Rew:56181.0,1187.0')] ).
cnf(56223,plain,
equal(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(u,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(rew,[status(thm),theory(equality)],[1228,56204]),
[iquote('0:Rew:1228.0,56204.0')] ).
cnf(56224,plain,
equal(c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),u,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(rew,[status(thm),theory(equality)],[28358,56223]),
[iquote('0:Rew:28358.0,56223.0')] ).
cnf(56397,plain,
( ~ class_Int_Onumber__ring(tc_RealDef_Oreal)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),u) ),
inference(spr,[status(thm),theory(equality)],[1251,56224]),
[iquote('0:SpR:1251.1,56224.0')] ).
cnf(56416,plain,
equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(u,u,tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),u),
inference(ssi,[status(thm)],[56397,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:56397.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(77251,plain,
( ~ class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(v,c_HOL_Ouminus__class_Ouminus(w,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[1234,1081]),
[iquote('0:SpR:1234.1,1081.0')] ).
cnf(77462,plain,
( ~ class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Ominus__class_Ominus(v,w,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[1081,77251]),
[iquote('0:Rew:1081.0,77251.1')] ).
cnf(77463,plain,
( ~ class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[22591,77462]),
[iquote('0:Rew:22591.0,77462.1')] ).
cnf(77464,plain,
equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(u,v,tc_RealDef_Oreal),w,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[77463,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:77463.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(119973,plain,
( ~ class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(u,v,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(w,c_HOL_Oinverse__class_Oinverse(v,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(u,w,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(v,tc_RealDef_Oreal),tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[1074,1247]),
[iquote('0:SpR:1074.0,1247.1')] ).
cnf(120112,plain,
( ~ class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(u,v,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(u,w,tc_RealDef_Oreal),v,tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[1074,119973]),
[iquote('0:Rew:1074.0,119973.1,1074.0,119973.1')] ).
cnf(120113,plain,
equal(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(u,v,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(w,v,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(u,w,tc_RealDef_Oreal),v,tc_RealDef_Oreal)),
inference(ssi,[status(thm)],[120112,1403,1399,1381,1352,1415,1405,1404,1396,1391,1383,1378,1375,1359,1350,1400,1395,1388,1386,1377,1370,1369,1368,1366,1365,1358,1356,1413,1409,1398,1394,1367,1361,1354,1351,1390,1389,1364,1348,1407,1397,1384,1416,1385,1410,1393,1392,1379,1374,1357,1411,1401,1349,1412,1408,1382,1363,1353,1402,1372,1362,1376,1355,1373,1406,1414,1360,1387,1371,1380]),
[iquote('0:SSi:120112.0,1403.0,1399.0,1381.0,1352.0,1415.0,1405.0,1404.0,1396.0,1391.0,1383.0,1378.0,1375.0,1359.0,1350.0,1400.0,1395.0,1388.0,1386.0,1377.0,1370.0,1369.0,1368.0,1366.0,1365.0,1358.0,1356.0,1413.0,1409.0,1398.0,1394.0,1367.0,1361.0,1354.0,1351.0,1390.0,1389.0,1364.0,1348.0,1407.0,1397.0,1384.0,1416.0,1385.0,1410.0,1393.0,1392.0,1379.0,1374.0,1357.0,1411.0,1401.0,1349.0,1412.0,1408.0,1382.0,1363.0,1353.0,1402.0,1372.0,1362.0,1376.0,1355.0,1373.0,1406.0,1414.0,1360.0,1387.0,1371.0,1380.0')] ).
cnf(120114,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v_x____,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(v_y____,v_y____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_x____,v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal)),v_x____,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),v_x____),
inference(rew,[status(thm),theory(equality)],[120113,20704]),
[iquote('0:Rew:120113.0,20704.0')] ).
cnf(120171,plain,
~ equal(v_x____,v_x____),
inference(rew,[status(thm),theory(equality)],[56416,120114,15680,20871,77464]),
[iquote('0:Rew:56416.0,120114.0,15680.0,120114.0,20871.0,120114.0,77464.0,120114.0')] ).
cnf(120172,plain,
$false,
inference(obv,[status(thm),theory(equality)],[120171]),
[iquote('0:Obv:120171.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : ALG337-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 03:07:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 137.74/137.98
% 137.74/137.98 SPASS V 3.9
% 137.74/137.98 SPASS beiseite: Proof found.
% 137.74/137.98 % SZS status Theorem
% 137.74/137.98 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 137.74/137.98 SPASS derived 80978 clauses, backtracked 0 clauses, performed 0 splits and kept 26479 clauses.
% 137.74/137.98 SPASS allocated 186308 KBytes.
% 137.74/137.98 SPASS spent 0:2:17.40 on the problem.
% 137.74/137.98 0:00:00.11 for the input.
% 137.74/137.98 0:00:00.00 for the FLOTTER CNF translation.
% 137.74/137.98 0:00:01.42 for inferences.
% 137.74/137.98 0:00:00.00 for the backtracking.
% 137.74/137.98 0:2:14.03 for the reduction.
% 137.74/137.98
% 137.74/137.98
% 137.74/137.98 Here is a proof with depth 5, length 143 :
% 137.74/137.98 % SZS output start Refutation
% See solution above
% 141.60/141.80 Formulae used in the proof : cls_cos__periodic__pi_0 cls_cos__zero_0 cls_ab__left__minus_0 cls_minus__minus_0 cls_real__add__eq__0__iff_0 cls_add__cancel__end_1 cls_add__0__left_0 cls_tan__pi_0 cls_class__semiring_Osemiring__rules_I4_J_0 cls_minus__diff__eq_0 cls_real__divide__def_0 cls_real__diff__def_0 cls_one__add__one__is__two_0 cls_real__sum__of__halves_0 cls_real__mult__assoc_0 cls_real__mult__commute_0 cls_ab__semigroup__add__class_Oadd__ac_I1_J_0 cls_mult_Odiff__left_0 cls_mult__2_0 cls_add__diff__cancel_0 cls_CHAINED_0 cls_CHAINED_0_01 clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring clsarity_RealDef__Oreal__RealVector_Oreal__normed__field clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom clsarity_RealDef__Oreal__RealVector_Oreal__div__algebra clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1 clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1 clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1 clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1 clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult clsarity_RealDef__Oreal__Ring__and__Field_Osemiring clsarity_RealDef__Oreal__RealVector_Oreal__algebra clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add clsarity_RealDef__Oreal__RealVector_Oreal__vector clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__1 clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if clsarity_RealDef__Oreal__RealVector_Oreal__field clsarity_RealDef__Oreal__Ring__and__Field_Ofield clsarity_RealDef__Oreal__Ring__and__Field_Oring clsarity_RealDef__Oreal__Ring__and__Field_Oidom clsarity_RealDef__Oreal__Ring__and__Field_Odvd clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__Int_Oring__char__0 clsarity_RealDef__Oreal__Int_Onumber__ring clsarity_RealDef__Oreal__Power_Opower clsarity_RealDef__Oreal__Int_Onumber cls_conjecture_0
% 141.60/141.80
%------------------------------------------------------------------------------