TSTP Solution File: SWW245+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n023.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 May  3 03:24:37 EDT 2024

% Result   : Theorem 28.60s 4.66s
% Output   : CNFRefutation 28.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   76 (  17 unt;   0 def)
%            Number of atoms       :  295 ( 261 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  355 ( 136   ~; 129   |;  63   &)
%                                         (   0 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-4 aty)
%            Number of variables   :  107 (   1 sgn  45   !;  45   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4,axiom,
    ( class_Rings_Oidom(t_a)
   => ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
     => ? [X4,X5] :
          ( ? [X6] :
              ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
              & ( 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(X6,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,X6))),X4)) = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,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,X6))),X4)) ) )
          & c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',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) ).

fof(f5,axiom,
    ( class_Rings_Oidom(t_a)
   => ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
     => ? [X4,X5] :
          ( ? [X6] :
              ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
              & ( 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(X6,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,X6))),X4)) = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,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,X6))),X4)) ) )
          & c_Groups_Ozero__class_Ozero(t_a) != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',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) ).

fof(f91,axiom,
    ! [X21] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X21),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(f188,axiom,
    ! [X18] : c_Nat_OSuc(X18) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X18),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(f1160,conjecture,
    ? [X4,X5] :
      ( ? [X6] :
          ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
          & ( 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(X6,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,X6))),X4)) = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,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,X6))),X4)) ) )
      & c_Groups_Ozero__class_Ozero(t_a) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1161,negated_conjecture,
    ~ ? [X4,X5] :
        ( ? [X6] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X4)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X5,X6)),X3))
            & ( 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(X6,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,X6))),X4)) = 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_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X6,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,X6))),X4)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X5 ),
    inference(negated_conjecture,[],[f1160]) ).

fof(f1162,axiom,
    class_Rings_Oidom(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

fof(f1165,plain,
    ( class_Rings_Oidom(t_a)
   => ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
     => ? [X0,X1] :
          ( ? [X2] :
              ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) )
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) ) )
          & c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ),
    inference(rectify,[],[f4]) ).

fof(f1166,plain,
    ( class_Rings_Oidom(t_a)
   => ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
     => ? [X0,X1] :
          ( ? [X2] :
              ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) )
              & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
               => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) ) )
          & c_Groups_Ozero__class_Ozero(t_a) != X1 ) ) ),
    inference(rectify,[],[f5]) ).

fof(f1252,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(rectify,[],[f91]) ).

fof(f1347,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(rectify,[],[f188]) ).

fof(f2231,plain,
    ~ ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
             => c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) )
            & ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
             => c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 ),
    inference(rectify,[],[f1161]) ).

fof(f2420,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(ennf_transformation,[],[f1165]) ).

fof(f2421,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(flattening,[],[f2420]) ).

fof(f2422,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(ennf_transformation,[],[f1166]) ).

fof(f2423,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(flattening,[],[f2422]) ).

fof(f3331,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ? [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
          | ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
            & c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
            & c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
      | c_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(ennf_transformation,[],[f2231]) ).

fof(f3342,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
   => ( ? [X2] :
          ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,X2)),X3))
          & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK5))
            | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK5))
            | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
      & c_Groups_Ozero__class_Ozero(t_a) != sK6 ) ),
    introduced(choice_axiom,[]) ).

fof(f3343,plain,
    ( ? [X2] :
        ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,X2)),X3))
        & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK5))
          | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK5))
          | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
   => ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3))
      & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f3344,plain,
    ( ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3))
      & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & c_Groups_Ozero__class_Ozero(t_a) != sK6 )
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f2421,f3343,f3342]) ).

fof(f3345,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
            & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
            & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
              | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
        & c_Groups_Ozero__class_Ozero(t_a) != X1 )
   => ( ? [X2] :
          ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,X2)),X3))
          & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK8))
            | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
          & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK8))
            | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
      & c_Groups_Ozero__class_Ozero(t_a) != sK9 ) ),
    introduced(choice_axiom,[]) ).

fof(f3346,plain,
    ( ? [X2] :
        ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,X2)),X3))
        & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK8))
          | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
        & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),sK8))
          | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
   => ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3))
      & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f3347,plain,
    ( ( ! [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3))
      & ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
        | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
      & c_Groups_Ozero__class_Ozero(t_a) != sK9 )
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f2423,f3346,f3345]) ).

fof(f3618,plain,
    ! [X0,X1,X2] :
      ( ? [X3] : hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),X3))
     => hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) ),
    introduced(choice_axiom,[]) ).

fof(f3619,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2)))
          | ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
            & c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) )
          | ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
            & c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) )
      | c_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f3331,f3618]) ).

fof(f3625,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != sK6
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3344]) ).

fof(f3626,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3344]) ).

fof(f3627,plain,
    ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,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,sK7))),sK5))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3344]) ).

fof(f3628,plain,
    ! [X3] :
      ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X3))
      | c_Groups_Ozero__class_Ozero(t_a) = v_c____
      | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3344]) ).

fof(f3629,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != sK9
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3347]) ).

fof(f3630,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3347]) ).

fof(f3631,plain,
    ( c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,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,sK10))),sK8))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3347]) ).

fof(f3632,plain,
    ! [X3] :
      ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X3),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X3))
      | c_Groups_Ozero__class_Ozero(t_a) != v_c____
      | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3347]) ).

fof(f3759,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
    inference(cnf_transformation,[],[f1252]) ).

fof(f3874,plain,
    ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(cnf_transformation,[],[f1347]) ).

fof(f4923,plain,
    ! [X2,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2)))
      | c_Nat_OSuc(c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,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,X2))),X0))
      | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
      | c_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(cnf_transformation,[],[f3619]) ).

fof(f4925,plain,
    class_Rings_Oidom(t_a),
    inference(cnf_transformation,[],[f1162]) ).

fof(f4926,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(definition_unfolding,[],[f3627,f3874,f3874,f3874]) ).

fof(f4927,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(definition_unfolding,[],[f3626,f3874,f3874]) ).

fof(f4928,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(definition_unfolding,[],[f3631,f3874,f3874,f3874]) ).

fof(f4929,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8))
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a) ),
    inference(definition_unfolding,[],[f3630,f3874,f3874]) ).

fof(f4964,plain,
    ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0),
    inference(definition_unfolding,[],[f3759,f3874]) ).

fof(f5056,plain,
    ! [X2,X0,X1] :
      ( hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2)))
      | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0))
      | c_Polynomial_OpCons(t_a,v_c____,v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
      | c_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(definition_unfolding,[],[f4923,f3874,f3874,f3874]) ).

cnf(c_54,plain,
    ( ~ class_Rings_Oidom(t_a)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cnf_transformation,[],[f3628]) ).

cnf(c_55,plain,
    ( ~ class_Rings_Oidom(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cnf_transformation,[],[f4926]) ).

cnf(c_56,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | ~ class_Rings_Oidom(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cnf_transformation,[],[f4927]) ).

cnf(c_57,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != sK6
    | ~ class_Rings_Oidom(t_a)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(cnf_transformation,[],[f3625]) ).

cnf(c_58,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) ),
    inference(cnf_transformation,[],[f3632]) ).

cnf(c_59,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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)) ),
    inference(cnf_transformation,[],[f4928]) ).

cnf(c_60,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | ~ class_Rings_Oidom(t_a)
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(cnf_transformation,[],[f4929]) ).

cnf(c_61,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != sK9
    | ~ class_Rings_Oidom(t_a) ),
    inference(cnf_transformation,[],[f3629]) ).

cnf(c_177,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(cnf_transformation,[],[f4964]) ).

cnf(c_1296,negated_conjecture,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),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_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(cnf_transformation,[],[f5056]) ).

cnf(c_1298,plain,
    class_Rings_Oidom(t_a),
    inference(cnf_transformation,[],[f4925]) ).

cnf(c_2052,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != sK6
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(global_subsumption_just,[status(thm)],[c_57,c_1298,c_57]) ).

cnf(c_2088,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(global_subsumption_just,[status(thm)],[c_56,c_1298,c_56]) ).

cnf(c_2090,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(global_subsumption_just,[status(thm)],[c_60,c_1298,c_60]) ).

cnf(c_2091,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(renaming,[status(thm)],[c_2090]) ).

cnf(c_5451,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(backward_subsumption_resolution,[status(thm)],[c_2088,c_177]) ).

cnf(c_5452,plain,
    ( c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(t_a) != v_c____ ),
    inference(backward_subsumption_resolution,[status(thm)],[c_2091,c_177]) ).

cnf(c_5455,plain,
    c_Polynomial_OpCons(t_a,v_c____,v_cs____) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(global_subsumption_just,[status(thm)],[c_5451,c_5452,c_5451]) ).

cnf(c_5479,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(t_a) = X1 ),
    inference(backward_subsumption_resolution,[status(thm)],[c_1296,c_5455]) ).

cnf(c_42661,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) ),
    inference(prop_impl_just,[status(thm)],[c_1298,c_58]) ).

cnf(c_42663,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) != v_c____
    | c_Groups_Ozero__class_Ozero(t_a) != sK9 ),
    inference(prop_impl_just,[status(thm)],[c_1298,c_61]) ).

cnf(c_42669,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) ),
    inference(prop_impl_just,[status(thm)],[c_1298,c_54]) ).

cnf(c_42670,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK5)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK6,sK7)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0)
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____ ),
    inference(renaming,[status(thm)],[c_42669]) ).

cnf(c_78861,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK7,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK7))),sK5)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | c_Groups_Ozero__class_Ozero(t_a) = v_c____
    | c_Groups_Ozero__class_Ozero(t_a) = sK6 ),
    inference(superposition,[status(thm)],[c_42670,c_5479]) ).

cnf(c_78879,plain,
    c_Groups_Ozero__class_Ozero(t_a) = v_c____,
    inference(global_subsumption_just,[status(thm)],[c_78861,c_1298,c_55,c_2052,c_5455,c_78861]) ).

cnf(c_78884,plain,
    ( v_c____ != v_c____
    | v_c____ != sK9 ),
    inference(demodulation,[status(thm)],[c_42663,c_78879]) ).

cnf(c_78885,plain,
    ( v_c____ != v_c____
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0) ),
    inference(demodulation,[status(thm)],[c_42661,c_78879]) ).

cnf(c_78893,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),sK32(X0,X1,X2)),X0)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,X1,X2)),sK32(X0,X1,X2))) != hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),sK32(X0,X1,X2))
    | c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,X2))),X0)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | X1 = v_c____ ),
    inference(demodulation,[status(thm)],[c_5479,c_78879]) ).

cnf(c_78894,plain,
    v_c____ != sK9,
    inference(equality_resolution_simp,[status(thm)],[c_78884]) ).

cnf(c_78901,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),X0),sK8)),hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,sK9,sK10)),X0)) = hAPP(c_Polynomial_Opoly(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)),X0),
    inference(equality_resolution_simp,[status(thm)],[c_78885]) ).

cnf(c_78997,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____)))
    | v_c____ = sK9 ),
    inference(superposition,[status(thm)],[c_78901,c_78893]) ).

cnf(c_78998,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_If(tc_Nat_Onat,c_fequal(sK10,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,sK10))),sK8)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Polynomial_Odegree(t_a,c_Polynomial_OpCons(t_a,v_c____,v_cs____))),
    inference(forward_subsumption_resolution,[status(thm)],[c_78997,c_78894]) ).

cnf(c_78999,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_78998,c_78879,c_5455,c_59,c_1298]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n023.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 22:43:39 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.60/4.66  % SZS status Started for theBenchmark.p
% 28.60/4.66  % SZS status Theorem for theBenchmark.p
% 28.60/4.66  
% 28.60/4.66  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 28.60/4.66  
% 28.60/4.66  ------  iProver source info
% 28.60/4.66  
% 28.60/4.66  git: date: 2024-05-02 19:28:25 +0000
% 28.60/4.66  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 28.60/4.66  git: non_committed_changes: false
% 28.60/4.66  
% 28.60/4.66  ------ Parsing...
% 28.60/4.66  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 28.60/4.66  
% 28.60/4.66  ------ Preprocessing... sup_sim: 73  sf_s  rm: 6 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 30  sf_s  rm: 9 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 9 0s  sf_e  pe_s  pe_e 
% 28.60/4.66  
% 28.60/4.66  ------ Preprocessing... gs_s  sp: 2 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 28.60/4.66  
% 28.60/4.66  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 28.60/4.66  ------ Proving...
% 28.60/4.66  ------ Problem Properties 
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  clauses                                 1026
% 28.60/4.66  conjectures                             0
% 28.60/4.66  EPR                                     108
% 28.60/4.66  Horn                                    890
% 28.60/4.66  unary                                   225
% 28.60/4.66  binary                                  435
% 28.60/4.66  lits                                    2328
% 28.60/4.66  lits eq                                 780
% 28.60/4.66  fd_pure                                 0
% 28.60/4.66  fd_pseudo                               0
% 28.60/4.66  fd_cond                                 74
% 28.60/4.66  fd_pseudo_cond                          80
% 28.60/4.66  AC symbols                              0
% 28.60/4.66  
% 28.60/4.66  ------ Schedule dynamic 5 is on 
% 28.60/4.66  
% 28.60/4.66  ------ no conjectures: strip conj schedule 
% 28.60/4.66  
% 28.60/4.66  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  ------ 
% 28.60/4.66  Current options:
% 28.60/4.66  ------ 
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  ------ Proving...
% 28.60/4.66  
% 28.60/4.66  
% 28.60/4.66  % SZS status Theorem for theBenchmark.p
% 28.60/4.66  
% 28.60/4.66  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 28.60/4.66  
% 28.60/4.67  
%------------------------------------------------------------------------------