TSTP Solution File: SWW192+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWW192+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 : n015.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 00:16:26 EDT 2023
% Result : Theorem 1.83s 1.93s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 126
% Syntax : Number of formulae : 149 ( 28 unt; 117 typ; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 4 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 135 ( 103 >; 32 *; 0 +; 0 <<)
% Number of predicates : 72 ( 70 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 14 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn; 12 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_Complex_Ocomplex: $i ).
tff(decl_24,type,
v_z: $i ).
tff(decl_25,type,
c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).
tff(decl_26,type,
tc_RealDef_Oreal: $i ).
tff(decl_27,type,
c_Groups_Oone__class_Oone: $i > $i ).
tff(decl_28,type,
v_x____: $i ).
tff(decl_29,type,
v_y____: $i ).
tff(decl_30,type,
c_Complex_Ocomplex_OComplex: ( $i * $i ) > $i ).
tff(decl_31,type,
class_Rings_Osemiring__1: $i > $o ).
tff(decl_32,type,
c_Power_Opower__class_Opower: $i > $i ).
tff(decl_33,type,
tc_Nat_Onat: $i ).
tff(decl_34,type,
c_Int_OPls: $i ).
tff(decl_35,type,
c_Int_OBit1: $i > $i ).
tff(decl_36,type,
c_Int_OBit0: $i > $i ).
tff(decl_37,type,
c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).
tff(decl_38,type,
class_Int_Onumber__ring: $i > $o ).
tff(decl_39,type,
c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
tc_Int_Oint: $i ).
tff(decl_41,type,
class_Int_Oring__char__0: $i > $o ).
tff(decl_42,type,
class_Int_Onumber: $i > $o ).
tff(decl_43,type,
c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).
tff(decl_44,type,
class_RealVector_Oreal__normed__div__algebra: $i > $o ).
tff(decl_45,type,
class_RealVector_Oreal__normed__algebra__1: $i > $o ).
tff(decl_46,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
tff(decl_47,type,
tc_Code__Numeral_Ocode__numeral: $i ).
tff(decl_48,type,
class_Groups_Omonoid__mult: $i > $o ).
tff(decl_49,type,
class_Rings_Olinordered__idom: $i > $o ).
tff(decl_50,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
tff(decl_51,type,
class_Rings_Oring__1__no__zero__divisors: $i > $o ).
tff(decl_52,type,
c_Groups_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_53,type,
c_NthRoot_Osqrt: $i > $i ).
tff(decl_54,type,
class_RealVector_Oreal__normed__vector: $i > $o ).
tff(decl_55,type,
class_Power_Opower: $i > $o ).
tff(decl_56,type,
class_Rings_Omult__zero: $i > $o ).
tff(decl_57,type,
class_Rings_Ono__zero__divisors: $i > $o ).
tff(decl_58,type,
class_Rings_Ozero__neq__one: $i > $o ).
tff(decl_59,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
tff(decl_60,type,
class_Rings_Olinordered__ring__strict: $i > $o ).
tff(decl_61,type,
class_Groups_Ocomm__monoid__mult: $i > $o ).
tff(decl_62,type,
class_Rings_Oring__1: $i > $o ).
tff(decl_63,type,
class_Rings_Osemiring__0: $i > $o ).
tff(decl_64,type,
class_Groups_Olinordered__ab__group__add: $i > $o ).
tff(decl_65,type,
class_Rings_Osemiring: $i > $o ).
tff(decl_66,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
tff(decl_67,type,
class_Rings_Ocomm__ring__1: $i > $o ).
tff(decl_68,type,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).
tff(decl_69,type,
class_Groups_Ogroup__add: $i > $o ).
tff(decl_70,type,
c_Complex_Ocomplex_Ocomplex__size: $i > $i ).
tff(decl_71,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_72,type,
class_Groups_Ozero: $i > $o ).
tff(decl_73,type,
class_Groups_Oab__semigroup__mult: $i > $o ).
tff(decl_74,type,
class_Groups_Oab__semigroup__add: $i > $o ).
tff(decl_75,type,
class_Groups_Ocancel__semigroup__add: $i > $o ).
tff(decl_76,type,
class_Groups_Ocancel__ab__semigroup__add: $i > $o ).
tff(decl_77,type,
class_Groups_Oone: $i > $o ).
tff(decl_78,type,
class_Rings_Oring__no__zero__divisors: $i > $o ).
tff(decl_79,type,
class_Groups_Omonoid__add: $i > $o ).
tff(decl_80,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
tff(decl_81,type,
class_Rings_Ocomm__semiring: $i > $o ).
tff(decl_82,type,
class_Rings_Oidom: $i > $o ).
tff(decl_83,type,
class_Rings_Oring: $i > $o ).
tff(decl_84,type,
c_Int_Oiszero: ( $i * $i ) > $o ).
tff(decl_85,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(decl_87,type,
class_Rings_Olinordered__semidom: $i > $o ).
tff(decl_88,type,
class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).
tff(decl_89,type,
class_Groups_Oordered__ab__semigroup__add: $i > $o ).
tff(decl_90,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_91,type,
class_Rings_Olinordered__ring: $i > $o ).
tff(decl_92,type,
class_Rings_Oordered__cancel__semiring: $i > $o ).
tff(decl_93,type,
class_Rings_Oordered__ring: $i > $o ).
tff(decl_94,type,
class_Rings_Oordered__semiring: $i > $o ).
tff(decl_95,type,
class_Rings_Oordered__comm__semiring: $i > $o ).
tff(decl_96,type,
class_Groups_Oordered__comm__monoid__add: $i > $o ).
tff(decl_97,type,
class_Rings_Olinordered__semiring__1: $i > $o ).
tff(decl_98,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_99,type,
c_Complex_Ocomplex_Ocomplex__rec: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
c_Complex_Ocomplex_Ocomplex__case: ( $i * $i * $i ) > $i ).
tff(decl_101,type,
c_Nat_OSuc: $i > $i ).
tff(decl_102,type,
c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).
tff(decl_103,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_104,type,
class_Orderings_Oord: $i > $o ).
tff(decl_105,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_106,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_107,type,
c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_108,type,
c_Int_OMin: $i ).
tff(decl_109,type,
c_Power_Opower_Opower: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(decl_111,type,
class_Rings_Olinordered__comm__semiring__strict: $i > $o ).
tff(decl_112,type,
class_Rings_Olinordered__semiring__strict: $i > $o ).
tff(decl_113,type,
class_Rings_Olinordered__semiring: $i > $o ).
tff(decl_114,type,
class_Rings_Olinordered__semiring__1__strict: $i > $o ).
tff(decl_115,type,
hBOOL: $i > $o ).
tff(decl_116,type,
c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
class_Rings_Odivision__ring: $i > $o ).
tff(decl_118,type,
class_Rings_Odivision__ring__inverse__zero: $i > $o ).
tff(decl_119,type,
class_Fields_Ofield: $i > $o ).
tff(decl_120,type,
class_Fields_Ofield__inverse__zero: $i > $o ).
tff(decl_121,type,
class_RealVector_Oreal__normed__field: $i > $o ).
tff(decl_122,type,
class_Fields_Olinordered__field__inverse__zero: $i > $o ).
tff(decl_123,type,
class_Fields_Olinordered__field: $i > $o ).
tff(decl_124,type,
c_Complex_Oii: $i ).
tff(decl_125,type,
c_Transcendental_Oarctan: $i > $i ).
tff(decl_126,type,
c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).
tff(decl_127,type,
tc_HOL_Obool: $i ).
tff(decl_128,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_129,type,
esk2_0: $i ).
tff(decl_130,type,
esk3_0: $i ).
tff(decl_131,type,
esk4_1: $i > $i ).
tff(decl_132,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_133,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_134,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_135,type,
esk8_1: $i > $i ).
tff(decl_136,type,
esk9_1: $i > $i ).
tff(decl_137,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_138,type,
esk11_2: ( $i * $i ) > $i ).
fof(fact_Bit0__def,axiom,
! [X10] : c_Int_OBit0(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [X10] : c_Int_OBit1(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(fact_complex__norm,axiom,
! [X12,X13] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X13,X12)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X13),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),X12),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_complex__norm) ).
fof(fact_nat__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,
! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Int_OPls) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(conj_0,conjecture,
c_Groups_Oplus__class_Oplus(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),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',conj_0) ).
fof(fact_real__sqrt__eq__1__iff,axiom,
! [X19] :
( c_NthRoot_Osqrt(X19) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> X19 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_real__sqrt__eq__1__iff) ).
fof(fact_z,axiom,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z) ).
fof(fact_assms,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms) ).
fof(c_0_9,plain,
! [X117] : c_Int_OBit0(X117) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X117,X117),
inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).
fof(c_0_10,plain,
! [X102] : c_Int_OBit1(X102) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X102),X102),
inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).
fof(c_0_11,plain,
! [X171,X172] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X172,X171)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X172),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),X171),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[fact_complex__norm]) ).
cnf(c_0_12,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_13,plain,
c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,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_10]) ).
fof(c_0_15,plain,
! [X113] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X113,c_Int_OPls) = X113,
inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).
fof(c_0_16,negated_conjecture,
c_Groups_Oplus__class_Oplus(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])]) ).
cnf(c_0_17,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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),X2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,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_12,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_19,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
c_Groups_Oplus__class_Oplus(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),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(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,plain,
! [X526] :
( ( c_NthRoot_Osqrt(X526) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| X526 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( X526 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X526) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff])]) ).
cnf(c_0_22,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,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),X2),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)],[c_0_17,c_0_13]),c_0_13]),c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_23,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_18,c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_24,negated_conjecture,
c_Groups_Oplus__class_Oplus(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)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),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),
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_20,c_0_13]),c_0_13]),c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_25,plain,
( X1 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(X1) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(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))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[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_22,c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_23]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_23]) ).
cnf(c_0_27,negated_conjecture,
c_Groups_Oplus__class_Oplus(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))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),v_y____),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(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_24,c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_23]),c_0_19]),c_0_19]),c_0_19]),c_0_19]),c_0_23]) ).
cnf(c_0_28,plain,
( c_Groups_Oplus__class_Oplus(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))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),X2),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_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(X1,X2)) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
inference(split_conjunct,[status(thm)],[fact_z]) ).
cnf(c_0_30,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(split_conjunct,[status(thm)],[fact_assms]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW192+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
% 0.17/0.35 % Computer : n015.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Sun Aug 27 20:57:54 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 1.83/1.93 % Version : CSE_E---1.5
% 1.83/1.93 % Problem : theBenchmark.p
% 1.83/1.93 % Proof found
% 1.83/1.93 % SZS status Theorem for theBenchmark.p
% 1.83/1.93 % SZS output start Proof
% See solution above
% 1.90/1.95 % Total time : 1.321000 s
% 1.90/1.95 % SZS output end Proof
% 1.90/1.95 % Total time : 1.360000 s
%------------------------------------------------------------------------------