TSTP Solution File: SWW173+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW173+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 : n029.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 2.86s 2.93s
% Output : CNFRefutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 134
% Syntax : Number of formulae : 229 ( 86 unt; 102 typ; 0 def)
% Number of atoms : 211 ( 146 equ)
% Maximal formula atoms : 30 ( 1 avg)
% Number of connectives : 147 ( 63 ~; 60 |; 8 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 114 ( 89 >; 25 *; 0 +; 0 <<)
% Number of predicates : 64 ( 62 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 13 con; 0-3 aty)
% Number of variables : 157 ( 6 sgn; 86 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
class_Fields_Ofield: $i > $o ).
tff(decl_24,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_25,type,
c_Int_OPls: $i ).
tff(decl_26,type,
c_Int_OBit1: $i > $i ).
tff(decl_27,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_30,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_31,type,
c_Int_OBit0: $i > $i ).
tff(decl_32,type,
tc_RealDef_Oreal: $i ).
tff(decl_33,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_34,type,
tc_Nat_Onat: $i ).
tff(decl_35,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_36,type,
class_Int_Onumber: $i > $o ).
tff(decl_37,type,
tc_Int_Oint: $i ).
tff(decl_38,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_39,type,
class_Int_Oring__char__0: $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_Rings_Odivision__ring: $i > $o ).
tff(decl_43,type,
c_Nat_OSuc: $i > $i ).
tff(decl_44,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_45,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_46,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_47,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_48,type,
class_Power_Opower: $i > $o ).
tff(decl_49,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_50,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_51,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_53,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_54,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_55,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_56,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_57,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_58,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_59,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_60,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_61,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_62,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_63,type,
c_Int_OMin: $i ).
tff(decl_64,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_66,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_67,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
v_y____: $i ).
tff(decl_69,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_70,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_71,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_72,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_73,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_74,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_75,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_76,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_77,type,
class_Rings_Oring: $i > $o ).
tff(decl_78,type,
class_Rings_Oidom: $i > $o ).
tff(decl_79,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_80,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_81,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_82,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_83,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_84,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_85,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_86,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_87,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_88,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_89,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_90,type,
hBOOL: $i > $o ).
tff(decl_91,type,
tc_Complex_Ocomplex: $i ).
tff(decl_92,type,
v_z: $i ).
tff(decl_93,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_94,type,
v_x____: $i ).
tff(decl_95,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_96,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_97,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_98,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_99,type,
class_Groups_Ozero: $i > $o ).
tff(decl_100,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_101,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_102,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_103,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_104,type,
class_Groups_Oone: $i > $o ).
tff(decl_105,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_106,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_107,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_108,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_109,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_110,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_111,type,
c_Complex_Oii: $i ).
tff(decl_112,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_113,type,
v_x: $i ).
tff(decl_114,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk5_1: $i > $i ).
tff(decl_119,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_121,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk9_0: $i ).
tff(decl_123,type,
esk10_0: $i ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,c_Groups_Ozero__class_Ozero(X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_minus__real__def,axiom,
! [X23,X6] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X6,X23) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X6,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__real__def) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(fact_number__of__Min,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).
fof(arity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(fact_real__add__minus__iff,axiom,
! [X26,X20] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X20,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X26)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> X20 = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_minus__minus,axiom,
! [X4,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ouminus__class_Ouminus(X5,c_Groups_Ouminus__class_Ouminus(X5,X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(fact_real__average__minus__first,axiom,
! [X8,X4] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X4,X8),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X4) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X8,X4),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__average__minus__first) ).
fof(fact_Bit0__def,axiom,
! [X12] : c_Int_OBit0(X12) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X12] : c_Int_OBit1(X12) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X12),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(fact_real__sum__of__halves,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X6,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X6,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sum__of__halves) ).
fof(fact_add__Pls__right,axiom,
! [X12] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X12,c_Int_OPls) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(fact_divide__zero__left,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> c_Rings_Oinverse__class_Odivide(X5,c_Groups_Ozero__class_Ozero(X5),X4) = c_Groups_Ozero__class_Ozero(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).
fof(fact_four__x__squared,axiom,
! [X6] : hAPP(hAPP(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))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X6),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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)))),X6)),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_four__x__squared) ).
fof(fact_nat__1__add__1,axiom,
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_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_nat__1__add__1) ).
fof(fact_divide__self,axiom,
! [X4,X5] :
( class_Rings_Odivision__ring(X5)
=> ( X4 != c_Groups_Ozero__class_Ozero(X5)
=> c_Rings_Oinverse__class_Odivide(X5,X4,X4) = c_Groups_Oone__class_Oone(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).
fof(arity_RealDef__Oreal__Rings_Odivision__ring,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Rings_Odivision__ring) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [X21,X31,X26,X5] :
( ( class_Fields_Ofield__inverse__zero(X5)
& class_Int_Onumber(X5) )
=> ( X26 = c_Rings_Oinverse__class_Odivide(X5,X31,c_Int_Onumber__class_Onumber__of(X5,X21))
<=> ( ( c_Int_Onumber__class_Onumber__of(X5,X21) != c_Groups_Ozero__class_Ozero(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X26),c_Int_Onumber__class_Onumber__of(X5,X21)) = X31 )
& ( c_Int_Onumber__class_Onumber__of(X5,X21) = c_Groups_Ozero__class_Ozero(X5)
=> X26 = c_Groups_Ozero__class_Ozero(X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).
fof(fact_semiring__norm_I110_J,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oone__class_Oone(X5) = c_Int_Onumber__class_Onumber__of(X5,c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(fact_zadd__assoc,axiom,
! [X29,X27,X28] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,X27),X29) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X28,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X27,X29)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(fact_power__one,axiom,
! [X7,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X7) = c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(fact_real__mult__1,axiom,
! [X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X16) = X16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__mult__commute,axiom,
! [X13,X16] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X16),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X13),X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(arity_RealDef__Oreal__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(arity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Int_Onumber) ).
fof(arity_RealDef__Oreal__Fields_Ofield__inverse__zero,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',fact_real__zero__not__eq__one) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [X24,X4,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oplus__class_Oplus(X5,X4,X24) = c_Groups_Oplus__class_Oplus(X5,X24,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_number__of__add,axiom,
! [X13,X15,X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Onumber__class_Onumber__of(X5,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X13)) = c_Groups_Oplus__class_Oplus(X5,c_Int_Onumber__class_Onumber__of(X5,X15),c_Int_Onumber__class_Onumber__of(X5,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).
fof(conj_0,conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_power__divide,axiom,
! [X7,X8,X4,X5] :
( class_Fields_Ofield__inverse__zero(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Rings_Oinverse__class_Odivide(X5,X4,X8)),X7) = c_Rings_Oinverse__class_Odivide(X5,hAPP(hAPP(c_Power_Opower__class_Opower(X5),X4),X7),hAPP(hAPP(c_Power_Opower__class_Opower(X5),X8),X7)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).
fof(c_0_32,plain,
! [X269,X270] :
( ~ class_Rings_Ocomm__semiring__1(X270)
| c_Groups_Oplus__class_Oplus(X270,c_Groups_Ozero__class_Ozero(X270),X269) = X269 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).
fof(c_0_33,plain,
! [X657,X658] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X658,X657) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X658,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X657)),
inference(variable_rename,[status(thm)],[fact_minus__real__def]) ).
cnf(c_0_34,plain,
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X2) = X2
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(c_0_36,plain,
! [X767] :
( ~ class_Int_Onumber__ring(X767)
| c_Int_Onumber__class_Onumber__of(X767,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X767,c_Groups_Oone__class_Oone(X767)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).
cnf(c_0_37,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,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_34,c_0_35]) ).
cnf(c_0_39,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Int_OMin) = c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Oone__class_Oone(X1))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(c_0_41,plain,
! [X722,X723] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X723,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X722)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X723 = X722 )
& ( X723 != X722
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X723,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X722)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff])]) ).
fof(c_0_42,plain,
! [X2321,X2322] :
( ~ class_Groups_Ogroup__add(X2322)
| c_Groups_Ouminus__class_Ouminus(X2322,c_Groups_Ouminus__class_Ouminus(X2322,X2321)) = X2321 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).
cnf(c_0_43,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_40])]) ).
fof(c_0_45,plain,
! [X1548,X1549] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1549,X1548),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1549) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1548,X1549),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[fact_real__average__minus__first]) ).
fof(c_0_46,plain,
! [X389] : c_Int_OBit0(X389) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X389,X389),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_47,plain,
! [X286] : c_Int_OBit1(X286) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X286),X286),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
cnf(c_0_48,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( c_Groups_Ouminus__class_Ouminus(X1,c_Groups_Ouminus__class_Ouminus(X1,X2)) = X2
| ~ class_Groups_Ogroup__add(X1) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_38]) ).
cnf(c_0_51,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(c_0_52,plain,
! [X562] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X562,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X562,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X562,
inference(variable_rename,[status(thm)],[fact_real__sum__of__halves]) ).
cnf(c_0_53,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X1) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_54,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,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_47]) ).
fof(c_0_56,plain,
! [X388] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X388,c_Int_OPls) = X388,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
cnf(c_0_57,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,X1)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_58,plain,
c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
fof(c_0_59,plain,
! [X354,X355] :
( ~ class_Rings_Odivision__ring(X355)
| c_Rings_Oinverse__class_Odivide(X355,c_Groups_Ozero__class_Ozero(X355),X354) = c_Groups_Ozero__class_Ozero(X355) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).
fof(c_0_60,plain,
! [X104] : hAPP(hAPP(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))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X104),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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)))),X104)),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,plain,
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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).
cnf(c_0_62,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = X1,
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_63,plain,
! [X229,X230] :
( ~ class_Rings_Odivision__ring(X230)
| X229 = c_Groups_Ozero__class_Ozero(X230)
| c_Rings_Oinverse__class_Odivide(X230,X229,X229) = c_Groups_Oone__class_Oone(X230) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).
cnf(c_0_64,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),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)))),
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_53,c_0_54]),c_0_54]),c_0_55]),c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_65,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(rw,[status(thm)],[c_0_57,c_0_37]) ).
cnf(c_0_67,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_37,c_0_58]) ).
cnf(c_0_68,plain,
( c_Rings_Oinverse__class_Odivide(X1,c_Groups_Ozero__class_Ozero(X1),X2) = c_Groups_Ozero__class_Ozero(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
fof(c_0_70,plain,
! [X531,X532,X533,X534] :
( ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) = X532
| X533 != c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Groups_Ozero__class_Ozero(X534)
| X533 != c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( X533 != c_Groups_Ozero__class_Ozero(X534)
| c_Int_Onumber__class_Onumber__of(X534,X531) != c_Groups_Ozero__class_Ozero(X534)
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( c_Int_Onumber__class_Onumber__of(X534,X531) = c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) != X532
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) )
& ( X533 != c_Groups_Ozero__class_Ozero(X534)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X534),X533),c_Int_Onumber__class_Onumber__of(X534,X531)) != X532
| X533 = c_Rings_Oinverse__class_Odivide(X534,X532,c_Int_Onumber__class_Onumber__of(X534,X531))
| ~ class_Fields_Ofield__inverse__zero(X534)
| ~ class_Int_Onumber(X534) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).
fof(c_0_71,plain,
! [X495] :
( ~ class_Int_Onumber__ring(X495)
| c_Groups_Oone__class_Oone(X495) = c_Int_Onumber__class_Onumber__of(X495,c_Int_OBit1(c_Int_OPls)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).
cnf(c_0_72,plain,
hAPP(hAPP(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))))),hAPP(hAPP(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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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_73,plain,
! [X622,X623,X624] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X624,X623),X622) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X624,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X623,X622)),
inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).
cnf(c_0_74,plain,
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_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)],[c_0_61,c_0_54]),c_0_55]),c_0_55]) ).
fof(c_0_75,plain,
! [X392,X393] :
( ~ class_Groups_Omonoid__mult(X393)
| hAPP(hAPP(c_Power_Opower__class_Opower(X393),c_Groups_Oone__class_Oone(X393)),X392) = c_Groups_Oone__class_Oone(X393) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
fof(c_0_76,plain,
! [X1488] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X1488) = X1488,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
fof(c_0_77,plain,
! [X1477,X1478] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1478),X1477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1477),X1478),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_78,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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,
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_62,c_0_54]),c_0_54]),c_0_55]),c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_79,plain,
( X2 = c_Groups_Ozero__class_Ozero(X1)
| c_Rings_Oinverse__class_Odivide(X1,X2,X2) = c_Groups_Oone__class_Oone(X1)
| ~ class_Rings_Odivision__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_80,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2),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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X2,X1),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)],[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_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]) ).
cnf(c_0_81,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_82,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_83,plain,
( X3 = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X2) != c_Groups_Ozero__class_Ozero(X1)
| X3 != c_Rings_Oinverse__class_Odivide(X1,X4,c_Int_Onumber__class_Onumber__of(X1,X2))
| ~ class_Fields_Ofield__inverse__zero(X1)
| ~ class_Int_Onumber(X1) ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_84,plain,
( c_Groups_Oone__class_Oone(X1) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_85,plain,
hAPP(hAPP(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))))),hAPP(hAPP(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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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_72,c_0_54]),c_0_54]),c_0_54]),c_0_54]),c_0_54]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_86,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_73]) ).
cnf(c_0_87,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)],[c_0_74,c_0_65]),c_0_65]),c_0_65]),c_0_65]) ).
cnf(c_0_88,plain,
( hAPP(hAPP(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_75]) ).
cnf(c_0_89,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
cnf(c_0_90,plain,
hAPP(hAPP(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_76]) ).
cnf(c_0_91,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X2),X1),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_92,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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,
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_78,c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]) ).
cnf(c_0_93,plain,
( c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,X1) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X1 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_79,c_0_69]) ).
cnf(c_0_94,plain,
c_Rings_Oinverse__class_Odivide(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_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_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_43]),c_0_58]),c_0_67]) ).
cnf(c_0_95,plain,
( c_Rings_Oinverse__class_Odivide(X1,X2,c_Int_Onumber__class_Onumber__of(X1,X3)) = c_Groups_Ozero__class_Ozero(X1)
| c_Int_Onumber__class_Onumber__of(X1,X3) != c_Groups_Ozero__class_Ozero(X1)
| ~ class_Int_Onumber(X1)
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(er,[status(thm)],[c_0_83]) ).
cnf(c_0_96,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).
cnf(c_0_97,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
cnf(c_0_98,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_99,plain,
( c_Groups_Oone__class_Oone(X1) = 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))
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[c_0_84,c_0_55]) ).
fof(c_0_100,plain,
! [X264,X265,X266] :
( ~ class_Rings_Ocomm__semiring__1(X266)
| c_Groups_Oplus__class_Oplus(X266,X265,X264) = c_Groups_Oplus__class_Oplus(X266,X264,X265) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).
cnf(c_0_101,plain,
hAPP(hAPP(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)))))),hAPP(hAPP(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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(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_85,c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_86]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_87]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_87]) ).
cnf(c_0_102,plain,
hAPP(hAPP(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_88,c_0_89]) ).
cnf(c_0_103,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
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),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))
| 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_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,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_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_96]),c_0_97])]),c_0_98]) ).
fof(c_0_106,plain,
! [X280,X281,X282] :
( ~ class_Int_Onumber__ring(X282)
| c_Int_Onumber__class_Onumber__of(X282,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X281,X280)) = c_Groups_Oplus__class_Oplus(X282,c_Int_Onumber__class_Onumber__of(X282,X281),c_Int_Onumber__class_Onumber__of(X282,X280)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).
cnf(c_0_107,plain,
( c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_65]),c_0_65]) ).
cnf(c_0_108,plain,
( c_Groups_Oplus__class_Oplus(X1,X2,X3) = c_Groups_Oplus__class_Oplus(X1,X3,X2)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
fof(c_0_109,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_110,plain,
hAPP(hAPP(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_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_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))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]),c_0_103]) ).
cnf(c_0_111,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(sr,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,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_106]) ).
cnf(c_0_113,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(spm,[status(thm)],[c_0_107,c_0_40]) ).
cnf(c_0_114,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X2) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X2,X1),
inference(spm,[status(thm)],[c_0_108,c_0_35]) ).
cnf(c_0_115,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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_109]) ).
fof(c_0_116,plain,
! [X92,X93,X94,X95] :
( ~ class_Fields_Ofield__inverse__zero(X95)
| hAPP(hAPP(c_Power_Opower__class_Opower(X95),c_Rings_Oinverse__class_Odivide(X95,X94,X93)),X92) = c_Rings_Oinverse__class_Odivide(X95,hAPP(hAPP(c_Power_Opower__class_Opower(X95),X94),X92),hAPP(hAPP(c_Power_Opower__class_Opower(X95),X93),X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).
cnf(c_0_117,plain,
hAPP(hAPP(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_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))))),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_118,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_112,c_0_113]),c_0_40])]) ).
cnf(c_0_119,plain,
c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,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_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X1)),
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_40])]),c_0_114]) ).
cnf(c_0_120,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),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_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))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_54]),c_0_54]),c_0_54]),c_0_54]),c_0_54]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_55]) ).
cnf(c_0_121,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Rings_Oinverse__class_Odivide(X1,X2,X3)),X4) = c_Rings_Oinverse__class_Odivide(X1,hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4))
| ~ class_Fields_Ofield__inverse__zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_122,plain,
hAPP(hAPP(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(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118]),c_0_118]),c_0_119]),c_0_113]) ).
cnf(c_0_123,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),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_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)))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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))),
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_120,c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_87]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_86]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_65]),c_0_87]) ).
cnf(c_0_124,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(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_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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,X1,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))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_97])]) ).
cnf(c_0_125,negated_conjecture,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_x),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))))) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v_x,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))),
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_123,c_0_118]),c_0_118]),c_0_119]),c_0_113]),c_0_119]),c_0_113]) ).
cnf(c_0_126,plain,
$false,
inference(cdclpropres,[status(thm)],[c_0_124,c_0_125]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW173+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
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 20:05:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 2.86/2.93 % Version : CSE_E---1.5
% 2.86/2.93 % Problem : theBenchmark.p
% 2.86/2.93 % Proof found
% 2.86/2.93 % SZS status Theorem for theBenchmark.p
% 2.86/2.93 % SZS output start Proof
% See solution above
% 2.86/2.95 % Total time : 2.309000 s
% 2.86/2.95 % SZS output end Proof
% 2.86/2.95 % Total time : 2.350000 s
%------------------------------------------------------------------------------