TSTP Solution File: SWW174+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW174+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:16:20 EDT 2023
% Result : Theorem 2.58s 2.70s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 143
% Syntax : Number of formulae : 231 ( 81 unt; 112 typ; 0 def)
% Number of atoms : 163 ( 105 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 85 ( 41 ~; 32 |; 0 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 137 ( 101 >; 36 *; 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 : 144 ( 2 sgn; 78 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_RealDef_Oreal: $i ).
tff(decl_23,type,
tc_Nat_Onat: $i ).
tff(decl_24,type,
c_Int_OPls: $i ).
tff(decl_25,type,
c_Int_OBit1: $i > $i ).
tff(decl_26,type,
c_Int_OBit0: $i > $i ).
tff(decl_27,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_31,type,
c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(decl_32,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_33,type,
class_Int_Onumber: $i > $o ).
tff(decl_34,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_35,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_36,type,
tc_Int_Oint: $i ).
tff(decl_37,type,
class_Fields_Ofield: $i > $o ).
tff(decl_38,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_39,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_40,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_41,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_43,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_44,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_45,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_46,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_47,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_48,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_49,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_50,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_52,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
v_y____: $i ).
tff(decl_54,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_55,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_56,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_57,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_58,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_59,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_60,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_61,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_62,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_63,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_64,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_65,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_66,type,
class_Power_Opower: $i > $o ).
tff(decl_67,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_68,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_69,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_70,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_71,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_72,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_73,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_74,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_75,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_76,type,
class_Rings_Oring: $i > $o ).
tff(decl_77,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_78,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_79,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_80,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_81,type,
class_Groups_Ozero: $i > $o ).
tff(decl_82,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_83,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_84,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_85,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_86,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_87,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_88,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_89,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_91,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_92,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_93,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_94,type,
tc_Complex_Ocomplex: $i ).
tff(decl_95,type,
v_z: $i ).
tff(decl_96,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_97,type,
v_x____: $i ).
tff(decl_98,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_99,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_100,type,
hBOOL: $i > $o ).
tff(decl_101,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_102,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_103,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_104,type,
class_Orderings_Oord: $i > $o ).
tff(decl_105,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_106,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_107,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_108,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_111,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_112,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_113,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_114,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_115,type,
c_Nat_OSuc: $i > $i ).
tff(decl_116,type,
class_Groups_Oone: $i > $o ).
tff(decl_117,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_118,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_119,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_120,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_121,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_122,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_123,type,
tc_HOL_Obool: $i ).
tff(decl_124,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk2_0: $i ).
tff(decl_126,type,
esk3_0: $i ).
tff(decl_127,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_130,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_131,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_132,type,
esk9_1: $i > $i ).
tff(decl_133,type,
esk10_2: ( $i * $i ) > $i ).
fof(fact_Bit0__def,axiom,
! [X2] : c_Int_OBit0(X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Suc__eq__plus1,axiom,
! [X17] : c_Nat_OSuc(X17) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(fact_Bit1__def,axiom,
! [X2] : c_Int_OBit1(X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_mult__numeral__1__right,axiom,
! [X11,X9] :
( class_Int_Onumber__ring(X9)
=> c_Groups_Otimes__class_Otimes(X9,X11,c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit1(c_Int_OPls))) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).
fof(conj_0,conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(fact_add__Pls__right,axiom,
! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Int_OPls) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_plus__nat_Oadd__0,axiom,
! [X17] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X17) = X17,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(fact_real__sqrt__abs,axiom,
! [X1] : 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
fof(fact_mult__2__right,axiom,
! [X10,X9] :
( class_Int_Onumber__ring(X9)
=> c_Groups_Otimes__class_Otimes(X9,X10,c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X9,X10,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_number__of__Bit1,axiom,
! [X6,X9] :
( class_Int_Onumber__ring(X9)
=> c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit1(X6)) = c_Groups_Oplus__class_Oplus(X9,c_Groups_Oplus__class_Oplus(X9,c_Groups_Oone__class_Oone(X9),c_Int_Onumber__class_Onumber__of(X9,X6)),c_Int_Onumber__class_Onumber__of(X9,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Bit1) ).
fof(fact_real__sqrt__power,axiom,
! [X2,X1] : 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_add__special_I2_J,axiom,
! [X6,X9] :
( class_Int_Onumber__ring(X9)
=> c_Groups_Oplus__class_Oplus(X9,c_Groups_Oone__class_Oone(X9),c_Int_Onumber__class_Onumber__of(X9,X6)) = c_Int_Onumber__class_Onumber__of(X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__special_I2_J) ).
fof(fact_zadd__commute,axiom,
! [X6,X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X6) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X6,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(fact_real__mult__1,axiom,
! [X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_divide__1,axiom,
! [X11,X9] :
( class_Rings_Odivision__ring(X9)
=> c_Rings_Oinverse__class_Odivide(X9,X11,c_Groups_Oone__class_Oone(X9)) = X11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divide__1) ).
fof(fact_real__mult__commute,axiom,
! [X6,X10] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X10,X6) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X6,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_four__x__squared,axiom,
! [X1] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(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))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_four__x__squared) ).
fof(fact_zadd__assoc,axiom,
! [X25,X23,X24] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,X23),X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X24,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X23,X25)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_add__num__frac,axiom,
! [X1,X10,X13,X9] :
( class_Fields_Ofield__inverse__zero(X9)
=> ( X13 != c_Groups_Ozero__class_Ozero(X9)
=> c_Groups_Oplus__class_Oplus(X9,X10,c_Rings_Oinverse__class_Odivide(X9,X1,X13)) = c_Rings_Oinverse__class_Odivide(X9,c_Groups_Oplus__class_Oplus(X9,X1,c_Groups_Otimes__class_Otimes(X9,X10,X13)),X13) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__num__frac) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(fact_number__of__add,axiom,
! [X6,X8,X9] :
( class_Int_Onumber__ring(X9)
=> c_Int_Onumber__class_Onumber__of(X9,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X6)) = c_Groups_Oplus__class_Oplus(X9,c_Int_Onumber__class_Onumber__of(X9,X8),c_Int_Onumber__class_Onumber__of(X9,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(fact_zero__less__two,axiom,
! [X9] :
( class_Rings_Olinordered__semidom(X9)
=> c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),c_Groups_Oplus__class_Oplus(X9,c_Groups_Oone__class_Oone(X9),c_Groups_Oone__class_Oone(X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__two) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Fields_Ofield__inverse__zero) ).
fof(fact_real__zero__not__eq__one,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_power__one,axiom,
! [X17,X9] :
( class_Groups_Omonoid__mult(X9)
=> c_Power_Opower__class_Opower(X9,c_Groups_Oone__class_Oone(X9),X17) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_abs__of__pos,axiom,
! [X11,X9] :
( class_Groups_Oordered__ab__group__add__abs(X9)
=> ( c_Orderings_Oord__class_Oless(X9,c_Groups_Ozero__class_Ozero(X9),X11)
=> c_Groups_Oabs__class_Oabs(X9,X11) = X11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__of__pos) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__semidom,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(c_0_31,plain,
! [X282] : c_Int_OBit0(X282) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X282,X282),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_32,plain,
! [X2738] : c_Nat_OSuc(X2738) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2738,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).
fof(c_0_33,plain,
! [X2714] : c_Int_OBit1(X2714) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2714),X2714),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_34,plain,
! [X128,X129] :
( ~ class_Int_Onumber__ring(X129)
| c_Groups_Otimes__class_Otimes(X129,X128,c_Int_Onumber__class_Onumber__of(X129,c_Int_OBit1(c_Int_OPls))) = X128 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).
fof(c_0_35,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_36,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_37,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,plain,
c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_40,plain,
! [X281] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X281,c_Int_OPls) = X281,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_41,plain,
! [X1751] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1751) = X1751,
inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).
fof(c_0_42,plain,
! [X101] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X101,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,X101),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
fof(c_0_43,plain,
! [X355,X356] :
( ~ class_Int_Onumber__ring(X356)
| c_Groups_Otimes__class_Otimes(X356,X355,c_Int_Onumber__class_Onumber__of(X356,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X356,X355,X355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
fof(c_0_44,plain,
! [X2593,X2594] :
( ~ class_Int_Onumber__ring(X2594)
| c_Int_Onumber__class_Onumber__of(X2594,c_Int_OBit1(X2593)) = c_Groups_Oplus__class_Oplus(X2594,c_Groups_Oplus__class_Oplus(X2594,c_Groups_Oone__class_Oone(X2594),c_Int_Onumber__class_Onumber__of(X2594,X2593)),c_Int_Onumber__class_Onumber__of(X2594,X2593)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).
cnf(c_0_45,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_46,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),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_35]) ).
cnf(c_0_47,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_38]),c_0_39]),c_0_39]) ).
cnf(c_0_48,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_41]) ).
fof(c_0_50,plain,
! [X88,X89] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X89,X88)) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X89),X88),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
cnf(c_0_51,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_42]) ).
cnf(c_0_52,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_53,plain,
! [X2691,X2692] :
( ~ class_Int_Onumber__ring(X2692)
| c_Groups_Oplus__class_Oplus(X2692,c_Groups_Oone__class_Oone(X2692),c_Int_Onumber__class_Onumber__of(X2692,X2691)) = c_Int_Onumber__class_Onumber__of(X2692,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2691)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).
cnf(c_0_54,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_55,plain,
! [X399,X400] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X400,X399) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X399,X400),
inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).
fof(c_0_56,plain,
! [X2495] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X2495) = X2495,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_57,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_45,c_0_39]) ).
fof(c_0_58,plain,
! [X2471,X2472] :
( ~ class_Rings_Odivision__ring(X2472)
| c_Rings_Oinverse__class_Odivide(X2472,X2471,c_Groups_Oone__class_Oone(X2472)) = X2471 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).
fof(c_0_59,plain,
! [X1331,X1332] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1332,X1331) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1331,X1332),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
fof(c_0_60,plain,
! [X98] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X98,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_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X98),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_four__x__squared]) ).
cnf(c_0_61,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),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)],[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_46,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_62,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_49]) ).
cnf(c_0_63,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_50]) ).
cnf(c_0_64,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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_37]),c_0_39]),c_0_39]) ).
fof(c_0_65,plain,
! [X406,X407,X408] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X408,X407),X406) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X408,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X407,X406)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
cnf(c_0_66,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_37]),c_0_39]),c_0_39]) ).
cnf(c_0_67,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_68,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2),X2)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_54,c_0_39]) ).
cnf(c_0_69,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_71,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oone__class_Oone(tc_Int_Oint))) = X2
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_48]),c_0_48]) ).
cnf(c_0_72,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_73,plain,
! [X1086,X1087,X1088,X1089] :
( ~ class_Fields_Ofield__inverse__zero(X1089)
| X1088 = c_Groups_Ozero__class_Ozero(X1089)
| c_Groups_Oplus__class_Oplus(X1089,X1087,c_Rings_Oinverse__class_Odivide(X1089,X1086,X1088)) = c_Rings_Oinverse__class_Odivide(X1089,c_Groups_Oplus__class_Oplus(X1089,X1086,c_Groups_Otimes__class_Otimes(X1089,X1087,X1088)),X1088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).
cnf(c_0_74,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Groups_Oone__class_Oone(X1)) = X2
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_75,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
cnf(c_0_76,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X2) = c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_77,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(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))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1),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_60]) ).
fof(c_0_78,plain,
! [X242,X243,X244] :
( ~ class_Int_Onumber__ring(X244)
| c_Int_Onumber__class_Onumber__of(X244,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X243,X242)) = c_Groups_Oplus__class_Oplus(X244,c_Int_Onumber__class_Onumber__of(X244,X243),c_Int_Onumber__class_Onumber__of(X244,X242)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
cnf(c_0_79,negated_conjecture,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
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_61,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_62]),c_0_63]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]) ).
cnf(c_0_80,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_NthRoot_Osqrt(X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
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_64,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_62]),c_0_63]) ).
cnf(c_0_81,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_82,plain,
( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_48]),c_0_48]),c_0_48]),c_0_48]) ).
cnf(c_0_83,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_67,c_0_39]) ).
cnf(c_0_84,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_85,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
fof(c_0_86,plain,
! [X2576] :
( ~ class_Rings_Olinordered__semidom(X2576)
| c_Orderings_Oord__class_Oless(X2576,c_Groups_Ozero__class_Ozero(X2576),c_Groups_Oplus__class_Oplus(X2576,c_Groups_Oone__class_Oone(X2576),c_Groups_Oone__class_Oone(X2576))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).
cnf(c_0_87,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Groups_Oplus__class_Oplus(X1,X3,c_Rings_Oinverse__class_Odivide(X1,X4,X2)) = c_Rings_Oinverse__class_Odivide(X1,c_Groups_Oplus__class_Oplus(X1,X4,c_Groups_Otimes__class_Otimes(X1,X3,X2)),X2)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_73]) ).
cnf(c_0_88,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_89,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_76]) ).
cnf(c_0_90,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(c_0_91,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__zero__not__eq__one]) ).
cnf(c_0_92,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),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)],[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_77,c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_37]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]),c_0_39]) ).
cnf(c_0_93,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)) = c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,X2),c_Int_Onumber__class_Onumber__of(X1,X3))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
fof(c_0_94,plain,
! [X2473,X2474] :
( ~ class_Groups_Omonoid__mult(X2474)
| c_Power_Opower__class_Opower(X2474,c_Groups_Oone__class_Oone(X2474),X2473) = c_Groups_Oone__class_Oone(X2474) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
cnf(c_0_95,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80]),c_0_81]) ).
cnf(c_0_96,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_82]),c_0_72])]) ).
cnf(c_0_97,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_83,c_0_48]),c_0_48]) ).
cnf(c_0_98,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_72])]) ).
fof(c_0_99,plain,
! [X1521,X1522] :
( ~ class_Groups_Oordered__ab__group__add__abs(X1522)
| ~ c_Orderings_Oord__class_Oless(X1522,c_Groups_Ozero__class_Ozero(X1522),X1521)
| c_Groups_Oabs__class_Oabs(X1522,X1521) = X1521 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).
cnf(c_0_100,plain,
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_101,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]),c_0_88]),c_0_90])]),c_0_91]) ).
cnf(c_0_102,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
cnf(c_0_103,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_81]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_62]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_48]),c_0_62]) ).
cnf(c_0_104,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_85]),c_0_72])]) ).
cnf(c_0_105,plain,
( c_Power_Opower__class_Opower(X1,c_Groups_Oone__class_Oone(X1),X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_106,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(c_0_107,negated_conjecture,
c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_108,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_96]),c_0_72])]) ).
cnf(c_0_109,plain,
( c_Groups_Oabs__class_Oabs(X1,X2) = X2
| ~ class_Groups_Oordered__ab__group__add__abs(X1)
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_110,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]) ).
cnf(c_0_111,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs]) ).
cnf(c_0_112,plain,
c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
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_103,c_0_104]),c_0_104]),c_0_104]),c_0_85]),c_0_104]),c_0_85]) ).
cnf(c_0_113,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_114,negated_conjecture,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_97]),c_0_72])]),c_0_98]),c_0_108]) ).
cnf(c_0_115,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_111])]) ).
cnf(c_0_116,plain,
c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_89]),c_0_89]) ).
cnf(c_0_117,negated_conjecture,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))) != c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_118,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_116]),c_0_80]),c_0_115]),c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW174+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 22:45:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.58/2.70 % Version : CSE_E---1.5
% 2.58/2.70 % Problem : theBenchmark.p
% 2.58/2.70 % Proof found
% 2.58/2.70 % SZS status Theorem for theBenchmark.p
% 2.58/2.70 % SZS output start Proof
% See solution above
% 2.58/2.71 % Total time : 2.089000 s
% 2.58/2.71 % SZS output end Proof
% 2.58/2.71 % Total time : 2.129000 s
%------------------------------------------------------------------------------