TSTP Solution File: SWW194+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW194+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 : n005.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 00:16:27 EDT 2023
% Result : Theorem 1.67s 1.81s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 141
% Syntax : Number of formulae : 212 ( 67 unt; 116 typ; 0 def)
% Number of atoms : 138 ( 59 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 77 ( 35 ~; 29 |; 2 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 133 ( 102 >; 31 *; 0 +; 0 <<)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-3 aty)
% Number of functors : 46 ( 46 usr; 14 con; 0-4 aty)
% Number of variables : 93 ( 2 sgn; 55 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_RealDef_Oreal: $i ).
tff(decl_24,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_25,type,
c_Int_OPls: $i ).
tff(decl_26,type,
c_Int_OBit1: $i > $i ).
tff(decl_27,type,
c_Int_OBit0: $i > $i ).
tff(decl_28,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_29,type,
v_x____: $i ).
tff(decl_30,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_31,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_32,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
v_y____: $i ).
tff(decl_34,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_35,type,
tc_Nat_Onat: $i ).
tff(decl_36,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_37,type,
class_Int_Onumber: $i > $o ).
tff(decl_38,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_39,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_40,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_41,type,
c_Int_OMin: $i ).
tff(decl_42,type,
tc_Int_Oint: $i ).
tff(decl_43,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_44,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
tc_Complex_Ocomplex: $i ).
tff(decl_46,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_47,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_48,type,
v_z: $i ).
tff(decl_49,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_50,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_51,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_52,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_53,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_54,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_55,type,
class_Groups_Oordered__ab__group__add__abs: $i > $o ).
tff(decl_56,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_57,type,
c_Nat_OSuc: $i > $i ).
tff(decl_58,type,
class_Power_Opower: $i > $o ).
tff(decl_59,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_61,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_62,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_63,type,
c_Complex_Oii: $i ).
tff(decl_64,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_65,type,
class_Groups_Ozero: $i > $o ).
tff(decl_66,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_67,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_68,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_69,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_70,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_71,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_72,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_73,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_74,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_75,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_76,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_77,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_78,type,
class_Rings_Oring: $i > $o ).
tff(decl_79,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_80,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_81,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_82,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_83,type,
class_Orderings_Oord: $i > $o ).
tff(decl_84,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_85,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_86,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_87,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_88,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_89,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Oone: $i > $o ).
tff(decl_91,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_92,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_93,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_94,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_95,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_96,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_97,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_98,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_99,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_100,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_101,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_102,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_103,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_104,type,
class_Rings_Oordered__ring__abs: $i > $o ).
tff(decl_105,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_106,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_108,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(decl_109,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_110,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_111,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_112,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_113,type,
class_Fields_Ofield: $i > $o ).
tff(decl_114,type,
class_RealVector_Oreal__field: $i > $o ).
tff(decl_115,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_116,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_117,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_118,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_119,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_120,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_121,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_122,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_123,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_124,type,
c_Transcendental_Opi: $i ).
tff(decl_125,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(decl_126,type,
c_RComplete_Onatceiling: $i > $i ).
tff(decl_127,type,
hBOOL: $i > $o ).
tff(decl_128,type,
tc_HOL_Obool: $i ).
tff(decl_129,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_130,type,
esk2_0: $i ).
tff(decl_131,type,
esk3_0: $i ).
tff(decl_132,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_133,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_136,type,
esk8_1: $i > $i ).
tff(decl_137,type,
esk9_2: ( $i * $i ) > $i ).
fof(fact_Bit0__def,axiom,
! [X18] : c_Int_OBit0(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X18] : c_Int_OBit1(X18) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X18),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_real__sqrt__abs,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),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,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs) ).
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_add__Pls__right,axiom,
! [X18] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X18,c_Int_OPls) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(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)))),v_x____))),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),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),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_real__sqrt__power,axiom,
! [X18,X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),X18)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X5)),X18),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__power) ).
fof(fact_real__sqrt__abs2,axiom,
! [X5] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X5),X5)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__abs2) ).
fof(fact_real__mult__1,axiom,
! [X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X17) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__1) ).
fof(fact_real__mult__commute,axiom,
! [X6,X17] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X17),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X6),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__mult__commute) ).
fof(fact_real__sqrt__one,axiom,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__one) ).
fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
fof(fact_less__one__imp__sqr__less__one,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X5),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__one__imp__sqr__less__one) ).
fof(fact_mult__2__right,axiom,
! [X17,X9] :
( class_Int_Onumber__ring(X9)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X9),X17),c_Int_Onumber__class_Onumber__of(X9,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X9,X17,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).
fof(fact_less__eq__real__def,axiom,
! [X26,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X26)
<=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,X26)
| X25 = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_abs__norm__cancel,axiom,
! [X8,X9] :
( class_RealVector_Oreal__normed__vector(X9)
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X9,X8)) = c_RealVector_Onorm__class_Onorm(X9,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__norm__cancel) ).
fof(fact_real__norm__def,axiom,
! [X50] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X50) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__norm__def) ).
fof(fact_real__le__antisym,axiom,
! [X6,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X17,X6)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X17)
=> X17 = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__antisym) ).
fof(fact_leI,axiom,
! [X24,X5,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X5,X24)
=> c_Orderings_Oord__class_Oless__eq(X9,X24,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).
fof(arity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
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(arity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(fact_power__one,axiom,
! [X4,X9] :
( class_Groups_Omonoid__mult(X9)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X9),c_Groups_Oone__class_Oone(X9)),X4) = c_Groups_Oone__class_Oone(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
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(fact_real__le__refl,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X6,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__le__refl) ).
fof(c_0_25,plain,
! [X574] : c_Int_OBit0(X574) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X574,X574),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_26,plain,
! [X569] : c_Int_OBit1(X569) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X569),X569),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_27,plain,
! [X897] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X897),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,X897),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs]) ).
cnf(c_0_28,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_29,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,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_26]) ).
fof(c_0_31,plain,
! [X570] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X570,c_Int_OPls) = X570,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_32,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(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)))),v_x____))),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),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),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_33,plain,
c_NthRoot_Osqrt(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))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,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_28,c_0_29]),c_0_30]),c_0_30]) ).
cnf(c_0_35,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_36,plain,
! [X563,X564] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X564),X563)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X564)),X563),
inference(variable_rename,[status(thm)],[fact_real__sqrt__power]) ).
fof(c_0_37,plain,
! [X685] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X685),X685)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X685),
inference(variable_rename,[status(thm)],[fact_real__sqrt__abs2]) ).
fof(c_0_38,plain,
! [X170] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X170) = X170,
inference(variable_rename,[status(thm)],[fact_real__mult__1]) ).
cnf(c_0_39,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(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)))),v_x____))),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),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),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_32]) ).
fof(c_0_40,plain,
! [X157,X158] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X158),X157) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X157),X158),
inference(variable_rename,[status(thm)],[fact_real__mult__commute]) ).
cnf(c_0_41,plain,
c_NthRoot_Osqrt(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))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_29]),c_0_30]),c_0_30]) ).
cnf(c_0_42,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_34,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_43,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X1),X2)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(X1)),X2),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X1),X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_45,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_38]) ).
cnf(c_0_46,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_real__sqrt__one]) ).
cnf(c_0_47,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(split_conjunct,[status(thm)],[fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096]) ).
cnf(c_0_48,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(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)))),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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),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)],[c_0_39,c_0_29]),c_0_29]),c_0_29]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_49,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_40]) ).
cnf(c_0_50,plain,
hAPP(hAPP(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_41,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_42]),c_0_43]) ).
cnf(c_0_51,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
fof(c_0_52,plain,
! [X2451] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X2451),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2451),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__one__imp__sqr__less__one])]) ).
cnf(c_0_53,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_29]),c_0_30]),c_0_30]) ).
fof(c_0_54,plain,
! [X333,X334] :
( ~ class_Int_Onumber__ring(X334)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X334),X333),c_Int_Onumber__class_Onumber__of(X334,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X334,X333,X333) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).
cnf(c_0_55,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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))),hAPP(hAPP(c_Power_Opower__class_Opower(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)],[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_48,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_49]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_42]),c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_42]) ).
cnf(c_0_56,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(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_Oone__class_Oone(tc_RealDef_Oreal),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_46]),c_0_51]) ).
fof(c_0_57,plain,
! [X1914,X1915] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1915,X1914)
| X1915 = X1914 )
& ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1915,X1914)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914) )
& ( X1915 != X1914
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1915,X1914) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__real__def])])]) ).
cnf(c_0_58,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
fof(c_0_59,plain,
! [X1088,X1089] :
( ~ class_RealVector_Oreal__normed__vector(X1089)
| c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1089,X1088)) = c_RealVector_Onorm__class_Onorm(X1089,X1088) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__norm__cancel])]) ).
fof(c_0_60,plain,
! [X1003] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1003) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1003),
inference(variable_rename,[status(thm)],[fact_real__norm__def]) ).
fof(c_0_61,plain,
! [X146,X147] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X147,X146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X146,X147)
| X147 = X146 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__le__antisym])]) ).
cnf(c_0_62,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(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)))),v_x____)),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_53,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_63,plain,
( hAPP(hAPP(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_54]) ).
fof(c_0_64,plain,
! [X24,X5,X9] :
( class_Orderings_Olinorder(X9)
=> ( ~ c_Orderings_Oord__class_Oless(X9,X5,X24)
=> c_Orderings_Oord__class_Oless__eq(X9,X24,X5) ) ),
inference(fof_simplification,[status(thm)],[fact_leI]) ).
cnf(c_0_65,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_67,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,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)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_29]),c_0_30]),c_0_30]) ).
cnf(c_0_68,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X2)) = c_RealVector_Onorm__class_Onorm(X1,X2)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X1) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_70,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
cnf(c_0_71,plain,
( X1 = X2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[c_0_62,c_0_49]) ).
cnf(c_0_73,plain,
( hAPP(hAPP(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_63,c_0_29]),c_0_30]),c_0_30]) ).
fof(c_0_74,plain,
! [X1998,X1999,X2000] :
( ~ class_Orderings_Olinorder(X2000)
| c_Orderings_Oord__class_Oless(X2000,X1999,X1998)
| c_Orderings_Oord__class_Oless__eq(X2000,X1998,X1999) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])]) ).
cnf(c_0_75,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_76,plain,
( c_Orderings_Oord__class_Oless(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_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),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(rw,[status(thm)],[c_0_67,c_0_35]),c_0_35]),c_0_35]),c_0_35]),c_0_42]) ).
cnf(c_0_77,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70])]) ).
cnf(c_0_78,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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)))))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_79,plain,
( hAPP(hAPP(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_73,c_0_35]),c_0_35]),c_0_35]),c_0_35]) ).
cnf(c_0_80,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
cnf(c_0_81,plain,
( c_Orderings_Oord__class_Oless(X1,X2,X3)
| c_Orderings_Oord__class_Oless__eq(X1,X3,X2)
| ~ class_Orderings_Olinorder(X1) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_82,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
cnf(c_0_83,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
fof(c_0_84,plain,
! [X362,X363] :
( ~ class_Groups_Omonoid__mult(X363)
| hAPP(hAPP(c_Power_Opower__class_Opower(X363),c_Groups_Oone__class_Oone(X363)),X362) = c_Groups_Oone__class_Oone(X363) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).
cnf(c_0_85,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(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,v_x____,v_x____))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80])]) ).
cnf(c_0_86,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X2,X1) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,negated_conjecture,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_79]),c_0_80])]) ).
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_84]) ).
cnf(c_0_89,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
fof(c_0_90,plain,
! [X153] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X153,X153),
inference(variable_rename,[status(thm)],[fact_real__le__refl]) ).
cnf(c_0_91,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,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_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_79]),c_0_80])]) ).
cnf(c_0_92,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_x____,v_x____)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87]) ).
cnf(c_0_93,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_94,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWW194+1 : TPTP v8.1.2. Released v5.2.0.
% 0.08/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n005.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun Aug 27 17:31:38 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.60 start to proof: theBenchmark
% 1.67/1.81 % Version : CSE_E---1.5
% 1.67/1.81 % Problem : theBenchmark.p
% 1.67/1.81 % Proof found
% 1.67/1.81 % SZS status Theorem for theBenchmark.p
% 1.67/1.81 % SZS output start Proof
% See solution above
% 1.79/1.82 % Total time : 1.160000 s
% 1.79/1.82 % SZS output end Proof
% 1.79/1.82 % Total time : 1.202000 s
%------------------------------------------------------------------------------