TSTP Solution File: SWW252+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWW252+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.SM1XSviZ5J true
% Computer : n032.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 01:41:19 EDT 2023
% Result : Theorem 126.80s 18.72s
% Output : Refutation 126.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 42
% Syntax : Number of formulae : 95 ( 28 unt; 29 typ; 0 def)
% Number of atoms : 144 ( 106 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2076 ( 57 ~; 53 |; 5 &;1941 @)
% ( 1 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 8 con; 0-5 aty)
% Number of variables : 44 ( 0 ^; 44 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Polynomial_Ocoeff_type,type,
c_Polynomial_Ocoeff: $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_fimplies_type,type,
c_fimplies: $i ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i ).
thf(c_HOL_OAll_type,type,
c_HOL_OAll: $i > $i ).
thf(c_Rings_Oinverse__class_Oinverse_type,type,
c_Rings_Oinverse__class_Oinverse: $i > $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Polynomial_Osmult_type,type,
c_Polynomial_Osmult: $i > $i > $i > $i ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(class_Groups_Ozero_type,type,
class_Groups_Ozero: $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i ).
thf(v_q_____type,type,
v_q____: $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(class_RealVector_Oreal__normed__algebra_type,type,
class_RealVector_Oreal__normed__algebra: $i > $o ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(fact_a00,axiom,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ).
thf(zip_derived_cl1,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(cnf,[status(esa)],[fact_a00]) ).
thf(fact_degree__smult__eq,axiom,
! [V_p: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Oidom @ T_a )
=> ( ( ( V_a
= ( c_Groups_Ozero__class_Ozero @ T_a ) )
=> ( ( c_Polynomial_Odegree @ T_a @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_p ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( V_a
!= ( c_Groups_Ozero__class_Ozero @ T_a ) )
=> ( ( c_Polynomial_Odegree @ T_a @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_p ) )
= ( c_Polynomial_Odegree @ T_a @ V_p ) ) ) ) ) ).
thf(zip_derived_cl325,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ( ( c_Polynomial_Odegree @ X0 @ ( c_Polynomial_Osmult @ X0 @ X1 @ X2 ) )
= ( c_Polynomial_Odegree @ X0 @ X2 ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_degree__smult__eq]) ).
thf(fact_degree__def,axiom,
! [V_pb_2: $i,T_a: $i] :
( ( class_Groups_Ozero @ T_a )
=> ( ( c_Polynomial_Odegree @ T_a @ V_pb_2 )
= ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ T_a @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ T_a @ ( tc_fun @ T_a @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ T_a @ V_pb_2 ) ) @ ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ) ) ) ) ).
thf(zip_derived_cl252,plain,
! [X0: $i,X1: $i] :
( ( ( c_Polynomial_Odegree @ X0 @ X1 )
= ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ X0 @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ X0 @ ( tc_fun @ X0 @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ X0 @ X1 ) ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) ) ) ) ) )
| ~ ( class_Groups_Ozero @ X0 ) ),
inference(cnf,[status(esa)],[fact_degree__def]) ).
thf(zip_derived_cl252_001,plain,
! [X0: $i,X1: $i] :
( ( ( c_Polynomial_Odegree @ X0 @ X1 )
= ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ X0 @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ X0 @ ( tc_fun @ X0 @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ X0 @ X1 ) ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) ) ) ) ) )
| ~ ( class_Groups_Ozero @ X0 ) ),
inference(cnf,[status(esa)],[fact_degree__def]) ).
thf(conj_0,conjecture,
( ( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) )
& ( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ( ( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) )
& ( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
=> ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl1129,plain,
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(fact_smult__eq__0__iff,axiom,
! [V_pb_2: $i,V_a_2: $i,T_a: $i] :
( ( class_Rings_Oidom @ T_a )
=> ( ( ( c_Polynomial_Osmult @ T_a @ V_a_2 @ V_pb_2 )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
<=> ( ( V_a_2
= ( c_Groups_Ozero__class_Ozero @ T_a ) )
| ( V_pb_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ( ( c_Polynomial_Osmult @ X0 @ X2 @ X1 )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_smult__eq__0__iff]) ).
thf(zip_derived_cl1122,plain,
( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl3119,plain,
( ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
!= v_q____ ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl1122]) ).
thf(zip_derived_cl3180,plain,
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= v_q____ )
| ~ ( class_Rings_Oidom @ tc_Complex_Ocomplex )
| ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl12,zip_derived_cl3119]) ).
thf(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1092,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
thf(zip_derived_cl3183,plain,
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= v_q____ )
| ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( v_q____
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl3180,zip_derived_cl1092]) ).
thf(zip_derived_cl3184,plain,
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= v_q____ ),
inference(simplify,[status(thm)],[zip_derived_cl3183]) ).
thf(zip_derived_cl62584,plain,
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) ) ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl1129,zip_derived_cl3184]) ).
thf(zip_derived_cl62587,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) )
| ~ ( class_Groups_Ozero @ tc_Complex_Ocomplex )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl252,zip_derived_cl62584]) ).
thf(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1091,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
thf(zip_derived_cl62591,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Orderings_Oord__class_OLeast @ tc_Nat_Onat @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ tc_HOL_Obool @ tc_Nat_Onat @ ( c_HOL_OAll @ tc_Nat_Onat ) ) @ ( c_COMBC @ tc_Nat_Onat @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( tc_fun @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBS @ tc_Nat_Onat @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_Nat_Onat @ tc_HOL_Obool ) @ ( tc_fun @ tc_Nat_Onat @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) ) @ tc_Nat_Onat @ ( c_COMBB @ tc_HOL_Obool @ ( tc_fun @ tc_HOL_Obool @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fimplies ) ) @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) ) ) @ ( c_COMBC @ tc_Nat_Onat @ tc_Complex_Ocomplex @ tc_HOL_Obool @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_HOL_Obool ) @ tc_Nat_Onat @ c_fequal ) @ ( c_Polynomial_Ocoeff @ tc_Complex_Ocomplex @ v_q____ ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) ) ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62587,zip_derived_cl1091]) ).
thf(zip_derived_cl62602,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) )
| ~ ( class_Groups_Ozero @ tc_Complex_Ocomplex )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl252,zip_derived_cl62591]) ).
thf(zip_derived_cl1091_002,plain,
class_Groups_Ozero @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
thf(zip_derived_cl62604,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ ) ) ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62602,zip_derived_cl1091]) ).
thf(zip_derived_cl62608,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) ) )
| ~ ( class_Rings_Oidom @ tc_Complex_Ocomplex )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl325,zip_derived_cl62604]) ).
thf(zip_derived_cl1092_003,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
thf(zip_derived_cl62615,plain,
( ( ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) )
!= ( hAPP @ c_Nat_OSuc @ ( c_Polynomial_Odegree @ tc_Complex_Ocomplex @ v_q____ ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62608,zip_derived_cl1092]) ).
thf(zip_derived_cl62616,plain,
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ) @ v_q____ )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62615]) ).
thf(zip_derived_cl14,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( c_Polynomial_Osmult @ X0 @ X1 @ X2 )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ( X1
= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ( X2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_smult__eq__0__iff]) ).
thf(zip_derived_cl62691,plain,
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ~ ( class_Rings_Oidom @ tc_Complex_Ocomplex )
| ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl62616,zip_derived_cl14]) ).
thf(zip_derived_cl1092_004,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
thf(zip_derived_cl62708,plain,
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62691,zip_derived_cl1092]) ).
thf(zip_derived_cl62709,plain,
( ( v_q____
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62708]) ).
thf(zip_derived_cl3184_005,plain,
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= v_q____ ),
inference(simplify,[status(thm)],[zip_derived_cl3183]) ).
thf(zip_derived_cl62710,plain,
( ( c_Rings_Oinverse__class_Oinverse @ tc_Complex_Ocomplex @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl62709,zip_derived_cl3184]) ).
thf(fact_field__inverse,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Fields_Ofield @ T_a )
=> ( ( V_a
!= ( c_Groups_Ozero__class_Ozero @ T_a ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( c_Rings_Oinverse__class_Oinverse @ T_a @ V_a ) ) @ V_a )
= ( c_Groups_Oone__class_Oone @ T_a ) ) ) ) ).
thf(zip_derived_cl612,plain,
! [X0: $i,X1: $i] :
( ( X1
= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( c_Rings_Oinverse__class_Oinverse @ X0 @ X1 ) ) @ X1 )
= ( c_Groups_Oone__class_Oone @ X0 ) )
| ~ ( class_Fields_Ofield @ X0 ) ),
inference(cnf,[status(esa)],[fact_field__inverse]) ).
thf(zip_derived_cl62745,plain,
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
| ~ ( class_Fields_Ofield @ tc_Complex_Ocomplex )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl62710,zip_derived_cl612]) ).
thf(arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1084,plain,
class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
thf(fact_mult_Ozero__left,axiom,
! [V_b: $i,T_a: $i] :
( ( class_RealVector_Oreal__normed__algebra @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( c_Groups_Ozero__class_Ozero @ T_a ) ) @ V_b )
= ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ).
thf(zip_derived_cl136,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) ) @ X1 )
= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ~ ( class_RealVector_Oreal__normed__algebra @ X0 ) ),
inference(cnf,[status(esa)],[fact_mult_Ozero__left]) ).
thf(zip_derived_cl2686,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl1084,zip_derived_cl136]) ).
thf(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1090,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
thf(zip_derived_cl62751,plain,
( ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62745,zip_derived_cl2686,zip_derived_cl1090]) ).
thf(zip_derived_cl1_006,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ v_q____ ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(cnf,[status(esa)],[fact_a00]) ).
thf(zip_derived_cl62752,plain,
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
inference('simplify_reflect-',[status(thm)],[zip_derived_cl62751,zip_derived_cl1]) ).
thf(fact_smult__1__left,axiom,
! [V_p: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Polynomial_Osmult @ T_a @ ( c_Groups_Oone__class_Oone @ T_a ) @ V_p )
= V_p ) ) ).
thf(zip_derived_cl583,plain,
! [X0: $i,X1: $i] :
( ( ( c_Polynomial_Osmult @ X1 @ ( c_Groups_Oone__class_Oone @ X1 ) @ X0 )
= X0 )
| ~ ( class_Rings_Ocomm__semiring__1 @ X1 ) ),
inference(cnf,[status(esa)],[fact_smult__1__left]) ).
thf(zip_derived_cl62774,plain,
! [X0: $i] :
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ X0 )
= X0 )
| ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl62752,zip_derived_cl583]) ).
thf(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ).
thf(zip_derived_cl1087,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl62789,plain,
! [X0: $i] :
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl62774,zip_derived_cl1087]) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
!= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ( ( c_Polynomial_Osmult @ X0 @ X1 @ X2 )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_smult__eq__0__iff]) ).
thf(zip_derived_cl62826,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ~ ( class_Rings_Oidom @ tc_Complex_Ocomplex )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl62789,zip_derived_cl13]) ).
thf(zip_derived_cl1092_007,plain,
class_Rings_Oidom @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
thf(zip_derived_cl62846,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl62826,zip_derived_cl1092]) ).
thf(zip_derived_cl62847,plain,
! [X0: $i] :
( X0
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62846]) ).
thf(zip_derived_cl62847_008,plain,
! [X0: $i] :
( X0
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62846]) ).
thf(zip_derived_cl62877,plain,
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
inference(demod,[status(thm)],[zip_derived_cl1,zip_derived_cl62847,zip_derived_cl62847]) ).
thf(zip_derived_cl62847_009,plain,
! [X0: $i] :
( X0
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl62846]) ).
thf(zip_derived_cl62878,plain,
$false,
inference('simplify_reflect+',[status(thm)],[zip_derived_cl62877,zip_derived_cl62847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW252+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.SM1XSviZ5J true
% 0.16/0.33 % Computer : n032.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Sun Aug 27 20:54:15 EDT 2023
% 0.16/0.33 % CPUTime :
% 0.16/0.33 % Running portfolio for 300 s
% 0.16/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.34 % Number of cores: 8
% 0.16/0.34 % Python version: Python 3.6.8
% 0.16/0.34 % Running in FO mode
% 0.20/0.63 % Total configuration time : 435
% 0.20/0.63 % Estimated wc time : 1092
% 0.20/0.63 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.20/0.77 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.20/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 126.80/18.72 % Solved by fo/fo3_bce.sh.
% 126.80/18.72 % BCE start: 1133
% 126.80/18.72 % BCE eliminated: 21
% 126.80/18.72 % PE start: 1112
% 126.80/18.72 logic: eq
% 126.80/18.72 % PE eliminated: -45
% 126.80/18.72 % done 2068 iterations in 17.898s
% 126.80/18.72 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 126.80/18.72 % SZS output start Refutation
% See solution above
% 126.80/18.72
% 126.80/18.72
% 126.80/18.72 % Terminating...
% 126.80/18.80 % Runner terminated.
% 126.80/18.82 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------