TSTP Solution File: SWW203+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW203+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 : Fri Sep 1 00:16:30 EDT 2023
% Result : Theorem 31.51s 31.61s
% Output : CNFRefutation 31.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 134
% Syntax : Number of formulae : 196 ( 66 unt; 112 typ; 0 def)
% Number of atoms : 121 ( 84 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 66 ( 29 ~; 26 |; 4 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 134 ( 101 >; 33 *; 0 +; 0 <<)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 11 con; 0-4 aty)
% Number of variables : 114 ( 2 sgn; 60 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_RealDef_Oreal: $i ).
tff(decl_23,type,
v_x: $i ).
tff(decl_24,type,
c_Complex_ORe: $i > $i ).
tff(decl_25,type,
v_y: $i ).
tff(decl_26,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_28,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
tc_Nat_Onat: $i ).
tff(decl_30,type,
c_Int_OPls: $i ).
tff(decl_31,type,
c_Int_OBit1: $i > $i ).
tff(decl_32,type,
c_Int_OBit0: $i > $i ).
tff(decl_33,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_34,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
c_Complex_OIm: $i > $i ).
tff(decl_36,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_37,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_39,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_40,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_41,type,
tc_Complex_Ocomplex: $i ).
tff(decl_42,type,
class_Groups_Ozero: $i > $o ).
tff(decl_43,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_44,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_45,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_46,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_47,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_48,type,
tc_Int_Oint: $i ).
tff(decl_49,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_50,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_51,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_52,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_53,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_54,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_55,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_56,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_57,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_58,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_59,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_60,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_61,type,
class_Power_Opower: $i > $o ).
tff(decl_62,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_63,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_64,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_65,type,
class_Int_Onumber: $i > $o ).
tff(decl_66,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_67,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_69,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_70,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_71,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_72,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_74,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_75,type,
class_Rings_Oring: $i > $o ).
tff(decl_76,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_77,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_78,type,
class_Orderings_Oord: $i > $o ).
tff(decl_79,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_80,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_81,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_82,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_83,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_84,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_85,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_86,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_87,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_88,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_89,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_90,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_91,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_92,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_93,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_94,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_95,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_96,type,
c_Nat_OSuc: $i > $i ).
tff(decl_97,type,
c_Complex_Ocnj: $i > $i ).
tff(decl_98,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_99,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_100,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_101,type,
c_RealVector_Oof__real: ( $i * $i ) > $i ).
tff(decl_102,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_103,type,
class_RealVector_Oreal__algebra__1: $i > $o ).
tff(decl_104,type,
c_Complex_Oii: $i ).
tff(decl_105,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_106,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(decl_108,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_110,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_111,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_112,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_113,type,
class_Rings_Oidom: $i > $o ).
tff(decl_114,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_115,type,
class_Fields_Ofield: $i > $o ).
tff(decl_116,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_117,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_118,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_119,type,
c_Rings_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(decl_120,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_121,type,
class_RealVector_Oreal__div__algebra: $i > $o ).
tff(decl_122,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_123,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_124,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_125,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_126,type,
class_Groups_Oabs__if: $i > $o ).
tff(decl_127,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_128,type,
tc_HOL_Obool: $i ).
tff(decl_129,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_131,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk4_0: $i ).
tff(decl_133,type,
esk5_0: $i ).
fof(fact_real__sqrt__abs,axiom,
! [X2] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(fact_Bit0__def,axiom,
! [X16] : c_Int_OBit0(X16) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_complex__norm,axiom,
! [X1,X2] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X2,X1)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__norm) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [X35,X8] :
( c_Power_Opower__class_Opower(tc_Nat_Onat,X8,X35) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( X35 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X8 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_complex__of__real__add__Complex,axiom,
! [X1,X2,X44] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X44),c_Complex_Ocomplex_OComplex(X2,X1)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X44,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__add__Complex) ).
fof(fact_complex__of__real__def,axiom,
! [X44] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X44) = c_Complex_Ocomplex_OComplex(X44,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__of__real__def) ).
fof(fact_semiring__norm_I115_J,axiom,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_complex__add,axiom,
! [X3,X5,X4,X6] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X6,X4),c_Complex_Ocomplex_OComplex(X5,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,X5),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__add) ).
fof(fact_add__0__iff,axiom,
! [X9,X10,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( X10 = c_Groups_Oplus__class_Oplus(X7,X10,X9)
<=> X9 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(fact_zero__eq__power2,axiom,
! [X9,X7] :
( class_Rings_Oring__1__no__zero__divisors(X7)
=> ( c_Power_Opower__class_Opower(X7,X9,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X7)
<=> X9 = c_Groups_Ozero__class_Ozero(X7) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).
fof(fact_real__sqrt__power,axiom,
! [X16,X2] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,X16)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X2),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096) ).
fof(fact_Re_Odiff,axiom,
! [X1,X2] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X2),c_Complex_ORe(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Re_Odiff) ).
fof(fact_Im_Odiff,axiom,
! [X1,X2] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X2,X1)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X2),c_Complex_OIm(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Im_Odiff) ).
fof(fact_add__0,axiom,
! [X6,X7] :
( class_Groups_Ocomm__monoid__add(X7)
=> c_Groups_Oplus__class_Oplus(X7,c_Groups_Ozero__class_Ozero(X7),X6) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(fact_complex__surj,axiom,
! [X17] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X17),c_Complex_OIm(X17)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__surj) ).
fof(arity_RealDef__Oreal__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(fact_norm__of__real,axiom,
! [X44,X7] :
( class_RealVector_Oreal__normed__algebra__1(X7)
=> c_RealVector_Onorm__class_Onorm(X7,c_RealVector_Oof__real(X7,X44)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__of__real) ).
fof(arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(c_0_22,plain,
! [X91] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X91,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X91),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
fof(c_0_23,plain,
! [X397] : c_Int_OBit0(X397) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X397,X397),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_24,plain,
! [X1256,X1257] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1257,X1256)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1257,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1256,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[fact_complex__norm]) ).
fof(c_0_25,plain,
! [X1312,X1313] :
( ( c_Power_Opower__class_Opower(tc_Nat_Onat,X1313,X1312) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| X1313 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X1312 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Power_Opower__class_Opower(tc_Nat_Onat,X1313,X1312) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( X1313 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Power_Opower__class_Opower(tc_Nat_Onat,X1313,X1312) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq__Suc__0__iff])])]) ).
fof(c_0_26,plain,
! [X1470,X1471,X1472] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1472),c_Complex_Ocomplex_OComplex(X1471,X1470)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1472,X1471),X1470),
inference(variable_rename,[status(thm)],[fact_complex__of__real__add__Complex]) ).
fof(c_0_27,plain,
! [X1450] : c_RealVector_Oof__real(tc_Complex_Ocomplex,X1450) = c_Complex_Ocomplex_OComplex(X1450,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[fact_complex__of__real__def]) ).
cnf(c_0_28,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_semiring__norm_I115_J]) ).
cnf(c_0_31,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( c_Power_Opower__class_Opower(tc_Nat_Onat,X2,X1) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_RealVector_Oof__real(tc_Complex_Ocomplex,X1),c_Complex_Ocomplex_OComplex(X2,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_34,plain,
c_RealVector_Oof__real(tc_Complex_Ocomplex,X1) = c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_35,plain,
! [X1368,X1369,X1370,X1371] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1371,X1370),c_Complex_Ocomplex_OComplex(X1369,X1368)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1371,X1369),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1370,X1368)),
inference(variable_rename,[status(thm)],[fact_complex__add]) ).
fof(c_0_36,plain,
! [X994,X995,X996] :
( ( X995 != c_Groups_Oplus__class_Oplus(X996,X995,X994)
| X994 = c_Groups_Ozero__class_Ozero(X996)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X996) )
& ( X994 != c_Groups_Ozero__class_Ozero(X996)
| X995 = c_Groups_Oplus__class_Oplus(X996,X995,X994)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X996) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).
fof(c_0_37,plain,
! [X208,X209] :
( ( c_Power_Opower__class_Opower(X209,X208,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X209)
| X208 = c_Groups_Ozero__class_Ozero(X209)
| ~ class_Rings_Oring__1__no__zero__divisors(X209) )
& ( X208 != c_Groups_Ozero__class_Ozero(X209)
| c_Power_Opower__class_Opower(X209,X208,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X209)
| ~ class_Rings_Oring__1__no__zero__divisors(X209) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).
cnf(c_0_38,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),
inference(rw,[status(thm)],[c_0_30,c_0_29]) ).
fof(c_0_40,plain,
! [X293,X294] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X294,X293)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X294),X293),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
fof(c_0_41,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_42,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(split_conjunct,[status(thm)],[fact__096sqrt_A_I_IRe_Ax_A_N_ARe_Ay_A_L_A0_J_A_094_A2_A_L_A_I0_A_L_A_IIm_Ax_A_N_AIm_Ay_J_J_A_094_A2_J_060_061_Asqrt_A_I_IRe_Ax_A_N_ARe_Ay_J_A_094_A2_A_L_A0_A_094_A2_J_A_L_Asqrt_A_I0_A_094_A2_A_L_A_IIm_Ax_A_N_AIm_Ay_J_A_094_A2_J_096]) ).
fof(c_0_43,plain,
! [X106,X107] : c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X107,X106)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X107),c_Complex_ORe(X106)),
inference(variable_rename,[status(thm)],[fact_Re_Odiff]) ).
fof(c_0_44,plain,
! [X104,X105] : c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X105,X104)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X105),c_Complex_OIm(X104)),
inference(variable_rename,[status(thm)],[fact_Im_Odiff]) ).
cnf(c_0_45,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_29]),c_0_29]) ).
cnf(c_0_46,plain,
c_Power_Opower__class_Opower(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(er,[status(thm)],[c_0_32]) ).
cnf(c_0_47,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_Ocomplex_OComplex(X2,X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2),c_Complex_Ocomplex_OComplex(X3,X4)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X3),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_49,plain,
( X3 = c_Groups_Oplus__class_Oplus(X2,X3,X1)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_50,plain,
( c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
fof(c_0_51,plain,
! [X116,X117] :
( ~ class_Groups_Ocomm__monoid__add(X117)
| c_Groups_Oplus__class_Oplus(X117,c_Groups_Ozero__class_Ozero(X117),X116) = X116 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).
cnf(c_0_52,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_53,plain,
c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,X2)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),X2),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_54,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))))),
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_42,c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_56,plain,
c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(X1),c_Complex_ORe(X2)),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_57,plain,
c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,X1,X2)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(X1),c_Complex_OIm(X2)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_58,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Nat_OSuc(c_Power_Opower__class_Opower(tc_Nat_Onat,tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X2,c_Nat_OSuc(c_Power_Opower__class_Opower(tc_Nat_Onat,tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_39]),c_0_46]),c_0_39]),c_0_46]) ).
cnf(c_0_59,plain,
c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),X3),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_60,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,c_Groups_Ozero__class_Ozero(X1)) = X2
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1) ),
inference(er,[status(thm)],[c_0_49]) ).
cnf(c_0_61,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(c_0_62,plain,
! [X1365] : c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1365),c_Complex_OIm(X1365)) = X1365,
inference(variable_rename,[status(thm)],[fact_complex__surj]) ).
cnf(c_0_63,plain,
( c_Power_Opower__class_Opower(X2,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X2)
| X1 != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Rings_Oring__1__no__zero__divisors(X2) ),
inference(rw,[status(thm)],[c_0_50,c_0_29]) ).
cnf(c_0_64,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
cnf(c_0_65,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
cnf(c_0_66,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_67,plain,
! [X1460,X1461] :
( ~ class_RealVector_Oreal__normed__algebra__1(X1461)
| c_RealVector_Onorm__class_Onorm(X1461,c_RealVector_Oof__real(X1461,X1460)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1460) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_norm__of__real])]) ).
cnf(c_0_68,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_29]),c_0_29]) ).
cnf(c_0_69,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_55,c_0_56]),c_0_39]),c_0_46]),c_0_57]),c_0_39]),c_0_46]),c_0_58]),c_0_59]),c_0_56]),c_0_39]),c_0_46]),c_0_39]),c_0_46]),c_0_58]),c_0_39]),c_0_46]),c_0_57]),c_0_39]),c_0_46]),c_0_58]) ).
cnf(c_0_70,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_71,plain,
c_Complex_Ocomplex_OComplex(c_Complex_ORe(X1),c_Complex_OIm(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Ozero__class_Ozero(X1),c_Nat_OSuc(c_Power_Opower__class_Opower(tc_Nat_Onat,tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_39]),c_0_46])]) ).
cnf(c_0_73,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_74,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Nat_OSuc(c_Power_Opower__class_Opower(tc_Nat_Onat,tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[c_0_66,c_0_46]) ).
cnf(c_0_75,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_76,plain,
( c_RealVector_Onorm__class_Onorm(X1,c_RealVector_Oof__real(X1,X2)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(split_conjunct,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
cnf(c_0_78,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_ORe(v_x),c_Complex_ORe(v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Complex_OIm(v_x),c_Complex_OIm(v_y))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_39]),c_0_39]) ).
cnf(c_0_79,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_70]),c_0_71]) ).
cnf(c_0_80,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_72]),c_0_73]),c_0_53]),c_0_74]),c_0_75])]) ).
cnf(c_0_81,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_34]) ).
cnf(c_0_82,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_ORe(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Complex_OIm(c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_x,v_y))))),
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_78,c_0_46]),c_0_46]),c_0_58]),c_0_71]),c_0_56]),c_0_57]) ).
cnf(c_0_83,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81]),c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW203+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 23:23:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 31.51/31.61 % Version : CSE_E---1.5
% 31.51/31.61 % Problem : theBenchmark.p
% 31.51/31.61 % Proof found
% 31.51/31.61 % SZS status Theorem for theBenchmark.p
% 31.51/31.61 % SZS output start Proof
% See solution above
% 31.51/31.62 % Total time : 30.975000 s
% 31.51/31.62 % SZS output end Proof
% 31.51/31.62 % Total time : 31.016000 s
%------------------------------------------------------------------------------