TSTP Solution File: SWW290+1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWW290+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.56IBbJAzLX true
% Computer : n004.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 01:41:27 EDT 2023
% Result : Theorem 118.30s 17.51s
% Output : Refutation 118.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 52
% Syntax : Number of formulae : 133 ( 51 unt; 25 typ; 0 def)
% Number of atoms : 180 ( 92 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 1205 ( 50 ~; 42 |; 4 &;1083 @)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 45 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 5 con; 0-5 aty)
% Number of variables : 175 ( 0 ^; 175 !; 0 ?; 175 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_q_type,type,
v_q: $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(c_Groups_Oone__class_Oone_type,type,
c_Groups_Oone__class_Oone: $i > $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Fields_Ofield_type,type,
class_Fields_Ofield: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(tc_Complex_Ocomplex_type,type,
tc_Complex_Ocomplex: $i ).
thf(c_Polynomial_Opdivmod__rel_type,type,
c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).
thf(c_Polynomial_Odegree_type,type,
c_Polynomial_Odegree: $i > $i > $i ).
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i > $i > $i ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(zip_tseitin_0_type,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(sk__type,type,
sk_: $i > $i > $i ).
thf(zip_tseitin_1_type,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(v_a_type,type,
v_a: $i ).
thf(class_Groups_Ocomm__monoid__add_type,type,
class_Groups_Ocomm__monoid__add: $i > $o ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i > $i > $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(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [T_1: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_1 )
=> ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ T_1 ) ) ) ).
thf(zip_derived_cl843,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ X0 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( c_Groups_Oone__class_Oone @ T_a ) )
= V_a ) ) ).
thf(zip_derived_cl106,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X1 ) @ X0 ) @ ( c_Groups_Oone__class_Oone @ X1 ) )
= X0 )
| ~ ( class_Rings_Ocomm__semiring__1 @ X1 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J]) ).
thf(fact_mult__smult__left,axiom,
! [V_q: $i,V_p: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_p ) ) @ V_q )
= ( c_Polynomial_Osmult @ T_a @ V_a @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_p ) @ V_q ) ) ) ) ).
thf(zip_derived_cl13,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ ( c_Polynomial_Osmult @ X0 @ X1 @ X2 ) ) @ X3 )
= ( c_Polynomial_Osmult @ X0 @ X1 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X2 ) @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_mult__smult__left]) ).
thf(fact_mult__smult__right,axiom,
! [V_q: $i,V_a: $i,V_p: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_p ) @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_q ) )
= ( c_Polynomial_Osmult @ T_a @ V_a @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_p ) @ V_q ) ) ) ) ).
thf(zip_derived_cl12,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X2 ) @ ( c_Polynomial_Osmult @ X0 @ X1 @ X3 ) )
= ( c_Polynomial_Osmult @ X0 @ X1 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X2 ) @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_mult__smult__right]) ).
thf(zip_derived_cl4117,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X3 ) ) @ X1 ) @ ( c_Polynomial_Osmult @ X3 @ X2 @ X0 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X3 ) ) @ ( c_Polynomial_Osmult @ X3 @ X2 @ X1 ) ) @ X0 ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X3 )
| ~ ( class_Rings_Ocomm__semiring__0 @ X3 ) ),
inference('sup+',[status(thm)],[zip_derived_cl13,zip_derived_cl12]) ).
thf(zip_derived_cl4121,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ( class_Rings_Ocomm__semiring__0 @ X3 )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X3 ) ) @ X1 ) @ ( c_Polynomial_Osmult @ X3 @ X2 @ X0 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X3 ) ) @ ( c_Polynomial_Osmult @ X3 @ X2 @ X1 ) ) @ X0 ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl4117]) ).
thf(conj_0,conjecture,
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ v_q ) @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ v_q ) @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl852,plain,
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ v_q ) @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(fact_one__poly__def,axiom,
! [T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ T_a ) )
= ( c_Polynomial_OpCons @ T_a @ ( c_Groups_Oone__class_Oone @ T_a ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ) ).
thf(zip_derived_cl105,plain,
! [X0: $i] :
( ( ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ X0 ) )
= ( c_Polynomial_OpCons @ X0 @ ( c_Groups_Oone__class_Oone @ X0 ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_one__poly__def]) ).
thf(arity_Complex__Ocomplex__Fields_Ofield,axiom,
class_Fields_Ofield @ tc_Complex_Ocomplex ).
thf(zip_derived_cl839,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
thf(fact_pdivmod__rel__def,axiom,
! [V_r_2: $i,V_qa_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( class_Fields_Ofield @ T_a )
=> ( ( c_Polynomial_Opdivmod__rel @ T_a @ V_x_2 @ V_y_2 @ V_qa_2 @ V_r_2 )
<=> ( ( ( V_y_2
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
=> ( ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ T_a @ V_r_2 ) @ ( c_Polynomial_Odegree @ T_a @ V_y_2 ) )
| ( V_r_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) )
& ( ( V_y_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
=> ( V_qa_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) )
& ( V_x_2
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_qa_2 ) @ V_y_2 ) @ V_r_2 ) ) ) ) ) ).
thf(zf_stmt_1,type,
zip_tseitin_1: $i > $i > $i > $o ).
thf(zf_stmt_2,axiom,
! [T_a: $i,V_y_2: $i,V_qa_2: $i] :
( ( zip_tseitin_1 @ T_a @ V_y_2 @ V_qa_2 )
<=> ( ( V_y_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
=> ( V_qa_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ) ).
thf(zf_stmt_3,type,
zip_tseitin_0: $i > $i > $i > $o ).
thf(zf_stmt_4,axiom,
! [T_a: $i,V_y_2: $i,V_r_2: $i] :
( ( zip_tseitin_0 @ T_a @ V_y_2 @ V_r_2 )
<=> ( ( V_y_2
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
=> ( ( V_r_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
| ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat @ ( c_Polynomial_Odegree @ T_a @ V_r_2 ) @ ( c_Polynomial_Odegree @ T_a @ V_y_2 ) ) ) ) ) ).
thf(zf_stmt_5,axiom,
! [V_r_2: $i,V_qa_2: $i,V_y_2: $i,V_x_2: $i,T_a: $i] :
( ( class_Fields_Ofield @ T_a )
=> ( ( c_Polynomial_Opdivmod__rel @ T_a @ V_x_2 @ V_y_2 @ V_qa_2 @ V_r_2 )
<=> ( ( V_x_2
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_qa_2 ) @ V_y_2 ) @ V_r_2 ) )
& ( zip_tseitin_1 @ T_a @ V_y_2 @ V_qa_2 )
& ( zip_tseitin_0 @ T_a @ V_y_2 @ V_r_2 ) ) ) ) ).
thf(zip_derived_cl643,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ ( c_Polynomial_Opdivmod__rel @ X0 @ X1 @ X2 @ X3 @ X4 )
| ( X1
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ X0 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X3 ) @ X2 ) @ X4 ) )
| ~ ( class_Fields_Ofield @ X0 ) ),
inference(cnf,[status(esa)],[zf_stmt_5]) ).
thf(zip_derived_cl3973,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X3
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ X1 ) @ X2 ) @ X0 ) )
| ~ ( c_Polynomial_Opdivmod__rel @ tc_Complex_Ocomplex @ X3 @ X2 @ X1 @ X0 ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl839,zip_derived_cl643]) ).
thf(zip_derived_cl839_001,plain,
class_Fields_Ofield @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
thf(fact_pdivmod__rel__0,axiom,
! [V_y: $i,T_a: $i] :
( ( class_Fields_Ofield @ T_a )
=> ( c_Polynomial_Opdivmod__rel @ T_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_y @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ).
thf(zip_derived_cl111,plain,
! [X0: $i,X1: $i] :
( ( c_Polynomial_Opdivmod__rel @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) @ X1 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Fields_Ofield @ X0 ) ),
inference(cnf,[status(esa)],[fact_pdivmod__rel__0]) ).
thf(zip_derived_cl3965,plain,
! [X0: $i] : ( c_Polynomial_Opdivmod__rel @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference('dp-resolution',[status(thm)],[zip_derived_cl839,zip_derived_cl111]) ).
thf(zip_derived_cl22541,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl3973,zip_derived_cl3965]) ).
thf(fact_add__poly__code_I2_J,axiom,
! [V_p: $i,T_a: $i] :
( ( class_Groups_Ocomm__monoid__add @ T_a )
=> ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ T_a ) @ V_p @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
= V_p ) ) ).
thf(zip_derived_cl69,plain,
! [X0: $i,X1: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ ( tc_Polynomial_Opoly @ X1 ) @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X1 ) ) )
= X0 )
| ~ ( class_Groups_Ocomm__monoid__add @ X1 ) ),
inference(cnf,[status(esa)],[fact_add__poly__code_I2_J]) ).
thf(zip_derived_cl23295,plain,
! [X0: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) )
| ~ ( class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl22541,zip_derived_cl69]) ).
thf(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex ).
thf(zip_derived_cl833,plain,
class_Groups_Ocomm__monoid__add @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
thf(zip_derived_cl23310,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl23295,zip_derived_cl833]) ).
thf(zip_derived_cl12_002,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X2 ) @ ( c_Polynomial_Osmult @ X0 @ X1 @ X3 ) )
= ( c_Polynomial_Osmult @ X0 @ X1 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ X0 ) ) @ X2 ) @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_mult__smult__right]) ).
thf(zip_derived_cl25960,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X1 @ X0 ) )
= ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X1 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl23310,zip_derived_cl12]) ).
thf(zip_derived_cl23310_003,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl23295,zip_derived_cl833]) ).
thf(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ).
thf(zip_derived_cl835,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl26003,plain,
! [X1: $i] :
( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) )
= ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X1 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl25960,zip_derived_cl23310,zip_derived_cl835]) ).
thf(fact_poly__smult,axiom,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ T_a @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_p ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ ( hAPP @ ( c_Polynomial_Opoly @ T_a @ V_p ) @ V_x ) ) ) ) ).
thf(zip_derived_cl87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Polynomial_Osmult @ X0 @ X1 @ X2 ) ) @ X3 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X2 ) @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_poly__smult]) ).
thf(zip_derived_cl26034,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X1 ) @ ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl26003,zip_derived_cl87]) ).
thf(fact_mpoly__base__conv_I1_J,axiom,
! [V_x: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ V_x ) ) ).
thf(zip_derived_cl90,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ),
inference(cnf,[status(esa)],[fact_mpoly__base__conv_I1_J]) ).
thf(zip_derived_cl90_004,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ),
inference(cnf,[status(esa)],[fact_mpoly__base__conv_I1_J]) ).
thf(zip_derived_cl835_005,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl26056,plain,
! [X1: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X1 ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26034,zip_derived_cl90,zip_derived_cl90,zip_derived_cl835]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
! [V_rx: $i,V_ly: $i,V_lx: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_ly ) ) @ V_rx )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_lx ) @ V_rx ) ) @ V_ly ) ) ) ).
thf(zip_derived_cl76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X3 ) ) @ X2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) ) @ X3 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J]) ).
thf(zip_derived_cl26501,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X1 ) @ X0 ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl26056,zip_derived_cl76]) ).
thf(zip_derived_cl26056_006,plain,
! [X1: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X1 ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26034,zip_derived_cl90,zip_derived_cl90,zip_derived_cl835]) ).
thf(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ).
thf(zip_derived_cl834,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl26550,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl26501,zip_derived_cl26056,zip_derived_cl834]) ).
thf(zip_derived_cl90_007,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) @ X0 ) ),
inference(cnf,[status(esa)],[fact_mpoly__base__conv_I1_J]) ).
thf(fact_ext,axiom,
! [V_g_2: $i,V_f_2: $i] :
( ! [B_x: $i] :
( ( hAPP @ V_f_2 @ B_x )
= ( hAPP @ V_g_2 @ B_x ) )
=> ( V_f_2 = V_g_2 ) ) ).
thf(zip_derived_cl0,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( ( hAPP @ X1 @ ( sk_ @ X1 @ X0 ) )
!= ( hAPP @ X0 @ ( sk_ @ X1 @ X0 ) ) ) ),
inference(cnf,[status(esa)],[fact_ext]) ).
thf(zip_derived_cl3993,plain,
! [X0: $i] :
( ( ( hAPP @ X0 @ ( sk_ @ X0 @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( X0
= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl90,zip_derived_cl0]) ).
thf(zip_derived_cl45436,plain,
( ( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
!= ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
| ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl26550,zip_derived_cl3993]) ).
thf(zip_derived_cl45466,plain,
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
= ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl45436]) ).
thf(fact_poly__pCons,axiom,
! [V_x: $i,V_p: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ T_a @ ( c_Polynomial_OpCons @ T_a @ V_a @ V_p ) ) @ V_x )
= ( c_Groups_Oplus__class_Oplus @ T_a @ V_a @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_x ) @ ( hAPP @ ( c_Polynomial_Opoly @ T_a @ V_p ) @ V_x ) ) ) ) ) ).
thf(zip_derived_cl85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Polynomial_OpCons @ X0 @ X1 @ X3 ) ) @ X2 )
= ( c_Groups_Oplus__class_Oplus @ X0 @ X1 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X2 ) @ ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X3 ) @ X2 ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_poly__pCons]) ).
thf(zip_derived_cl45523,plain,
! [X0: $i,X1: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X1 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) @ X0 )
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ X1 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X0 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl45466,zip_derived_cl85]) ).
thf(fact_mpoly__base__conv_I2_J,axiom,
! [V_x: $i,V_c: $i] :
( V_c
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ V_c @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) @ V_x ) ) ).
thf(zip_derived_cl93,plain,
! [X0: $i,X1: $i] :
( X0
= ( hAPP @ ( c_Polynomial_Opoly @ tc_Complex_Ocomplex @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) @ X1 ) ),
inference(cnf,[status(esa)],[fact_mpoly__base__conv_I2_J]) ).
thf(zip_derived_cl26550_008,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl26501,zip_derived_cl26056,zip_derived_cl834]) ).
thf(zip_derived_cl26056_009,plain,
! [X1: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X1 ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26034,zip_derived_cl90,zip_derived_cl90,zip_derived_cl835]) ).
thf(zip_derived_cl835_010,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl45533,plain,
! [X1: $i] :
( X1
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ X1 @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl45523,zip_derived_cl93,zip_derived_cl26550,zip_derived_cl26056,zip_derived_cl835]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Oplus__class_Oplus @ T_a @ V_a @ V_c )
= ( c_Groups_Oplus__class_Oplus @ T_a @ V_c @ V_a ) ) ) ).
thf(zip_derived_cl55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ X0 @ X2 @ X1 )
= ( c_Groups_Oplus__class_Oplus @ X0 @ X1 @ X2 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J]) ).
thf(zip_derived_cl45782,plain,
! [X0: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ 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_cl45533,zip_derived_cl55]) ).
thf(zip_derived_cl834_011,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl45814,plain,
! [X0: $i] :
( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ X0 )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl45782,zip_derived_cl834]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [V_a: $i,V_m: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( c_Groups_Oplus__class_Oplus @ T_a @ V_m @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_m ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( c_Groups_Oplus__class_Oplus @ T_a @ V_a @ ( c_Groups_Oone__class_Oone @ T_a ) ) ) @ V_m ) ) ) ).
thf(zip_derived_cl120,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ X0 @ X2 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( c_Groups_Oplus__class_Oplus @ X0 @ X1 @ ( c_Groups_Oone__class_Oone @ X0 ) ) ) @ X2 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
thf(zip_derived_cl46398,plain,
! [X0: $i] :
( ( ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ X0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ X0 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl45814,zip_derived_cl120]) ).
thf(zip_derived_cl26550_012,plain,
! [X0: $i] :
( ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl26501,zip_derived_cl26056,zip_derived_cl834]) ).
thf(zip_derived_cl45533_013,plain,
! [X1: $i] :
( X1
= ( c_Groups_Oplus__class_Oplus @ tc_Complex_Ocomplex @ X1 @ ( c_Groups_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ) ),
inference(demod,[status(thm)],[zip_derived_cl45523,zip_derived_cl93,zip_derived_cl26550,zip_derived_cl26056,zip_derived_cl835]) ).
thf(zip_derived_cl834_014,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl46426,plain,
! [X0: $i] :
( X0
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ X0 ) ),
inference(demod,[status(thm)],[zip_derived_cl46398,zip_derived_cl26550,zip_derived_cl45533,zip_derived_cl834]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_b ) @ V_a ) ) ) ).
thf(zip_derived_cl80,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X2 ) @ X1 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J]) ).
thf(zip_derived_cl71802,plain,
! [X0: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X0 ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= X0 )
| ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl46426,zip_derived_cl80]) ).
thf(zip_derived_cl834_015,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl71874,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ tc_Complex_Ocomplex ) @ X0 ) @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) )
= X0 ),
inference(demod,[status(thm)],[zip_derived_cl71802,zip_derived_cl834]) ).
thf(fact_smult__0__right,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( c_Polynomial_Osmult @ T_a @ V_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ).
thf(zip_derived_cl16,plain,
! [X0: $i,X1: $i] :
( ( ( c_Polynomial_Osmult @ X0 @ X1 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_smult__0__right]) ).
thf(fact_smult__pCons,axiom,
! [V_p: $i,V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( c_Polynomial_Osmult @ T_a @ V_a @ ( c_Polynomial_OpCons @ T_a @ V_b @ V_p ) )
= ( c_Polynomial_OpCons @ T_a @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) @ ( c_Polynomial_Osmult @ T_a @ V_a @ V_p ) ) ) ) ).
thf(zip_derived_cl3,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( c_Polynomial_Osmult @ X0 @ X1 @ ( c_Polynomial_OpCons @ X0 @ X2 @ X3 ) )
= ( c_Polynomial_OpCons @ X0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) @ ( c_Polynomial_Osmult @ X0 @ X1 @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_smult__pCons]) ).
thf(zip_derived_cl4173,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( c_Polynomial_Osmult @ X0 @ X1 @ ( c_Polynomial_OpCons @ X0 @ X2 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) )
= ( c_Polynomial_OpCons @ X0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference('sup+',[status(thm)],[zip_derived_cl16,zip_derived_cl3]) ).
thf(zip_derived_cl4176,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( class_Rings_Ocomm__semiring__0 @ X0 )
| ( ( c_Polynomial_Osmult @ X0 @ X1 @ ( c_Polynomial_OpCons @ X0 @ X2 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) )
= ( c_Polynomial_OpCons @ X0 @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl4173]) ).
thf(zip_derived_cl74337,plain,
! [X0: $i] :
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X0 @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
= ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl71874,zip_derived_cl4176]) ).
thf(zip_derived_cl835_016,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl74411,plain,
! [X0: $i] :
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X0 @ ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ ( c_Groups_Oone__class_Oone @ tc_Complex_Ocomplex ) @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
= ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl74337,zip_derived_cl835]) ).
thf(zip_derived_cl74575,plain,
! [X0: $i] :
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
= ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ) ),
inference('sup+',[status(thm)],[zip_derived_cl105,zip_derived_cl74411]) ).
thf(zip_derived_cl834_017,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl74578,plain,
! [X0: $i] :
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) )
= ( c_Polynomial_OpCons @ tc_Complex_Ocomplex @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl74575,zip_derived_cl834]) ).
thf(zip_derived_cl120964,plain,
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ v_q ) @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl852,zip_derived_cl74578]) ).
thf(zip_derived_cl121084,plain,
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q ) ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex ) ),
inference('sup-',[status(thm)],[zip_derived_cl4121,zip_derived_cl120964]) ).
thf(zip_derived_cl835_018,plain,
class_Rings_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl121091,plain,
( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) @ ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q ) ) @ ( c_Groups_Oone__class_Oone @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl121084,zip_derived_cl835]) ).
thf(zip_derived_cl121606,plain,
( ( ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q )
!= ( c_Polynomial_Osmult @ tc_Complex_Ocomplex @ v_a @ v_q ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ) ),
inference('sup-',[status(thm)],[zip_derived_cl106,zip_derived_cl121091]) ).
thf(zip_derived_cl121613,plain,
~ ( class_Rings_Ocomm__semiring__1 @ ( tc_Polynomial_Opoly @ tc_Complex_Ocomplex ) ),
inference(simplify,[status(thm)],[zip_derived_cl121606]) ).
thf(zip_derived_cl121623,plain,
~ ( class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex ),
inference('sup-',[status(thm)],[zip_derived_cl843,zip_derived_cl121613]) ).
thf(zip_derived_cl834_019,plain,
class_Rings_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
inference(cnf,[status(esa)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
thf(zip_derived_cl121624,plain,
$false,
inference(demod,[status(thm)],[zip_derived_cl121623,zip_derived_cl834]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW290+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.56IBbJAzLX true
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 22:14:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.22/0.64 % Total configuration time : 435
% 0.22/0.64 % Estimated wc time : 1092
% 0.22/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.22/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.22/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.22/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 1.22/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 118.30/17.51 % Solved by fo/fo3_bce.sh.
% 118.30/17.51 % BCE start: 853
% 118.30/17.51 % BCE eliminated: 51
% 118.30/17.51 % PE start: 802
% 118.30/17.51 logic: eq
% 118.30/17.51 % PE eliminated: 4
% 118.30/17.51 % done 7891 iterations in 16.732s
% 118.30/17.51 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 118.30/17.51 % SZS output start Refutation
% See solution above
% 118.30/17.51
% 118.30/17.51
% 118.30/17.51 % Terminating...
% 118.30/17.61 % Runner terminated.
% 118.30/17.62 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------