TSTP Solution File: SWW245+1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SWW245+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.JdO3jM3QFk true

% Computer : n024.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 73.13s 11.18s
% Output   : Refutation 73.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   96 (  27 unt;  24 typ;   0 def)
%            Number of atoms       :  175 ( 154 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives : 1386 (  77   ~;  79   |;  12   &;1206   @)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   27 (  27   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  11 con; 0-4 aty)
%            Number of variables   :   44 (   0   ^;  32   !;  12   ?;  44   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Polynomial_Opoly_type,type,
    c_Polynomial_Opoly: $i > $i > $i ).

thf(tc_Nat_Onat_type,type,
    tc_Nat_Onat: $i ).

thf(c_Nat_OSuc_type,type,
    c_Nat_OSuc: $i > $i ).

thf(v_cs_____type,type,
    v_cs____: $i ).

thf(c_If_type,type,
    c_If: $i > $i > $i > $i > $i ).

thf(sk__4_type,type,
    sk__4: $i ).

thf(sk__5_type,type,
    sk__5: $i ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_Groups_Ozero__class_Ozero_type,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

thf(sk__2_type,type,
    sk__2: $i ).

thf(v_c_____type,type,
    v_c____: $i ).

thf(c_Groups_Oplus__class_Oplus_type,type,
    c_Groups_Oplus__class_Oplus: $i > $i > $i > $i ).

thf(c_fequal_type,type,
    c_fequal: $i > $i > $i ).

thf(sk__3_type,type,
    sk__3: $i ).

thf(c_Polynomial_OpCons_type,type,
    c_Polynomial_OpCons: $i > $i > $i > $i ).

thf(c_Power_Opower__class_Opower_type,type,
    c_Power_Opower__class_Opower: $i > $i ).

thf(tc_Polynomial_Opoly_type,type,
    tc_Polynomial_Opoly: $i > $i ).

thf(c_Polynomial_Odegree_type,type,
    c_Polynomial_Odegree: $i > $i > $i ).

thf(sk__6_type,type,
    sk__6: $i ).

thf(sk__7_type,type,
    sk__7: $i ).

thf(c_Groups_Otimes__class_Otimes_type,type,
    c_Groups_Otimes__class_Otimes: $i > $i ).

thf(class_Rings_Oidom_type,type,
    class_Rings_Oidom: $i > $o ).

thf(sk__30_type,type,
    sk__30: $i > $i > $i > $i ).

thf(t_a_type,type,
    t_a: $i ).

thf(fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096,axiom,
    ( ( class_Rings_Oidom @ t_a )
   => ( ( v_c____
        = ( c_Groups_Ozero__class_Ozero @ t_a ) )
     => ? [B_k: $i,B_a: $i] :
          ( ? [B_q: $i] :
              ( ! [B_z: $i] :
                  ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ B_z )
                  = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B_z ) @ B_k ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ B_a @ B_q ) ) @ B_z ) ) )
              & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
                 != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
               => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                  = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) )
              & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
                  = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
               => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                  = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          & ( B_a
           != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ) ) ).

thf(zip_derived_cl9,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) @ sk__5 ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(fact_nat__add__commute,axiom,
    ! [V_n: $i,V_m: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_m @ V_n )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ V_n @ V_m ) ) ).

thf(zip_derived_cl92,plain,
    ! [X0: $i,X1: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X1 @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_nat__add__commute]) ).

thf(tfree_0,axiom,
    class_Rings_Oidom @ t_a ).

thf(zip_derived_cl1047,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4043,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__5 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl9,zip_derived_cl92,zip_derived_cl1047]) ).

thf(zip_derived_cl8,plain,
    ! [X0: $i] :
      ( ( v_c____
       != ( c_Groups_Ozero__class_Ozero @ t_a ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ X0 )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ X0 ) @ sk__5 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ sk__6 @ sk__7 ) ) @ X0 ) ) )
      | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl1047_001,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4032,plain,
    ! [X0: $i] :
      ( ( v_c____
       != ( c_Groups_Ozero__class_Ozero @ t_a ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ X0 )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ X0 ) @ sk__5 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ sk__6 @ sk__7 ) ) @ X0 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8,zip_derived_cl1047]) ).

thf(conj_0,conjecture,
    ? [B_k: $i,B_a: $i] :
      ( ? [B_q: $i] :
          ( ! [B_z: $i] :
              ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ B_z )
              = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B_z ) @ B_k ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ B_a @ B_q ) ) @ B_z ) ) )
          & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
             != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
           => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
              = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) )
          & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
              = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
           => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
              = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
      & ( B_a
       != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ? [B_k: $i,B_a: $i] :
        ( ? [B_q: $i] :
            ( ! [B_z: $i] :
                ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ B_z )
                = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B_z ) @ B_k ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ B_a @ B_q ) ) @ B_z ) ) )
            & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
               != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
             => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) )
            & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
                = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
             => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
        & ( B_a
         != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl1051,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
        = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
      | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ X0 ) ) ) @ X1 ) )
       != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) @ X1 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ X2 @ X0 ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) ) )
      | ( X2
        = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl10,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) @ sk__5 ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl92_002,plain,
    ! [X0: $i,X1: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X1 @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_nat__add__commute]) ).

thf(zip_derived_cl1047_003,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4050,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__5 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl10,zip_derived_cl92,zip_derived_cl1047]) ).

thf(fact_Zero__not__Suc,axiom,
    ! [V_m: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ V_m ) ) ).

thf(zip_derived_cl109,plain,
    ! [X0: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ X0 ) ),
    inference(cnf,[status(esa)],[fact_Zero__not__Suc]) ).

thf(zip_derived_cl4051,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl4050,zip_derived_cl109]) ).

thf(fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096,axiom,
    ( ( class_Rings_Oidom @ t_a )
   => ( ( v_c____
       != ( c_Groups_Ozero__class_Ozero @ t_a ) )
     => ? [B_k: $i,B_a: $i] :
          ( ? [B_q: $i] :
              ( ! [B_z: $i] :
                  ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ B_z )
                  = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ B_z ) @ B_k ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ B_a @ B_q ) ) @ B_z ) ) )
              & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
                 != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
               => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                  = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) )
              & ( ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
                  = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
               => ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ B_q @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ B_q ) ) ) @ B_k ) )
                  = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
          & ( B_a
           != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ) ) ) ).

thf(zip_derived_cl6,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) @ sk__2 ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl1047_004,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4022,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) @ sk__2 ) )
      = ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl6,zip_derived_cl1047]) ).

thf(zip_derived_cl109_005,plain,
    ! [X0: $i] :
      ( ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat )
     != ( c_Nat_OSuc @ X0 ) ),
    inference(cnf,[status(esa)],[fact_Zero__not__Suc]) ).

thf(zip_derived_cl4023,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
     != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl4022,zip_derived_cl109]) ).

thf(zip_derived_cl4052,plain,
    ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4051,zip_derived_cl4023]) ).

thf(zip_derived_cl50326,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ X0 ) ) ) @ X1 ) )
       != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) @ X1 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ X2 @ X0 ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) ) )
      | ( X2
        = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1051,zip_derived_cl4052]) ).

thf(zip_derived_cl50330,plain,
    ( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__7 @ sk__6 @ sk__5 ) )
     != ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__7 @ sk__6 @ sk__5 ) ) )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__6
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) @ sk__5 ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4032,zip_derived_cl50326]) ).

thf(zip_derived_cl92_006,plain,
    ! [X0: $i,X1: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X1 @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_nat__add__commute]) ).

thf(zip_derived_cl50342,plain,
    ( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__7 @ sk__6 @ sk__5 ) )
     != ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__7 @ sk__6 @ sk__5 ) ) )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__6
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__5 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl50330,zip_derived_cl92]) ).

thf(zip_derived_cl50343,plain,
    ( ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__5 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ( sk__6
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl50342]) ).

thf(zip_derived_cl50344,plain,
    ( ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__5 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__7 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__7 ) ) ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ( sk__6 = v_c____ )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl50343]) ).

thf(zip_derived_cl50349,plain,
    ( ( ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__6 = v_c____ ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4043,zip_derived_cl50344]) ).

thf(zip_derived_cl50355,plain,
    ( ( sk__6 = v_c____ )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl50349]) ).

thf(zip_derived_cl4052_007,plain,
    ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4051,zip_derived_cl4023]) ).

thf(zip_derived_cl50356,plain,
    ( ( sk__6 = v_c____ )
    | ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl50355,zip_derived_cl4052]) ).

thf(zip_derived_cl4,plain,
    ! [X0: $i] :
      ( ( v_c____
        = ( c_Groups_Ozero__class_Ozero @ t_a ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ X0 )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ X0 ) @ sk__2 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ sk__3 @ sk__4 ) ) @ X0 ) ) )
      | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl1047_008,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4011,plain,
    ! [X0: $i] :
      ( ( v_c____
        = ( c_Groups_Ozero__class_Ozero @ t_a ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ X0 )
        = ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ X0 ) @ sk__2 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ sk__3 @ sk__4 ) ) @ X0 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4,zip_derived_cl1047]) ).

thf(zip_derived_cl50326_009,plain,
    ! [X0: $i,X1: $i,X2: $i] :
      ( ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ X0 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ X0 ) ) ) @ X1 ) )
       != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
      | ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) )
       != ( hAPP @ ( hAPP @ ( c_Groups_Otimes__class_Otimes @ t_a ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ t_a ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) @ X1 ) ) @ ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ X2 @ X0 ) ) @ ( sk__30 @ X0 @ X2 @ X1 ) ) ) )
      | ( X2
        = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl1051,zip_derived_cl4052]) ).

thf(zip_derived_cl50329,plain,
    ( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__4 @ sk__3 @ sk__2 ) )
     != ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__4 @ sk__3 @ sk__2 ) ) )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__3
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) @ sk__2 ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference('sup-',[status(thm)],[zip_derived_cl4011,zip_derived_cl50326]) ).

thf(zip_derived_cl92_010,plain,
    ! [X0: $i,X1: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X1 @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_nat__add__commute]) ).

thf(zip_derived_cl50340,plain,
    ( ( ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__4 @ sk__3 @ sk__2 ) )
     != ( hAPP @ ( c_Polynomial_Opoly @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) @ ( sk__30 @ sk__4 @ sk__3 @ sk__2 ) ) )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__3
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__2 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl50329,zip_derived_cl92]) ).

thf(zip_derived_cl50341,plain,
    ( ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__2 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) ) )
     != ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ( sk__3
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl50340]) ).

thf(zip_derived_cl5,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) @ sk__2 ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl1047_011,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4013,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) @ sk__2 ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl5,zip_derived_cl1047]) ).

thf(zip_derived_cl92_012,plain,
    ! [X0: $i,X1: $i] :
      ( ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X1 @ X0 )
      = ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ X0 @ X1 ) ),
    inference(cnf,[status(esa)],[fact_nat__add__commute]) ).

thf(zip_derived_cl4034,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
      = ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__2 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4013,zip_derived_cl92]) ).

thf(zip_derived_cl4052_013,plain,
    ( ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ )
   != ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl4051,zip_derived_cl4023]) ).

thf(zip_derived_cl44289,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( ( c_Nat_OSuc @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat @ sk__2 @ ( c_If @ tc_Nat_Onat @ ( c_fequal @ sk__4 @ ( c_Groups_Ozero__class_Ozero @ ( tc_Polynomial_Opoly @ t_a ) ) ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ sk__4 ) ) ) ) )
      = ( c_Nat_OSuc @ ( c_Polynomial_Odegree @ t_a @ ( c_Polynomial_OpCons @ t_a @ v_c____ @ v_cs____ ) ) ) ) ),
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl4034,zip_derived_cl4052]) ).

thf(zip_derived_cl50745,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__3
      = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl50341,zip_derived_cl44289]) ).

thf(zip_derived_cl3,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__3
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_126_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl4004,plain,
    ( ( v_c____ = sk__3 )
    | ( sk__3
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(local_rewriting,[status(thm)],[zip_derived_cl3]) ).

thf(zip_derived_cl1047_014,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4010,plain,
    ( ( v_c____ = sk__3 )
    | ( sk__3
     != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl4004,zip_derived_cl1047]) ).

thf(zip_derived_cl50775,plain,
    ( ( sk__3 != sk__3 )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( v_c____ = sk__3 ) ),
    inference('sup-',[status(thm)],[zip_derived_cl50745,zip_derived_cl4010]) ).

thf(zip_derived_cl50779,plain,
    ( ( v_c____ = sk__3 )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(simplify,[status(thm)],[zip_derived_cl50775]) ).

thf(zip_derived_cl50745_015,plain,
    ( ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__3
      = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(clc,[status(thm)],[zip_derived_cl50341,zip_derived_cl44289]) ).

thf(zip_derived_cl50777,plain,
    ( ( sk__3 != v_c____ )
    | ( v_c____
      = ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(eq_fact,[status(thm)],[zip_derived_cl50745]) ).

thf(zip_derived_cl50816,plain,
    ( v_c____
    = ( c_Groups_Ozero__class_Ozero @ t_a ) ),
    inference(clc,[status(thm)],[zip_derived_cl50779,zip_derived_cl50777]) ).

thf(zip_derived_cl50844,plain,
    ( ( sk__6 = v_c____ )
    | ( v_c____ != v_c____ ) ),
    inference(demod,[status(thm)],[zip_derived_cl50356,zip_derived_cl50816]) ).

thf(zip_derived_cl50845,plain,
    sk__6 = v_c____,
    inference(simplify,[status(thm)],[zip_derived_cl50844]) ).

thf(zip_derived_cl7,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__6
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ~ ( class_Rings_Oidom @ t_a ) ),
    inference(cnf,[status(esa)],[fact__096c_A_061_A_I0_058_058_Ha_J_061_061_062_AEX_Ak_Aa_Aq_O_Aa_A_126_061_A_I0_058_058_Ha_J_A_G_ASuc_A_I_Iif_Aq_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_Aq_J_J_A_L_Ak_J_A_061_A_Iif_ApCons_Ac_Acs_A_061_A0_Athen_A0_Aelse_ASuc_A_Idegree_A_IpCons_Ac_Acs_J_J_J_A_G_A_IALL_Az_O_Apoly_A_IpCons_Ac_Acs_J_Az_A_061_Az_A_094_Ak_A_K_Apoly_A_IpCons_Aa_Aq_J_Az_J_096]) ).

thf(zip_derived_cl1047_016,plain,
    class_Rings_Oidom @ t_a,
    inference(cnf,[status(esa)],[tfree_0]) ).

thf(zip_derived_cl4009,plain,
    ( ( v_c____
     != ( c_Groups_Ozero__class_Ozero @ t_a ) )
    | ( sk__6
     != ( c_Groups_Ozero__class_Ozero @ t_a ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl7,zip_derived_cl1047]) ).

thf(zip_derived_cl50816_017,plain,
    ( v_c____
    = ( c_Groups_Ozero__class_Ozero @ t_a ) ),
    inference(clc,[status(thm)],[zip_derived_cl50779,zip_derived_cl50777]) ).

thf(zip_derived_cl50816_018,plain,
    ( v_c____
    = ( c_Groups_Ozero__class_Ozero @ t_a ) ),
    inference(clc,[status(thm)],[zip_derived_cl50779,zip_derived_cl50777]) ).

thf(zip_derived_cl50819,plain,
    ( ( v_c____ != v_c____ )
    | ( sk__6 != v_c____ ) ),
    inference(demod,[status(thm)],[zip_derived_cl4009,zip_derived_cl50816,zip_derived_cl50816]) ).

thf(zip_derived_cl50820,plain,
    sk__6 != v_c____,
    inference(simplify,[status(thm)],[zip_derived_cl50819]) ).

thf(zip_derived_cl50885,plain,
    $false,
    inference('simplify_reflect-',[status(thm)],[zip_derived_cl50845,zip_derived_cl50820]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.JdO3jM3QFk true
% 0.13/0.37  % Computer : n024.cluster.edu
% 0.13/0.37  % Model    : x86_64 x86_64
% 0.13/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37  % Memory   : 8042.1875MB
% 0.13/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.37  % CPULimit : 300
% 0.13/0.37  % WCLimit  : 300
% 0.13/0.37  % DateTime : Sun Aug 27 22:38:38 EDT 2023
% 0.13/0.37  % CPUTime  : 
% 0.13/0.37  % Running portfolio for 300 s
% 0.13/0.37  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.37  % Number of cores: 8
% 0.13/0.38  % Python version: Python 3.6.8
% 0.13/0.38  % Running in FO mode
% 0.20/0.70  % Total configuration time : 435
% 0.20/0.70  % Estimated wc time : 1092
% 0.20/0.70  % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.73  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.76  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.53/0.78  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.53/0.78  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.53/0.78  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.53/0.79  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 0.55/0.79  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 73.13/11.18  % Solved by fo/fo3_bce.sh.
% 73.13/11.18  % BCE start: 1052
% 73.13/11.18  % BCE eliminated: 189
% 73.13/11.18  % PE start: 863
% 73.13/11.18  logic: eq
% 73.13/11.18  % PE eliminated: 13
% 73.13/11.18  % done 1529 iterations in 10.396s
% 73.13/11.18  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 73.13/11.18  % SZS output start Refutation
% See solution above
% 73.13/11.18  
% 73.13/11.18  
% 73.13/11.18  % Terminating...
% 73.82/11.30  % Runner terminated.
% 73.82/11.31  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------