TSTP Solution File: SWV621-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yYBtHup2xl true
% 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 00:11:35 EDT 2023
% Result : Unsatisfiable 16.60s 3.11s
% Output : Refutation 16.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV621-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.yYBtHup2xl true
% 0.14/0.34 % Computer : n015.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 : Tue Aug 29 04:12:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % Running portfolio for 300 s
% 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.34 % Number of cores: 8
% 0.14/0.34 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.20/0.65 % Total configuration time : 435
% 0.20/0.65 % Estimated wc time : 1092
% 0.20/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.20/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 16.60/3.11 % Solved by fo/fo3_bce.sh.
% 16.60/3.11 % BCE start: 648
% 16.60/3.11 % BCE eliminated: 220
% 16.60/3.11 % PE start: 428
% 16.60/3.11 logic: eq
% 16.60/3.11 % PE eliminated: -34
% 16.60/3.11 % done 884 iterations in 2.352s
% 16.60/3.11 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 16.60/3.11 % SZS output start Refutation
% 16.60/3.11 thf(c_HOL_Ozero__class_Ozero_type, type, c_HOL_Ozero__class_Ozero: $i > $i).
% 16.60/3.11 thf(c_SetInterval_Oord__class_OatLeastLessThan_type, type, c_SetInterval_Oord__class_OatLeastLessThan:
% 16.60/3.11 $i > $i > $i > $i).
% 16.60/3.11 thf(c_HOL_Ouminus__class_Ouminus_type, type, c_HOL_Ouminus__class_Ouminus:
% 16.60/3.11 $i > $i > $i).
% 16.60/3.11 thf(tc_Complex_Ocomplex_type, type, tc_Complex_Ocomplex: $i).
% 16.60/3.11 thf(class_Ring__and__Field_Ocomm__semiring__1_type, type, class_Ring__and__Field_Ocomm__semiring__1:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(class_Ring__and__Field_Ofield_type, type, class_Ring__and__Field_Ofield:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(tc_nat_type, type, tc_nat: $i).
% 16.60/3.11 thf(hBOOL_type, type, hBOOL: $i > $o).
% 16.60/3.11 thf(hAPP_type, type, hAPP: $i > $i > $i).
% 16.60/3.11 thf(class_OrderedGroup_Oab__group__add_type, type, class_OrderedGroup_Oab__group__add:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(class_Ring__and__Field_Odivision__by__zero_type, type, class_Ring__and__Field_Odivision__by__zero:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(v_k_type, type, v_k: $i).
% 16.60/3.11 thf(c_HOL_Otimes__class_Otimes_type, type, c_HOL_Otimes__class_Otimes:
% 16.60/3.11 $i > $i > $i > $i).
% 16.60/3.11 thf(c_HOL_Oone__class_Oone_type, type, c_HOL_Oone__class_Oone: $i > $i).
% 16.60/3.11 thf(c_Power_Opower__class_Opower_type, type, c_Power_Opower__class_Opower:
% 16.60/3.11 $i > $i > $i).
% 16.60/3.11 thf(class_OrderedGroup_Ogroup__add_type, type, class_OrderedGroup_Ogroup__add:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(c_HOL_Oinverse__class_Oinverse_type, type, c_HOL_Oinverse__class_Oinverse:
% 16.60/3.11 $i > $i > $i).
% 16.60/3.11 thf(c_HOL_Oord__class_Oless_type, type, c_HOL_Oord__class_Oless: $i > $i > $i).
% 16.60/3.11 thf(c_HOL_Ominus__class_Ominus_type, type, c_HOL_Ominus__class_Ominus:
% 16.60/3.11 $i > $i > $i > $i).
% 16.60/3.11 thf(c_FFT__Mirabelle_Oroot_type, type, c_FFT__Mirabelle_Oroot: $i > $i).
% 16.60/3.11 thf(class_RealVector_Oreal__normed__algebra_type, type, class_RealVector_Oreal__normed__algebra:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(c_Finite__Set_Osetsum_type, type, c_Finite__Set_Osetsum: $i > $i > $i >
% 16.60/3.11 $i > $i).
% 16.60/3.11 thf(class_Ring__and__Field_Odivision__ring_type, type, class_Ring__and__Field_Odivision__ring:
% 16.60/3.11 $i > $o).
% 16.60/3.11 thf(v_n_type, type, v_n: $i).
% 16.60/3.11 thf(c_HOL_Oinverse__class_Odivide_type, type, c_HOL_Oinverse__class_Odivide:
% 16.60/3.11 $i > $i > $i > $i).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, axiom,
% 16.60/3.11 (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl643, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Ofield])).
% 16.60/3.11 thf(cls_geometric__sum_0, axiom,
% 16.60/3.11 (( ~( class_Ring__and__Field_Ofield @ T_a ) ) |
% 16.60/3.11 ( ( c_Finite__Set_Osetsum @
% 16.60/3.11 ( c_Power_Opower__class_Opower @ V_x @ T_a ) @
% 16.60/3.11 ( c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) @
% 16.60/3.11 tc_nat @ T_a ) =
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 ( hAPP @ ( c_Power_Opower__class_Opower @ V_x @ T_a ) @ V_n ) @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 V_x @ ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) @
% 16.60/3.11 T_a ) ) |
% 16.60/3.11 ( ( V_x ) = ( c_HOL_Oone__class_Oone @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl604, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.11 (~ (class_Ring__and__Field_Ofield @ X0)
% 16.60/3.11 | ((c_Finite__Set_Osetsum @
% 16.60/3.11 (c_Power_Opower__class_Opower @ X1 @ X0) @
% 16.60/3.11 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 (c_HOL_Ozero__class_Ozero @ tc_nat) @ X2 @ tc_nat) @
% 16.60/3.11 tc_nat @ X0)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (hAPP @ (c_Power_Opower__class_Opower @ X1 @ X0) @ X2) @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ X0) @ X0) @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ X0) @ X0) @
% 16.60/3.11 X0))
% 16.60/3.11 | ((X1) = (c_HOL_Oone__class_Oone @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_geometric__sum_0])).
% 16.60/3.11 thf(zip_derived_cl2634, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (((X1) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))
% 16.60/3.11 | ((c_Finite__Set_Osetsum @
% 16.60/3.11 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 (c_HOL_Ozero__class_Ozero @ tc_nat) @ X0 @ tc_nat) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 X0) @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl604])).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, axiom,
% 16.60/3.11 (class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl640, plain,
% 16.60/3.11 ( (class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add])).
% 16.60/3.11 thf(cls_minus__diff__eq_0, axiom,
% 16.60/3.11 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @ V_a @ V_b @ T_a ) @ T_a ) =
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @ V_b @ V_a @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl224, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.11 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.60/3.11 | ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X2 @ X1 @ X0) @ X0)
% 16.60/3.11 = (c_HOL_Ominus__class_Ominus @ X1 @ X2 @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_minus__diff__eq_0])).
% 16.60/3.11 thf(zip_derived_cl1511, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ominus__class_Ominus @ X0 @ X1 @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl640, zip_derived_cl224])).
% 16.60/3.11 thf(zip_derived_cl643, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Ofield])).
% 16.60/3.11 thf(cls_divide__inverse_0, axiom,
% 16.60/3.11 (( ~( class_Ring__and__Field_Ofield @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) =
% 16.60/3.11 ( c_HOL_Otimes__class_Otimes @
% 16.60/3.11 V_a @ ( c_HOL_Oinverse__class_Oinverse @ V_b @ T_a ) @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl488, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.11 (~ (class_Ring__and__Field_Ofield @ X0)
% 16.60/3.11 | ((c_HOL_Oinverse__class_Odivide @ X1 @ X2 @ X0)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X2 @ X0) @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_divide__inverse_0])).
% 16.60/3.11 thf(zip_derived_cl2620, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl488])).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, axiom,
% 16.60/3.11 (class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl636, plain,
% 16.60/3.11 ( (class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra])).
% 16.60/3.11 thf(cls_mult_Ominus__left_0, axiom,
% 16.60/3.11 (( ~( class_RealVector_Oreal__normed__algebra @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Otimes__class_Otimes @
% 16.60/3.11 ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ V_b @ T_a ) =
% 16.60/3.11 ( c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 ( c_HOL_Otimes__class_Otimes @ V_a @ V_b @ T_a ) @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl310, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.11 (~ (class_RealVector_Oreal__normed__algebra @ X0)
% 16.60/3.11 | ((c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ X0) @ X2 @ X0)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @ X2 @ X0) @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_mult_Ominus__left_0])).
% 16.60/3.11 thf(zip_derived_cl1565, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl636, zip_derived_cl310])).
% 16.60/3.11 thf(zip_derived_cl16905, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (((X1) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))
% 16.60/3.11 | ((c_Finite__Set_Osetsum @
% 16.60/3.11 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 (c_HOL_Ozero__class_Ozero @ tc_nat) @ X0 @ tc_nat) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 X0) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)))),
% 16.60/3.11 inference('demod', [status(thm)],
% 16.60/3.11 [zip_derived_cl2634, zip_derived_cl1511, zip_derived_cl2620,
% 16.60/3.11 zip_derived_cl1565])).
% 16.60/3.11 thf(cls_conjecture_0, conjecture,
% 16.60/3.11 (( c_Finite__Set_Osetsum @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex ) =
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_n ) @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ))).
% 16.60/3.11 thf(zf_stmt_0, negated_conjecture,
% 16.60/3.11 (( c_Finite__Set_Osetsum @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex ) !=
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_n ) @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_HOL_Ominus__class_Ominus @
% 16.60/3.11 ( hAPP @
% 16.60/3.11 ( c_Power_Opower__class_Opower @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @
% 16.60/3.11 ( c_FFT__Mirabelle_Oroot @ v_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex ) @
% 16.60/3.11 v_k ) @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @
% 16.60/3.11 tc_Complex_Ocomplex )),
% 16.60/3.11 inference('cnf.neg', [status(esa)], [cls_conjecture_0])).
% 16.60/3.11 thf(zip_derived_cl647, plain,
% 16.60/3.11 (((c_Finite__Set_Osetsum @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.11 != (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_n) @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('cnf', [status(esa)], [zf_stmt_0])).
% 16.60/3.11 thf(zip_derived_cl643, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Ofield])).
% 16.60/3.11 thf(cls_inverse__eq__divide_0, axiom,
% 16.60/3.11 (( ~( class_Ring__and__Field_Ofield @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) =
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 ( c_HOL_Oone__class_Oone @ T_a ) @ V_a @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl549, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (~ (class_Ring__and__Field_Ofield @ X0)
% 16.60/3.11 | ((c_HOL_Oinverse__class_Oinverse @ X1 @ X0)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ X0) @ X1 @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_inverse__eq__divide_0])).
% 16.60/3.11 thf(zip_derived_cl2624, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl549])).
% 16.60/3.11 thf(zip_derived_cl2624, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl549])).
% 16.60/3.11 thf(zip_derived_cl1511, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ominus__class_Ominus @ X0 @ X1 @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl640, zip_derived_cl224])).
% 16.60/3.11 thf(zip_derived_cl2624, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl549])).
% 16.60/3.11 thf(zip_derived_cl1511, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ominus__class_Ominus @ X0 @ X1 @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl640, zip_derived_cl224])).
% 16.60/3.11 thf(zip_derived_cl2620, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl488])).
% 16.60/3.11 thf(zip_derived_cl1565, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl636, zip_derived_cl310])).
% 16.60/3.11 thf(zip_derived_cl643, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Ofield])).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, axiom,
% 16.60/3.11 (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl634, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero])).
% 16.60/3.11 thf(cls_inverse__divide_0, axiom,
% 16.60/3.11 (( ~( class_Ring__and__Field_Ofield @ T_a ) ) |
% 16.60/3.11 ( ~( class_Ring__and__Field_Odivision__by__zero @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @ V_a @ V_b @ T_a ) @ T_a ) =
% 16.60/3.11 ( c_HOL_Oinverse__class_Odivide @ V_b @ V_a @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl386, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.11 (~ (class_Ring__and__Field_Ofield @ X0)
% 16.60/3.11 | ~ (class_Ring__and__Field_Odivision__by__zero @ X0)
% 16.60/3.11 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @ X2 @ X1 @ X0) @ X0)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @ X1 @ X2 @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_inverse__divide_0])).
% 16.60/3.11 thf(zip_derived_cl2406, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @ X0 @ X1 @ tc_Complex_Ocomplex))
% 16.60/3.11 | ~ (class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl634, zip_derived_cl386])).
% 16.60/3.11 thf(zip_derived_cl2685, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (((tc_Complex_Ocomplex) != (tc_Complex_Ocomplex))
% 16.60/3.11 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @ X0 @ X1 @ tc_Complex_Ocomplex)))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl2406])).
% 16.60/3.11 thf(zip_derived_cl4095, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Oinverse__class_Odivide @ X0 @ X1 @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('simplify', [status(thm)], [zip_derived_cl2685])).
% 16.60/3.11 thf(zip_derived_cl2620, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl488])).
% 16.60/3.11 thf(zip_derived_cl2620, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Odivide @ X1 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl643, zip_derived_cl488])).
% 16.60/3.11 thf(zip_derived_cl4096, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X0 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('demod', [status(thm)],
% 16.60/3.11 [zip_derived_cl4095, zip_derived_cl2620, zip_derived_cl2620])).
% 16.60/3.11 thf(zip_derived_cl1565, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl636, zip_derived_cl310])).
% 16.60/3.11 thf(zip_derived_cl634, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero])).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, axiom,
% 16.60/3.11 (class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl637, plain,
% 16.60/3.11 ( (class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring])).
% 16.60/3.11 thf(cls_inverse__minus__eq_0, axiom,
% 16.60/3.11 (( ~( class_Ring__and__Field_Odivision__ring @ T_a ) ) |
% 16.60/3.11 ( ~( class_Ring__and__Field_Odivision__by__zero @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 ( c_HOL_Ouminus__class_Ouminus @ V_a @ T_a ) @ T_a ) =
% 16.60/3.11 ( c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) ))).
% 16.60/3.11 thf(zip_derived_cl204, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (~ (class_Ring__and__Field_Odivision__ring @ X0)
% 16.60/3.11 | ~ (class_Ring__and__Field_Odivision__by__zero @ X0)
% 16.60/3.11 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ X0) @ X0)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X1 @ X0) @ X0)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_inverse__minus__eq_0])).
% 16.60/3.11 thf(zip_derived_cl1606, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))
% 16.60/3.11 | ~ (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl637, zip_derived_cl204])).
% 16.60/3.11 thf(zip_derived_cl2445, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 (((tc_Complex_Ocomplex) != (tc_Complex_Ocomplex))
% 16.60/3.11 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl634, zip_derived_cl1606])).
% 16.60/3.11 thf(zip_derived_cl5319, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('simplify', [status(thm)], [zip_derived_cl2445])).
% 16.60/3.11 thf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, axiom,
% 16.60/3.11 (class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex)).
% 16.60/3.11 thf(zip_derived_cl642, plain,
% 16.60/3.11 ( (class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex)),
% 16.60/3.11 inference('cnf', [status(esa)],
% 16.60/3.11 [clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add])).
% 16.60/3.11 thf(cls_minus__equation__iff_1, axiom,
% 16.60/3.11 (( ~( class_OrderedGroup_Ogroup__add @ T_a ) ) |
% 16.60/3.11 ( ( c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 ( c_HOL_Ouminus__class_Ouminus @ V_b @ T_a ) @ T_a ) =
% 16.60/3.11 ( V_b ) ))).
% 16.60/3.11 thf(zip_derived_cl98, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 (~ (class_OrderedGroup_Ogroup__add @ X0)
% 16.60/3.11 | ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ X0) @ X0) = (X1)))),
% 16.60/3.11 inference('cnf', [status(esa)], [cls_minus__equation__iff_1])).
% 16.60/3.11 thf(zip_derived_cl1583, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) = (X0))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl642, zip_derived_cl98])).
% 16.60/3.11 thf(zip_derived_cl14037, plain,
% 16.60/3.11 (((c_Finite__Set_Osetsum @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.11 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.11 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.11 != (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_n) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('demod', [status(thm)],
% 16.60/3.11 [zip_derived_cl647, zip_derived_cl2624, zip_derived_cl2624,
% 16.60/3.11 zip_derived_cl1511, zip_derived_cl2624, zip_derived_cl1511,
% 16.60/3.11 zip_derived_cl2620, zip_derived_cl1565, zip_derived_cl4096,
% 16.60/3.11 zip_derived_cl1565, zip_derived_cl5319, zip_derived_cl1583])).
% 16.60/3.11 thf(zip_derived_cl16911, plain,
% 16.60/3.11 ((((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_n) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 != (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_n) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))
% 16.60/3.11 | ((hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)))),
% 16.60/3.11 inference('sup-', [status(thm)],
% 16.60/3.11 [zip_derived_cl16905, zip_derived_cl14037])).
% 16.60/3.11 thf(zip_derived_cl1511, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ominus__class_Ominus @ X0 @ X1 @ tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl640, zip_derived_cl224])).
% 16.60/3.11 thf(zip_derived_cl4096, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Otimes__class_Otimes @ X0 @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('demod', [status(thm)],
% 16.60/3.11 [zip_derived_cl4095, zip_derived_cl2620, zip_derived_cl2620])).
% 16.60/3.11 thf(zip_derived_cl1565, plain,
% 16.60/3.11 (![X0 : $i, X1 : $i]:
% 16.60/3.11 ((c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X1 @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @ X1 @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl636, zip_derived_cl310])).
% 16.60/3.11 thf(zip_derived_cl5319, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex)
% 16.60/3.11 = (c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex))),
% 16.60/3.11 inference('simplify', [status(thm)], [zip_derived_cl2445])).
% 16.60/3.11 thf(zip_derived_cl1583, plain,
% 16.60/3.11 (![X0 : $i]:
% 16.60/3.11 ((c_HOL_Ouminus__class_Ouminus @
% 16.60/3.11 (c_HOL_Ouminus__class_Ouminus @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) = (X0))),
% 16.60/3.11 inference('dp-resolution', [status(thm)],
% 16.60/3.11 [zip_derived_cl642, zip_derived_cl98])).
% 16.60/3.11 thf(zip_derived_cl16927, plain,
% 16.60/3.11 ((((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_HOL_Otimes__class_Otimes @
% 16.60/3.11 (c_HOL_Ominus__class_Ominus @
% 16.60/3.11 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.11 (hAPP @
% 16.60/3.11 (c_Power_Opower__class_Opower @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.11 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 v_k) @
% 16.60/3.11 tc_Complex_Ocomplex) @
% 16.60/3.11 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ominus__class_Ominus @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 != (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Otimes__class_Otimes @
% 16.60/3.12 (c_HOL_Ominus__class_Ominus @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ominus__class_Ominus @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex))
% 16.60/3.12 | ((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl16911, zip_derived_cl1511, zip_derived_cl4096,
% 16.60/3.12 zip_derived_cl1565, zip_derived_cl5319, zip_derived_cl1583])).
% 16.60/3.12 thf(zip_derived_cl16928, plain,
% 16.60/3.12 (((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl16927])).
% 16.60/3.12 thf(zip_derived_cl634, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero])).
% 16.60/3.12 thf(zip_derived_cl637, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring])).
% 16.60/3.12 thf(cls_power__inverse_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Odivision__ring @ T_a ) ) |
% 16.60/3.12 ( ~( class_Ring__and__Field_Odivision__by__zero @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 ( hAPP @ ( c_Power_Opower__class_Opower @ V_a @ T_a ) @ V_n ) @ T_a ) =
% 16.60/3.12 ( hAPP @
% 16.60/3.12 ( c_Power_Opower__class_Opower @
% 16.60/3.12 ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) @
% 16.60/3.12 V_n ) ))).
% 16.60/3.12 thf(zip_derived_cl380, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i, X2 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Odivision__ring @ X0)
% 16.60/3.12 | ~ (class_Ring__and__Field_Odivision__by__zero @ X0)
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (hAPP @ (c_Power_Opower__class_Opower @ X1 @ X0) @ X2) @ X0)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ X0) @ X0) @
% 16.60/3.12 X2)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_power__inverse_0])).
% 16.60/3.12 thf(zip_derived_cl1612, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @ X0) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0))
% 16.60/3.12 | ~ (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl637, zip_derived_cl380])).
% 16.60/3.12 thf(zip_derived_cl2448, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (((tc_Complex_Ocomplex) != (tc_Complex_Ocomplex))
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @ X0) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0)))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl634, zip_derived_cl1612])).
% 16.60/3.12 thf(zip_derived_cl8678, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (hAPP @ (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 X0) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl2448])).
% 16.60/3.12 thf(zip_derived_cl17005, plain,
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k))),
% 16.60/3.12 inference('sup+', [status(thm)],
% 16.60/3.12 [zip_derived_cl16928, zip_derived_cl8678])).
% 16.60/3.12 thf(zip_derived_cl637, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring])).
% 16.60/3.12 thf(cls_inverse__1_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Odivision__ring @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 ( c_HOL_Oone__class_Oone @ T_a ) @ T_a ) =
% 16.60/3.12 ( c_HOL_Oone__class_Oone @ T_a ) ))).
% 16.60/3.12 thf(zip_derived_cl279, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Odivision__ring @ X0)
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @ (c_HOL_Oone__class_Oone @ X0) @
% 16.60/3.12 X0) = (c_HOL_Oone__class_Oone @ X0)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_inverse__1_0])).
% 16.60/3.12 thf(zip_derived_cl1609, plain,
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl637, zip_derived_cl279])).
% 16.60/3.12 thf(zip_derived_cl634, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero])).
% 16.60/3.12 thf(zip_derived_cl637, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring])).
% 16.60/3.12 thf(cls_inverse__inverse__eq_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Odivision__ring @ T_a ) ) |
% 16.60/3.12 ( ~( class_Ring__and__Field_Odivision__by__zero @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 ( c_HOL_Oinverse__class_Oinverse @ V_a @ T_a ) @ T_a ) =
% 16.60/3.12 ( V_a ) ))).
% 16.60/3.12 thf(zip_derived_cl22, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Odivision__ring @ X0)
% 16.60/3.12 | ~ (class_Ring__and__Field_Odivision__by__zero @ X0)
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ X0) @ X0) = (X1)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_inverse__inverse__eq_0])).
% 16.60/3.12 thf(zip_derived_cl1597, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) = (X0))
% 16.60/3.12 | ~ (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl637, zip_derived_cl22])).
% 16.60/3.12 thf(zip_derived_cl2433, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 (((tc_Complex_Ocomplex) != (tc_Complex_Ocomplex))
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) = (X0)))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl634, zip_derived_cl1597])).
% 16.60/3.12 thf(zip_derived_cl3976, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) = (X0))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl2433])).
% 16.60/3.12 thf(zip_derived_cl17035, plain,
% 16.60/3.12 (((c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl17005, zip_derived_cl1609, zip_derived_cl3976])).
% 16.60/3.12 thf(cls_root__summation_0, axiom,
% 16.60/3.12 (( ( c_Finite__Set_Osetsum @
% 16.60/3.12 ( c_Power_Opower__class_Opower @
% 16.60/3.12 ( hAPP @
% 16.60/3.12 ( c_Power_Opower__class_Opower @
% 16.60/3.12 ( c_FFT__Mirabelle_Oroot @ V_n ) @ tc_Complex_Ocomplex ) @
% 16.60/3.12 V_k ) @
% 16.60/3.12 tc_Complex_Ocomplex ) @
% 16.60/3.12 ( c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex ) =
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) |
% 16.60/3.12 ( ~( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ V_k @ tc_nat ) @ V_n ) ) ) |
% 16.60/3.12 ( ~( hBOOL @
% 16.60/3.12 ( hAPP @
% 16.60/3.12 ( c_HOL_Oord__class_Oless @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @
% 16.60/3.12 V_k ) ) ))).
% 16.60/3.12 thf(zip_derived_cl568, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (((c_Finite__Set_Osetsum @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ (c_FFT__Mirabelle_Oroot @ X0) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X1) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ X0 @ tc_nat) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))
% 16.60/3.12 | ~ (hBOOL @ (hAPP @ (c_HOL_Oord__class_Oless @ X1 @ tc_nat) @ X0))
% 16.60/3.12 | ~ (hBOOL @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_HOL_Oord__class_Oless @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ tc_nat) @
% 16.60/3.12 X1)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_root__summation_0])).
% 16.60/3.12 thf(zip_derived_cl17088, plain,
% 16.60/3.12 ((((c_Finite__Set_Osetsum @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))
% 16.60/3.12 | ~ (hBOOL @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_HOL_Oord__class_Oless @ (c_HOL_Ozero__class_Ozero @ tc_nat) @
% 16.60/3.12 tc_nat) @
% 16.60/3.12 v_k))
% 16.60/3.12 | ~ (hBOOL @ (hAPP @ (c_HOL_Oord__class_Oless @ v_k @ tc_nat) @ v_n)))),
% 16.60/3.12 inference('sup+', [status(thm)], [zip_derived_cl17035, zip_derived_cl568])).
% 16.60/3.12 thf(cls_k_I1_J_0, axiom,
% 16.60/3.12 (hBOOL @
% 16.60/3.12 ( hAPP @
% 16.60/3.12 ( c_HOL_Oord__class_Oless @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @
% 16.60/3.12 v_k ))).
% 16.60/3.12 thf(zip_derived_cl551, plain,
% 16.60/3.12 ( (hBOOL @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_HOL_Oord__class_Oless @ (c_HOL_Ozero__class_Ozero @ tc_nat) @
% 16.60/3.12 tc_nat) @
% 16.60/3.12 v_k))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_k_I1_J_0])).
% 16.60/3.12 thf(cls_k_I2_J_0, axiom,
% 16.60/3.12 (hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_k @ tc_nat ) @ v_n ))).
% 16.60/3.12 thf(zip_derived_cl552, plain,
% 16.60/3.12 ( (hBOOL @ (hAPP @ (c_HOL_Oord__class_Oless @ v_k @ tc_nat) @ v_n))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_k_I2_J_0])).
% 16.60/3.12 thf(zip_derived_cl17119, plain,
% 16.60/3.12 (((c_Finite__Set_Osetsum @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl17088, zip_derived_cl551, zip_derived_cl552])).
% 16.60/3.12 thf(zip_derived_cl14037, plain,
% 16.60/3.12 (((c_Finite__Set_Osetsum @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.12 != (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Otimes__class_Otimes @
% 16.60/3.12 (c_HOL_Ominus__class_Ominus @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ominus__class_Ominus @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_FFT__Mirabelle_Oroot @ v_n) @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl647, zip_derived_cl2624, zip_derived_cl2624,
% 16.60/3.12 zip_derived_cl1511, zip_derived_cl2624, zip_derived_cl1511,
% 16.60/3.12 zip_derived_cl2620, zip_derived_cl1565, zip_derived_cl4096,
% 16.60/3.12 zip_derived_cl1565, zip_derived_cl5319, zip_derived_cl1583])).
% 16.60/3.12 thf(zip_derived_cl16928, plain,
% 16.60/3.12 (((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl16927])).
% 16.60/3.12 thf(zip_derived_cl16928, plain,
% 16.60/3.12 (((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl16927])).
% 16.60/3.12 thf(zip_derived_cl640, plain,
% 16.60/3.12 ( (class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add])).
% 16.60/3.12 thf(cls_eq__iff__diff__eq__0_0, axiom,
% 16.60/3.12 (( ~( class_OrderedGroup_Oab__group__add @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Ominus__class_Ominus @ V_x @ V_x @ T_a ) =
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ T_a ) ))).
% 16.60/3.12 thf(zip_derived_cl586, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (~ (class_OrderedGroup_Oab__group__add @ X0)
% 16.60/3.12 | ((c_HOL_Ominus__class_Ominus @ X1 @ X1 @ X0)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ X0)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_eq__iff__diff__eq__0_0])).
% 16.60/3.12 thf(zip_derived_cl1513, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Ominus__class_Ominus @ X0 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl640, zip_derived_cl586])).
% 16.60/3.12 thf(zip_derived_cl16928, plain,
% 16.60/3.12 (((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ (c_FFT__Mirabelle_Oroot @ v_n) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 v_k) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl16927])).
% 16.60/3.12 thf(zip_derived_cl3976, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) = (X0))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl2433])).
% 16.60/3.12 thf(cls_class__semiring_Opwr__0_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Ocomm__semiring__1 @ T_a ) ) |
% 16.60/3.12 ( ( hAPP @
% 16.60/3.12 ( c_Power_Opower__class_Opower @ V_x @ T_a ) @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) =
% 16.60/3.12 ( c_HOL_Oone__class_Oone @ T_a ) ))).
% 16.60/3.12 thf(zip_derived_cl579, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Ocomm__semiring__1 @ X0)
% 16.60/3.12 | ((hAPP @ (c_Power_Opower__class_Opower @ X1 @ X0) @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat))
% 16.60/3.12 = (c_HOL_Oone__class_Oone @ X0)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_class__semiring_Opwr__0_0])).
% 16.60/3.12 thf(zip_derived_cl8678, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (hAPP @ (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 X0) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0))),
% 16.60/3.12 inference('simplify', [status(thm)], [zip_derived_cl2448])).
% 16.60/3.12 thf(zip_derived_cl8697, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat)))
% 16.60/3.12 | ~ (class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('sup+', [status(thm)], [zip_derived_cl579, zip_derived_cl8678])).
% 16.60/3.12 thf(zip_derived_cl1609, plain,
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl637, zip_derived_cl279])).
% 16.60/3.12 thf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, axiom,
% 16.60/3.12 (class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex)).
% 16.60/3.12 thf(zip_derived_cl635, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1])).
% 16.60/3.12 thf(zip_derived_cl8701, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oinverse__class_Oinverse @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat)))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl8697, zip_derived_cl1609, zip_derived_cl635])).
% 16.60/3.12 thf(zip_derived_cl9453, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat)))),
% 16.60/3.12 inference('sup+', [status(thm)], [zip_derived_cl3976, zip_derived_cl8701])).
% 16.60/3.12 thf(cls_class__semiring_Opwr__pwr_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Ocomm__semiring__1 @ T_a ) ) |
% 16.60/3.12 ( ( hAPP @
% 16.60/3.12 ( c_Power_Opower__class_Opower @
% 16.60/3.12 ( hAPP @ ( c_Power_Opower__class_Opower @ V_x @ T_a ) @ V_p ) @ T_a ) @
% 16.60/3.12 V_q ) =
% 16.60/3.12 ( hAPP @
% 16.60/3.12 ( c_Power_Opower__class_Opower @ V_x @ T_a ) @
% 16.60/3.12 ( c_HOL_Otimes__class_Otimes @ V_p @ V_q @ tc_nat ) ) ))).
% 16.60/3.12 thf(zip_derived_cl382, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Ocomm__semiring__1 @ X0)
% 16.60/3.12 | ((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (hAPP @ (c_Power_Opower__class_Opower @ X1 @ X0) @ X2) @ X0) @
% 16.60/3.12 X3)
% 16.60/3.12 = (hAPP @ (c_Power_Opower__class_Opower @ X1 @ X0) @
% 16.60/3.12 (c_HOL_Otimes__class_Otimes @ X2 @ X3 @ tc_nat))))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_class__semiring_Opwr__pwr_0])).
% 16.60/3.12 thf(zip_derived_cl13534, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ X1 @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Otimes__class_Otimes @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ X0 @ tc_nat)))
% 16.60/3.12 | ~ (class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('sup+', [status(thm)], [zip_derived_cl9453, zip_derived_cl382])).
% 16.60/3.12 thf(cls_mult__is__0_1, axiom,
% 16.60/3.12 (( c_HOL_Otimes__class_Otimes @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ V_n @ tc_nat ) =
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ tc_nat ))).
% 16.60/3.12 thf(zip_derived_cl291, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Otimes__class_Otimes @ (c_HOL_Ozero__class_Ozero @ tc_nat) @
% 16.60/3.12 X0 @ tc_nat) = (c_HOL_Ozero__class_Ozero @ tc_nat))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_mult__is__0_1])).
% 16.60/3.12 thf(zip_derived_cl9453, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex)
% 16.60/3.12 = (hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @ X0 @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat)))),
% 16.60/3.12 inference('sup+', [status(thm)], [zip_derived_cl3976, zip_derived_cl8701])).
% 16.60/3.12 thf(zip_derived_cl635, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1])).
% 16.60/3.12 thf(zip_derived_cl13574, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((hAPP @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @
% 16.60/3.12 tc_Complex_Ocomplex) @
% 16.60/3.12 X0) = (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl13534, zip_derived_cl291, zip_derived_cl9453,
% 16.60/3.12 zip_derived_cl635])).
% 16.60/3.12 thf(zip_derived_cl1513, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Ominus__class_Ominus @ X0 @ X0 @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl640, zip_derived_cl586])).
% 16.60/3.12 thf(zip_derived_cl634, plain,
% 16.60/3.12 ( (class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero])).
% 16.60/3.12 thf(cls_inverse__zero_0, axiom,
% 16.60/3.12 (( ~( class_Ring__and__Field_Odivision__by__zero @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ T_a ) @ T_a ) =
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ T_a ) ))).
% 16.60/3.12 thf(zip_derived_cl129, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 (~ (class_Ring__and__Field_Odivision__by__zero @ X0)
% 16.60/3.12 | ((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ X0) @ X0)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ X0)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_inverse__zero_0])).
% 16.60/3.12 thf(zip_derived_cl2389, plain,
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl634, zip_derived_cl129])).
% 16.60/3.12 thf(zip_derived_cl636, plain,
% 16.60/3.12 ( (class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex)),
% 16.60/3.12 inference('cnf', [status(esa)],
% 16.60/3.12 [clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra])).
% 16.60/3.12 thf(cls_mult_Ozero__left_0, axiom,
% 16.60/3.12 (( ~( class_RealVector_Oreal__normed__algebra @ T_a ) ) |
% 16.60/3.12 ( ( c_HOL_Otimes__class_Otimes @
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ T_a ) @ V_b @ T_a ) =
% 16.60/3.12 ( c_HOL_Ozero__class_Ozero @ T_a ) ))).
% 16.60/3.12 thf(zip_derived_cl122, plain,
% 16.60/3.12 (![X0 : $i, X1 : $i]:
% 16.60/3.12 (~ (class_RealVector_Oreal__normed__algebra @ X0)
% 16.60/3.12 | ((c_HOL_Otimes__class_Otimes @ (c_HOL_Ozero__class_Ozero @ X0) @
% 16.60/3.12 X1 @ X0) = (c_HOL_Ozero__class_Ozero @ X0)))),
% 16.60/3.12 inference('cnf', [status(esa)], [cls_mult_Ozero__left_0])).
% 16.60/3.12 thf(zip_derived_cl1559, plain,
% 16.60/3.12 (![X0 : $i]:
% 16.60/3.12 ((c_HOL_Otimes__class_Otimes @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex) @ X0 @
% 16.60/3.12 tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl636, zip_derived_cl122])).
% 16.60/3.12 thf(zip_derived_cl2389, plain,
% 16.60/3.12 (((c_HOL_Oinverse__class_Oinverse @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex)
% 16.60/3.12 = (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('dp-resolution', [status(thm)],
% 16.60/3.12 [zip_derived_cl634, zip_derived_cl129])).
% 16.60/3.12 thf(zip_derived_cl16961, plain,
% 16.60/3.12 (((c_Finite__Set_Osetsum @
% 16.60/3.12 (c_Power_Opower__class_Opower @
% 16.60/3.12 (c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex) @ tc_Complex_Ocomplex) @
% 16.60/3.12 (c_SetInterval_Oord__class_OatLeastLessThan @
% 16.60/3.12 (c_HOL_Ozero__class_Ozero @ tc_nat) @ v_n @ tc_nat) @
% 16.60/3.12 tc_nat @ tc_Complex_Ocomplex)
% 16.60/3.12 != (c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex))),
% 16.60/3.12 inference('demod', [status(thm)],
% 16.60/3.12 [zip_derived_cl14037, zip_derived_cl16928,
% 16.60/3.12 zip_derived_cl16928, zip_derived_cl1513, zip_derived_cl16928,
% 16.60/3.12 zip_derived_cl13574, zip_derived_cl1513, zip_derived_cl2389,
% 16.60/3.12 zip_derived_cl1559, zip_derived_cl2389])).
% 16.60/3.12 thf(zip_derived_cl17148, plain, ($false),
% 16.60/3.12 inference('simplify_reflect-', [status(thm)],
% 16.60/3.12 [zip_derived_cl17119, zip_derived_cl16961])).
% 16.60/3.12
% 16.60/3.12 % SZS output end Refutation
% 16.60/3.12
% 16.60/3.12
% 16.60/3.12 % Terminating...
% 16.60/3.17 % Runner terminated.
% 16.60/3.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------