TSTP Solution File: ALG355-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG355-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 : Wed Aug 30 16:07:27 EDT 2023
% Result : Unsatisfiable 219.84s 220.25s
% Output : CNFRefutation 219.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 109
% Syntax : Number of formulae : 145 ( 43 unt; 92 typ; 0 def)
% Number of atoms : 63 ( 43 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 27 ( 17 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 105 ( 84 >; 21 *; 0 +; 0 <<)
% Number of predicates : 68 ( 66 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 8 con; 0-3 aty)
% Number of variables : 55 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_23,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
tc_RealDef_Oreal: $i ).
tff(decl_26,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(decl_28,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
tc_nat: $i ).
tff(decl_30,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(decl_32,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(decl_34,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(decl_35,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
tff(decl_36,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
c_HOL_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_38,type,
class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).
tff(decl_39,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(decl_40,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_41,type,
c_Transcendental_Opi: $i ).
tff(decl_42,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_43,type,
tc_Complex_Ocomplex: $i ).
tff(decl_44,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_45,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_46,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(decl_47,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_48,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_49,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_50,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_51,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_52,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(decl_53,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_54,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_55,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_56,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_57,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(decl_58,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
class_Ring__and__Field_Oabs__if: $i > $o ).
tff(decl_60,type,
class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).
tff(decl_61,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(decl_62,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(decl_63,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_64,type,
class_Int_Onumber: $i > $o ).
tff(decl_65,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_66,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_67,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_68,type,
c_Int_OPls: $i ).
tff(decl_69,type,
c_Int_OBit1: $i > $i ).
tff(decl_70,type,
c_Int_OBit0: $i > $i ).
tff(decl_71,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(decl_72,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(decl_73,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(decl_74,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(decl_75,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(decl_76,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_77,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(decl_78,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(decl_79,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_80,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(decl_81,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(decl_82,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(decl_83,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(decl_84,type,
c_Complex_ORe: $i > $i ).
tff(decl_85,type,
c_Complex_OIm: $i > $i ).
tff(decl_86,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(decl_87,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(decl_88,type,
class_Ring__and__Field_Opordered__ring__abs: $i > $o ).
tff(decl_89,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_90,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(decl_91,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_92,type,
v_z: $i ).
tff(decl_93,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_94,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(decl_95,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(decl_96,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(decl_97,type,
class_Power_Opower: $i > $o ).
tff(decl_98,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(decl_99,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(decl_100,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_101,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(decl_102,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_103,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(decl_104,type,
v_b: $i ).
tff(decl_105,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(decl_106,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_107,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(decl_108,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(decl_109,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(decl_110,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(decl_111,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(decl_112,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_113,type,
tc_Int_Oint: $i ).
cnf(cls_conjecture_0,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_real__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).
cnf(cls_calculation_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).
cnf(cls_real__sqrt__abs_0,axiom,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs_0) ).
cnf(cls_real__sqrt__power_0,axiom,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X1),X2,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__power_0) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
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(cls_class__semiring_Osemiring__rules_I29_J_0,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I29_J_0) ).
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(cls_real__sqrt__pow2_0,axiom,
( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__pow2_0) ).
cnf(cls_comp__arith_I112_J_0,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).
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(cls_real__mult__assoc_0,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).
cnf(cls_real__sqrt__abs2_0,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).
cnf(cls_real__sqrt__mult_0,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).
cnf(cls_realpow__two__le__add__order_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_realpow__two__le__add__order_0) ).
cnf(cls_cmod__def_0,axiom,
c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cmod__def_0) ).
cnf(c_0_17,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_conjecture_0 ).
cnf(c_0_18,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),
cls_real__mult__commute_0 ).
cnf(c_0_19,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_calculation_0 ).
cnf(c_0_20,axiom,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
cls_real__sqrt__abs_0 ).
cnf(c_0_21,axiom,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X1),X2,tc_RealDef_Oreal),
cls_real__sqrt__power_0 ).
cnf(c_0_22,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_18]),c_0_18]) ).
cnf(c_0_24,axiom,
( c_HOL_Oplus__class_Oplus(X2,X3,X1) = c_HOL_Oplus__class_Oplus(X3,X2,X1)
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_comm__monoid__add_Omult__commute_0 ).
cnf(c_0_25,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add ).
cnf(c_0_26,axiom,
( c_HOL_Otimes__class_Otimes(X2,X2,X1) = c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Osemiring__rules_I29_J_0 ).
cnf(c_0_27,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_28,axiom,
( c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
cls_real__sqrt__pow2_0 ).
cnf(c_0_29,plain,
c_Power_Opower__class_Opower(c_NthRoot_Osqrt(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_30,axiom,
( c_HOL_Ozero__class_Ozero(X1) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,X1)
| ~ class_Int_Onumber__ring(X1) ),
cls_comp__arith_I112_J_0 ).
cnf(c_0_31,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
clsarity_RealDef__Oreal__Int_Onumber__ring ).
cnf(c_0_32,negated_conjecture,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_33,plain,
c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X2,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_34,plain,
c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_35,axiom,
c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),X3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_real__mult__assoc_0 ).
cnf(c_0_36,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
cls_real__sqrt__abs2_0 ).
cnf(c_0_37,axiom,
c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X2),tc_RealDef_Oreal),
cls_real__sqrt__mult_0 ).
cnf(c_0_38,plain,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
cls_realpow__two__le__add__order_0 ).
cnf(c_0_41,negated_conjecture,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33]),c_0_33]),c_0_33]),c_0_34]),c_0_34]),c_0_35]) ).
cnf(c_0_42,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_33]),c_0_33]),c_0_33]),c_0_33]),c_0_34]),c_0_34]) ).
cnf(c_0_43,plain,
c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(X1),c_NthRoot_Osqrt(X1),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,axiom,
c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex) = c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_Complex_ORe(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_Complex_OIm(X1),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)),
cls_cmod__def_0 ).
cnf(c_0_45,plain,
( c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal) = X1
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
c_lessequals(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(X1,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),c_Power_Opower__class_Opower(X2,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_40,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(v_b),c_Complex_ORe(v_b),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(v_b),c_Complex_OIm(v_b),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_48,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(X1),c_Complex_ORe(X1),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(X1),c_Complex_OIm(X1),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_34]),c_0_34]) ).
cnf(c_0_49,plain,
c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_34]),c_0_34]),c_0_34]),c_0_34]) ).
cnf(c_0_50,negated_conjecture,
c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_ORe(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),c_Complex_OIm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v_b,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(v_b,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_35]) ).
cnf(c_0_51,plain,
c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Complex_ORe(X1),c_Complex_ORe(X1),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Complex_OIm(X1),c_Complex_OIm(X1),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(X1,tc_Complex_Ocomplex),tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_50,c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ALG355-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Mon Aug 28 05:34:45 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.15/0.46 start to proof: theBenchmark
% 219.84/220.25 % Version : CSE_E---1.5
% 219.84/220.25 % Problem : theBenchmark.p
% 219.84/220.25 % Proof found
% 219.84/220.25 % SZS status Theorem for theBenchmark.p
% 219.84/220.25 % SZS output start Proof
% See solution above
% 219.84/220.26 % Total time : 219.761000 s
% 219.84/220.26 % SZS output end Proof
% 219.84/220.26 % Total time : 219.799000 s
%------------------------------------------------------------------------------