TSTP Solution File: SWW247+1 by Zipperpin---2.1.9999
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%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWW247+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wKiyR0Ch8F true
% Computer : n003.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 01:41:18 EDT 2023
% Result : Theorem 50.52s 7.97s
% Output : Refutation 51.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 37
% Syntax : Number of formulae : 142 ( 36 unt; 21 typ; 0 def)
% Number of atoms : 237 ( 150 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1468 ( 106 ~; 99 |; 0 &;1246 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 7 con; 0-3 aty)
% Number of variables : 138 ( 0 ^; 138 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Polynomial_Opoly_type,type,
c_Polynomial_Opoly: $i > $i > $i ).
thf(c_Polynomial_Opcompose_type,type,
c_Polynomial_Opcompose: $i > $i > $i > $i ).
thf(v_cs_____type,type,
v_cs____: $i ).
thf(class_Rings_Ocomm__semiring__0_type,type,
class_Rings_Ocomm__semiring__0: $i > $o ).
thf(tc_Polynomial_Opoly_type,type,
tc_Polynomial_Opoly: $i > $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(v_x_____type,type,
v_x____: $i ).
thf(c_Polynomial_Oorder_type,type,
c_Polynomial_Oorder: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Groups_Ouminus__class_Ouminus_type,type,
c_Groups_Ouminus__class_Ouminus: $i > $i ).
thf(class_Rings_Oring_type,type,
class_Rings_Oring: $i > $o ).
thf(class_Rings_Ocomm__semiring__1_type,type,
class_Rings_Ocomm__semiring__1: $i > $o ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Groups_Otimes__class_Otimes_type,type,
c_Groups_Otimes__class_Otimes: $i > $i ).
thf(v_y_____type,type,
v_y____: $i ).
thf(v_c_____type,type,
v_c____: $i ).
thf(sk__type,type,
sk_: $i > $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(class_Rings_Oidom_type,type,
class_Rings_Oidom: $i > $o ).
thf(c_Polynomial_OpCons_type,type,
c_Polynomial_OpCons: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(fact_C,axiom,
( ( class_Rings_Oidom @ t_a )
=> ! [B_z: $i] :
( ( B_z
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ B_z )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ) ).
thf(zip_derived_cl2,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ~ ( class_Rings_Oidom @ t_a ) ),
inference(cnf,[status(esa)],[fact_C]) ).
thf(tfree_0,axiom,
class_Rings_Oidom @ t_a ).
thf(zip_derived_cl1639,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl5126,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl1639]) ).
thf(clrel_Rings_Oidom__Rings_Ocomm__semiring__1,axiom,
! [T: $i] :
( ( class_Rings_Oidom @ T )
=> ( class_Rings_Ocomm__semiring__1 @ T ) ) ).
thf(zip_derived_cl1431,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__1 @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__1]) ).
thf(clrel_Rings_Oidom__Rings_Oring,axiom,
! [T: $i] :
( ( class_Rings_Oidom @ T )
=> ( class_Rings_Oring @ T ) ) ).
thf(zip_derived_cl1450,plain,
! [X0: $i] :
( ( class_Rings_Oring @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Oring]) ).
thf(zip_derived_cl1450_001,plain,
! [X0: $i] :
( ( class_Rings_Oring @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Oring]) ).
thf(clrel_Rings_Oidom__Rings_Ocomm__semiring__0,axiom,
! [T: $i] :
( ( class_Rings_Oidom @ T )
=> ( class_Rings_Ocomm__semiring__0 @ T ) ) ).
thf(zip_derived_cl1432,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__0 @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl5126_002,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl1639]) ).
thf(fact_pcompose__0,axiom,
! [V_q: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( c_Polynomial_Opcompose @ T_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) @ V_q )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_a ) ) ) ) ).
thf(zip_derived_cl23,plain,
! [X0: $i,X1: $i] :
( ( ( c_Polynomial_Opcompose @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) @ X1 )
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_pcompose__0]) ).
thf(fact_poly__pcompose,axiom,
! [V_x: $i,V_q: $i,V_p: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__0 @ T_a )
=> ( ( hAPP @ ( c_Polynomial_Opoly @ T_a @ ( c_Polynomial_Opcompose @ T_a @ V_p @ V_q ) ) @ V_x )
= ( hAPP @ ( c_Polynomial_Opoly @ T_a @ V_p ) @ ( hAPP @ ( c_Polynomial_Opoly @ T_a @ V_q ) @ V_x ) ) ) ) ).
thf(zip_derived_cl10,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Polynomial_Opcompose @ X0 @ X1 @ X2 ) ) @ X3 )
= ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X1 ) @ ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X2 ) @ X3 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(cnf,[status(esa)],[fact_poly__pcompose]) ).
thf(zip_derived_cl5290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ( class_Rings_Ocomm__semiring__0 @ X0 )
| ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) @ X1 )
= ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X2 ) @ X1 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl23,zip_derived_cl10]) ).
thf(zip_derived_cl5291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) @ X1 )
= ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X2 ) @ X1 ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ X0 ) ),
inference(simplify,[status(thm)],[zip_derived_cl5290]) ).
thf(zip_derived_cl5306,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) )
| ~ ( class_Rings_Ocomm__semiring__0 @ t_a ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl5126,zip_derived_cl5291]) ).
thf(zip_derived_cl14716,plain,
! [X0: $i] :
( ~ ( class_Rings_Ocomm__semiring__0 @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference(condensation,[status(thm)],[zip_derived_cl5306]) ).
thf(zip_derived_cl14717,plain,
! [X0: $i] :
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1432,zip_derived_cl14716]) ).
thf(zip_derived_cl1639_003,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl14718,plain,
! [X0: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl14717,zip_derived_cl1639]) ).
thf(fact_order__root,axiom,
! [V_a_2: $i,V_pa_2: $i,T_b: $i] :
( ( class_Rings_Oidom @ T_b )
=> ( ( ( hAPP @ ( c_Polynomial_Opoly @ T_b @ V_pa_2 ) @ V_a_2 )
= ( c_Groups_Ozero__class_Ozero @ T_b ) )
<=> ( ( V_pa_2
= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ T_b ) ) )
| ( ( c_Polynomial_Oorder @ T_b @ V_a_2 @ V_pa_2 )
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ) ).
thf(zip_derived_cl66,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ X0 ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ X1 ) @ X2 )
= ( c_Groups_Ozero__class_Ozero @ X0 ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_order__root]) ).
thf(zip_derived_cl14725,plain,
! [X0: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ~ ( class_Rings_Oidom @ t_a ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl14718,zip_derived_cl66]) ).
thf(zip_derived_cl1639_004,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl14758,plain,
! [X0: $i] :
( ( ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) )
!= ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl14725,zip_derived_cl1639]) ).
thf(zip_derived_cl14759,plain,
! [X0: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl14758]) ).
thf(zip_derived_cl1431_005,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__1 @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__1]) ).
thf(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
! [V_a: $i,T_a: $i] :
( ( class_Rings_Ocomm__semiring__1 @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( c_Groups_Ozero__class_Ozero @ T_a ) ) @ V_a )
= ( c_Groups_Ozero__class_Ozero @ T_a ) ) ) ).
thf(zip_derived_cl104,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_Rings_Ocomm__semiring__1 @ X0 ) ),
inference(cnf,[status(esa)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J]) ).
thf(zip_derived_cl14759_006,plain,
! [X0: $i] :
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl14758]) ).
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_cl14919,plain,
! [X0: $i] :
( ( X0
= ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
| ( ( hAPP @ X0 @ ( sk_ @ X0 @ ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ) )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl14759,zip_derived_cl0]) ).
thf(zip_derived_cl18677,plain,
! [X0: $i] :
( ~ ( class_Rings_Ocomm__semiring__1 @ X0 )
| ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( c_Groups_Ozero__class_Ozero @ X0 ) )
= ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
| ( ( c_Groups_Ozero__class_Ozero @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl104,zip_derived_cl14919]) ).
thf(zip_derived_cl18792,plain,
( ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ t_a ) ),
inference(eq_res,[status(thm)],[zip_derived_cl18677]) ).
thf(zip_derived_cl18793,plain,
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1431,zip_derived_cl18792]) ).
thf(zip_derived_cl1639_007,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl18794,plain,
( ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Polynomial_Opoly @ t_a @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl18793,zip_derived_cl1639]) ).
thf(zip_derived_cl18906,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl14759,zip_derived_cl18794]) ).
thf(fact_minus__mult__right,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Oring @ T_a )
=> ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ 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_a ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ T_a ) @ V_b ) ) ) ) ).
thf(zip_derived_cl170,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X2 ) ) )
| ~ ( class_Rings_Oring @ X0 ) ),
inference(cnf,[status(esa)],[fact_minus__mult__right]) ).
thf(zip_derived_cl19090,plain,
! [X0: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 ) ) )
| ~ ( class_Rings_Oring @ t_a ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl18906,zip_derived_cl170]) ).
thf(zip_derived_cl18906_008,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl14759,zip_derived_cl18794]) ).
thf(zip_derived_cl19160,plain,
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ~ ( class_Rings_Oring @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl19090,zip_derived_cl18906]) ).
thf(zip_derived_cl19219,plain,
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl19160]) ).
thf(zip_derived_cl1639_009,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl19220,plain,
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl19219,zip_derived_cl1639]) ).
thf(fact_square__eq__iff,axiom,
! [V_b_2: $i,V_a_2: $i,T_b: $i] :
( ( class_Rings_Oidom @ T_b )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_b ) @ V_a_2 ) @ V_a_2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_b ) @ V_b_2 ) @ V_b_2 ) )
<=> ( ( V_a_2 = V_b_2 )
| ( V_a_2
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ T_b ) @ V_b_2 ) ) ) ) ) ).
thf(zip_derived_cl178,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2
!= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X1 ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X2 ) @ X2 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X1 ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_square__eq__iff]) ).
thf(zip_derived_cl19236,plain,
! [X0: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) )
| ~ ( class_Rings_Oidom @ t_a ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19220,zip_derived_cl178]) ).
thf(zip_derived_cl18906_010,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl14759,zip_derived_cl18794]) ).
thf(zip_derived_cl1639_011,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl19271,plain,
! [X0: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19236,zip_derived_cl18906,zip_derived_cl1639]) ).
thf(zip_derived_cl1450_012,plain,
! [X0: $i] :
( ( class_Rings_Oring @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Oring]) ).
thf(fact_minus__mult__minus,axiom,
! [V_b: $i,V_a: $i,T_a: $i] :
( ( class_Rings_Oring @ T_a )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ T_a ) @ V_a ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ T_a ) @ V_b ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ T_a ) @ V_a ) @ V_b ) ) ) ).
thf(zip_derived_cl177,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) )
| ~ ( class_Rings_Oring @ X0 ) ),
inference(cnf,[status(esa)],[fact_minus__mult__minus]) ).
thf(zip_derived_cl18906_013,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl14759,zip_derived_cl18794]) ).
thf(zip_derived_cl180,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X2 ) @ X2 )
!= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X1 ) )
| ( X2 = X1 )
| ( X2
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X1 ) )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[fact_square__eq__iff]) ).
thf(zip_derived_cl19112,plain,
! [X0: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( X0
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) )
| ~ ( class_Rings_Oidom @ t_a ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl18906,zip_derived_cl180]) ).
thf(zip_derived_cl1639_014,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl19168,plain,
! [X0: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( X0
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl19112,zip_derived_cl1639]) ).
thf(zip_derived_cl25569,plain,
! [X0: $i] :
( ~ ( class_Rings_Oring @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl177,zip_derived_cl19168]) ).
thf(zip_derived_cl19220_015,plain,
( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl19219,zip_derived_cl1639]) ).
thf(zip_derived_cl25604,plain,
! [X0: $i] :
( ~ ( class_Rings_Oring @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl25569,zip_derived_cl19220]) ).
thf(zip_derived_cl25605,plain,
! [X0: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ~ ( class_Rings_Oring @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl25604]) ).
thf(zip_derived_cl25941,plain,
! [X0: $i] :
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl25605]) ).
thf(zip_derived_cl1639_016,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl25942,plain,
! [X0: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X0 )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl25941,zip_derived_cl1639]) ).
thf(zip_derived_cl25945,plain,
! [X0: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl19271,zip_derived_cl25942]) ).
thf(zip_derived_cl25965,plain,
! [X0: $i] :
( ( ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl25945]) ).
thf(zip_derived_cl177_017,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X1 ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ X0 ) @ X2 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ X0 ) @ X1 ) @ X2 ) )
| ~ ( class_Rings_Oring @ X0 ) ),
inference(cnf,[status(esa)],[fact_minus__mult__minus]) ).
thf(zip_derived_cl25995,plain,
! [X0: $i,X1: $i] :
( ( X1
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ ( hAPP @ ( c_Groups_Ouminus__class_Ouminus @ t_a ) @ X0 ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 ) )
| ~ ( class_Rings_Oring @ t_a ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl25965,zip_derived_cl177]) ).
thf(zip_derived_cl18906_018,plain,
! [X0: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl14759,zip_derived_cl18794]) ).
thf(zip_derived_cl26043,plain,
! [X0: $i,X1: $i] :
( ( X1
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 ) )
| ~ ( class_Rings_Oring @ t_a ) ),
inference(demod,[status(thm)],[zip_derived_cl25995,zip_derived_cl18906]) ).
thf(zip_derived_cl26410,plain,
! [X0: $i,X1: $i] :
( ~ ( class_Rings_Oidom @ t_a )
| ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X1 ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1450,zip_derived_cl26043]) ).
thf(zip_derived_cl1639_019,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl26411,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26410,zip_derived_cl1639]) ).
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_cl83,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_cl26920,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ~ ( class_Rings_Ocomm__semiring__1 @ t_a ) ),
inference('s_sup+',[status(thm)],[zip_derived_cl26411,zip_derived_cl83]) ).
thf(zip_derived_cl32468,plain,
! [X0: $i,X1: $i] :
( ~ ( class_Rings_Oidom @ t_a )
| ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1431,zip_derived_cl26920]) ).
thf(zip_derived_cl1639_020,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl32469,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl32468,zip_derived_cl1639]) ).
thf(zip_derived_cl5126_021,plain,
! [X0: $i] :
( ( X0
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl2,zip_derived_cl1639]) ).
thf(zip_derived_cl32469_022,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X1 ) @ X0 )
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(demod,[status(thm)],[zip_derived_cl32468,zip_derived_cl1639]) ).
thf(zip_derived_cl1432_023,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__0 @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0]) ).
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 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ T_a ) @ V_a ) @ V_p ) ) @ V_x )
= ( hAPP @ ( hAPP @ ( 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_cl15,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ X0 ) @ X1 ) @ X3 ) ) @ X2 )
= ( hAPP @ ( hAPP @ ( 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_cl1432_024,plain,
! [X0: $i] :
( ( class_Rings_Ocomm__semiring__0 @ X0 )
| ~ ( class_Rings_Oidom @ X0 ) ),
inference(cnf,[status(esa)],[clrel_Rings_Oidom__Rings_Ocomm__semiring__0]) ).
thf(zip_derived_cl15_025,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( hAPP @ ( c_Polynomial_Opoly @ X0 @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ X0 ) @ X1 ) @ X3 ) ) @ X2 )
= ( hAPP @ ( hAPP @ ( 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(conj_0,conjecture,
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_y____ ) ) ).
thf(zf_stmt_0,negated_conjecture,
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
!= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_y____ ) ),
inference('cnf.neg',[status(esa)],[conj_0]) ).
thf(zip_derived_cl1638,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
!= ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_y____ ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl5199,plain,
( ~ ( class_Rings_Ocomm__semiring__0 @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl1638]) ).
thf(zip_derived_cl5829,plain,
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1432,zip_derived_cl5199]) ).
thf(zip_derived_cl1639_026,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl5830,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( hAPP @ ( hAPP @ ( c_Polynomial_OpCons @ t_a ) @ v_c____ ) @ v_cs____ ) ) @ v_x____ )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5829,zip_derived_cl1639]) ).
thf(zip_derived_cl5831,plain,
( ~ ( class_Rings_Ocomm__semiring__0 @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl15,zip_derived_cl5830]) ).
thf(zip_derived_cl5832,plain,
( ~ ( class_Rings_Oidom @ t_a )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl1432,zip_derived_cl5831]) ).
thf(zip_derived_cl1639_027,plain,
class_Rings_Oidom @ t_a,
inference(cnf,[status(esa)],[tfree_0]) ).
thf(zip_derived_cl5833,plain,
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5832,zip_derived_cl1639]) ).
thf(zip_derived_cl32850,plain,
( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32469,zip_derived_cl5833]) ).
thf(zip_derived_cl32993,plain,
( ( v_y____
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5126,zip_derived_cl32850]) ).
thf(zip_derived_cl32998,plain,
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) )
| ( v_y____
= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(simplify,[status(thm)],[zip_derived_cl32993]) ).
thf(zip_derived_cl26411_028,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26410,zip_derived_cl1639]) ).
thf(zip_derived_cl5833_029,plain,
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_y____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_y____ ) ) ) ),
inference(demod,[status(thm)],[zip_derived_cl5832,zip_derived_cl1639]) ).
thf(zip_derived_cl27020,plain,
( ( v_y____
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26411,zip_derived_cl5833]) ).
thf(zip_derived_cl33074,plain,
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(clc,[status(thm)],[zip_derived_cl32998,zip_derived_cl27020]) ).
thf(zip_derived_cl33075,plain,
( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl32469,zip_derived_cl33074]) ).
thf(zip_derived_cl33081,plain,
( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl33075]) ).
thf(zip_derived_cl33093,plain,
( ( v_x____
= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl5126,zip_derived_cl33081]) ).
thf(zip_derived_cl33098,plain,
( v_x____
= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl33093]) ).
thf(zip_derived_cl26411_030,plain,
! [X0: $i,X1: $i] :
( ( X0
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( c_Groups_Ozero__class_Ozero @ t_a )
= ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ X0 ) @ X1 ) ) ),
inference(demod,[status(thm)],[zip_derived_cl26410,zip_derived_cl1639]) ).
thf(zip_derived_cl33074_031,plain,
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ v_x____ ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ v_cs____ ) @ v_x____ ) ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
inference(clc,[status(thm)],[zip_derived_cl32998,zip_derived_cl27020]) ).
thf(zip_derived_cl33076,plain,
( ( v_x____
!= ( c_Groups_Ozero__class_Ozero @ t_a ) )
| ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) )
!= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ t_a ) @ v_c____ ) @ ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ),
inference('s_sup-',[status(thm)],[zip_derived_cl26411,zip_derived_cl33074]) ).
thf(zip_derived_cl33082,plain,
( v_x____
!= ( c_Groups_Ozero__class_Ozero @ t_a ) ),
inference(simplify,[status(thm)],[zip_derived_cl33076]) ).
thf(zip_derived_cl33099,plain,
$false,
inference('simplify_reflect-',[status(thm)],[zip_derived_cl33098,zip_derived_cl33082]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWW247+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.wKiyR0Ch8F true
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 22:34:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % Number of cores: 8
% 0.20/0.36 % Python version: Python 3.6.8
% 0.20/0.36 % Running in FO mode
% 0.21/0.66 % Total configuration time : 435
% 0.21/0.66 % Estimated wc time : 1092
% 0.21/0.66 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.74 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.76 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 50.52/7.97 % Solved by fo/fo6_bce.sh.
% 50.52/7.97 % BCE start: 1640
% 50.52/7.97 % BCE eliminated: 56
% 50.52/7.97 % PE start: 1584
% 50.52/7.97 logic: eq
% 50.52/7.97 % PE eliminated: 12
% 50.52/7.97 % done 1930 iterations in 7.243s
% 50.52/7.97 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 50.52/7.97 % SZS output start Refutation
% See solution above
% 51.15/7.97
% 51.15/7.97
% 51.15/7.97 % Terminating...
% 51.47/8.07 % Runner terminated.
% 51.47/8.08 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------