TSTP Solution File: SWW186+1 by iProver---3.8

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%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n028.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 00:38:26 EDT 2023

% Result   : Theorem 97.37s 13.84s
% Output   : CNFRefutation 97.37s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   55 (  16 unt;   0 def)
%            Number of atoms       :  119 (  79 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  107 (  43   ~;  39   |;   9   &)
%                                         (   3 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   92 (   6 sgn;  70   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X3,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__single) ).

fof(f4,axiom,
    ! [X3,X6,X5,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,c_Polynomial_OpCons(X4,X5,X6),X3) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X6,X3)),c_Polynomial_OpCons(X4,X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X4,X6,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__pCons) ).

fof(f5,axiom,
    ! [X5,X6,X7,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X7,X6),c_Polynomial_OpCons(X4,X5,X6))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X6 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_offset__poly__eq__0__lemma) ).

fof(f12,axiom,
    ! [X10,X11,X12] :
      ( class_Groups_Ozero(X12)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) = c_Polynomial_OpCons(X12,X11,X10)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X12)) = X10
          & c_Groups_Ozero__class_Ozero(X12) = X11 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pCons__eq__0__iff) ).

fof(f1003,axiom,
    ! [X86] :
      ( class_Rings_Ocomm__semiring__0(X86)
     => class_Groups_Ozero(X86) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).

fof(f1179,axiom,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
   => v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

fof(f1180,axiom,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

fof(f1181,conjecture,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    & v_a = c_Groups_Ozero__class_Ozero(t_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).

fof(f1182,negated_conjecture,
    ~ ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
      & v_a = c_Groups_Ozero__class_Ozero(t_a) ),
    inference(negated_conjecture,[],[f1181]) ).

fof(f1183,axiom,
    class_Rings_Ocomm__semiring__0(t_a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).

fof(f1185,plain,
    ! [X0,X1,X2] :
      ( class_Rings_Ocomm__semiring__0(X2)
     => c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0) ),
    inference(rectify,[],[f3]) ).

fof(f1186,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0))) ),
    inference(rectify,[],[f4]) ).

fof(f1187,plain,
    ! [X0,X1,X2,X3] :
      ( class_Rings_Ocomm__semiring__0(X3)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
       => c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1 ) ),
    inference(rectify,[],[f5]) ).

fof(f1194,plain,
    ! [X0,X1,X2] :
      ( class_Groups_Ozero(X2)
     => ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
    inference(rectify,[],[f12]) ).

fof(f2179,plain,
    ! [X0] :
      ( class_Rings_Ocomm__semiring__0(X0)
     => class_Groups_Ozero(X0) ),
    inference(rectify,[],[f1003]) ).

fof(f2365,plain,
    ! [X0,X1,X2] :
      ( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(ennf_transformation,[],[f1185]) ).

fof(f2366,plain,
    ! [X0,X1,X2,X3] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f1186]) ).

fof(f2367,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(ennf_transformation,[],[f1187]) ).

fof(f2368,plain,
    ! [X0,X1,X2,X3] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(flattening,[],[f2367]) ).

fof(f2376,plain,
    ! [X0,X1,X2] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
      <=> ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
          & c_Groups_Ozero__class_Ozero(X2) = X1 ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(ennf_transformation,[],[f1194]) ).

fof(f3377,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(ennf_transformation,[],[f2179]) ).

fof(f3441,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(ennf_transformation,[],[f1179]) ).

fof(f3442,plain,
    ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_a != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(ennf_transformation,[],[f1182]) ).

fof(f3447,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(nnf_transformation,[],[f2376]) ).

fof(f3448,plain,
    ! [X0,X1,X2] :
      ( ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = c_Polynomial_OpCons(X2,X1,X0)
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != X0
          | c_Groups_Ozero__class_Ozero(X2) != X1 )
        & ( ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = X0
            & c_Groups_Ozero__class_Ozero(X2) = X1 )
          | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0) ) )
      | ~ class_Groups_Ozero(X2) ),
    inference(flattening,[],[f3447]) ).

fof(f3753,plain,
    ! [X2,X0,X1] :
      ( c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X2,c_Polynomial_OpCons(X2,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))),X0)
      | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(cnf_transformation,[],[f2365]) ).

fof(f3754,plain,
    ! [X2,X3,X0,X1] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,c_Polynomial_OpCons(X3,X2,X1),X0) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)),c_Polynomial_OpCons(X3,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X3,X1,X0)))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f2366]) ).

fof(f3755,plain,
    ! [X2,X3,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X3)) != c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X3),c_Polynomial_Osmult(X3,X2,X1),c_Polynomial_OpCons(X3,X0,X1))
      | ~ class_Rings_Ocomm__semiring__0(X3) ),
    inference(cnf_transformation,[],[f2368]) ).

fof(f3764,plain,
    ! [X2,X0,X1] :
      ( c_Groups_Ozero__class_Ozero(X2) = X1
      | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) != c_Polynomial_OpCons(X2,X1,X0)
      | ~ class_Groups_Ozero(X2) ),
    inference(cnf_transformation,[],[f3448]) ).

fof(f4969,plain,
    ! [X0] :
      ( class_Groups_Ozero(X0)
      | ~ class_Rings_Ocomm__semiring__0(X0) ),
    inference(cnf_transformation,[],[f3377]) ).

fof(f5139,plain,
    ( v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(cnf_transformation,[],[f3441]) ).

fof(f5140,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))),
    inference(cnf_transformation,[],[f1180]) ).

fof(f5141,plain,
    ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_a != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(cnf_transformation,[],[f3442]) ).

fof(f5142,plain,
    class_Rings_Ocomm__semiring__0(t_a),
    inference(cnf_transformation,[],[f1183]) ).

cnf(c_51,plain,
    ( ~ class_Rings_Ocomm__semiring__0(X0)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X2) = c_Polynomial_OpCons(X0,X1,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ),
    inference(cnf_transformation,[],[f3753]) ).

cnf(c_52,plain,
    ( ~ class_Rings_Ocomm__semiring__0(X0)
    | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1)),c_Polynomial_OpCons(X0,X3,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,X1))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,c_Polynomial_OpCons(X0,X3,X2),X1) ),
    inference(cnf_transformation,[],[f3754]) ).

cnf(c_53,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X0),c_Polynomial_Osmult(X0,X1,X2),c_Polynomial_OpCons(X0,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
    | ~ class_Rings_Ocomm__semiring__0(X0)
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2 ),
    inference(cnf_transformation,[],[f3755]) ).

cnf(c_64,plain,
    ( c_Polynomial_OpCons(X0,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))
    | ~ class_Groups_Ozero(X0)
    | c_Groups_Ozero__class_Ozero(X0) = X1 ),
    inference(cnf_transformation,[],[f3764]) ).

cnf(c_1203,plain,
    ( ~ class_Rings_Ocomm__semiring__0(X0)
    | class_Groups_Ozero(X0) ),
    inference(cnf_transformation,[],[f4969]) ).

cnf(c_1373,plain,
    ( c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p ),
    inference(cnf_transformation,[],[f5139]) ).

cnf(c_1374,plain,
    c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)),c_Polynomial_OpCons(t_a,v_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(cnf_transformation,[],[f5140]) ).

cnf(c_1375,negated_conjecture,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p
    | c_Groups_Ozero__class_Ozero(t_a) != v_a ),
    inference(cnf_transformation,[],[f5141]) ).

cnf(c_1376,plain,
    class_Rings_Ocomm__semiring__0(t_a),
    inference(cnf_transformation,[],[f5142]) ).

cnf(c_3306,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),X1) = c_Polynomial_OpCons(t_a,X0,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),
    inference(superposition,[status(thm)],[c_1376,c_51]) ).

cnf(c_3324,plain,
    c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,X0,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0)),c_Polynomial_OpCons(t_a,X2,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,X1,X0))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X2,X1),X0),
    inference(superposition,[status(thm)],[c_1376,c_52]) ).

cnf(c_3417,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,v_a,v_p),v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(superposition,[status(thm)],[c_3324,c_1374]) ).

cnf(c_3817,plain,
    ( ~ class_Rings_Ocomm__semiring__0(t_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(superposition,[status(thm)],[c_1374,c_53]) ).

cnf(c_3821,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(global_subsumption_just,[status(thm)],[c_3817,c_1376,c_3817]) ).

cnf(c_3835,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
    inference(backward_subsumption_resolution,[status(thm)],[c_1373,c_3821]) ).

cnf(c_3955,plain,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,c_Polynomial_OpCons(t_a,X0,v_p),X1) = c_Polynomial_OpCons(t_a,X0,v_p),
    inference(superposition,[status(thm)],[c_3835,c_3306]) ).

cnf(c_4499,plain,
    c_Polynomial_OpCons(t_a,v_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(superposition,[status(thm)],[c_3955,c_3417]) ).

cnf(c_4501,plain,
    c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
    inference(light_normalisation,[status(thm)],[c_4499,c_3835]) ).

cnf(c_5068,plain,
    class_Groups_Ozero(t_a),
    inference(superposition,[status(thm)],[c_1376,c_1203]) ).

cnf(c_80905,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) != v_p
    | ~ class_Groups_Ozero(t_a)
    | c_Groups_Ozero__class_Ozero(t_a) = v_a ),
    inference(superposition,[status(thm)],[c_4501,c_64]) ).

cnf(c_80909,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_80905,c_5068,c_3817,c_1373,c_1375,c_1376]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW186+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14  % Command  : run_iprover %s %d THM
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Sun Aug 27 21:22:09 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.48  Running first-order theorem proving
% 0.22/0.48  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 97.37/13.84  % SZS status Started for theBenchmark.p
% 97.37/13.84  % SZS status Theorem for theBenchmark.p
% 97.37/13.84  
% 97.37/13.84  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 97.37/13.84  
% 97.37/13.84  ------  iProver source info
% 97.37/13.84  
% 97.37/13.84  git: date: 2023-05-31 18:12:56 +0000
% 97.37/13.84  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 97.37/13.84  git: non_committed_changes: false
% 97.37/13.84  git: last_make_outside_of_git: false
% 97.37/13.84  
% 97.37/13.84  ------ Parsing...
% 97.37/13.84  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 97.37/13.84  
% 97.37/13.84  ------ Preprocessing... sf_s  rm: 5 0s  sf_e  sf_s  rm: 2 0s  sf_e 
% 97.37/13.84  
% 97.37/13.84  ------ Preprocessing...
% 97.37/13.84  
% 97.37/13.84  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 97.37/13.84  ------ Proving...
% 97.37/13.84  ------ Problem Properties 
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  clauses                                 1104
% 97.37/13.84  conjectures                             1
% 97.37/13.84  EPR                                     163
% 97.37/13.84  Horn                                    1008
% 97.37/13.84  unary                                   227
% 97.37/13.84  binary                                  440
% 97.37/13.84  lits                                    2653
% 97.37/13.84  lits eq                                 611
% 97.37/13.84  fd_pure                                 0
% 97.37/13.84  fd_pseudo                               0
% 97.37/13.84  fd_cond                                 36
% 97.37/13.84  fd_pseudo_cond                          97
% 97.37/13.84  AC symbols                              0
% 97.37/13.84  
% 97.37/13.84  ------ Input Options Time Limit: Unbounded
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  ------ 
% 97.37/13.84  Current options:
% 97.37/13.84  ------ 
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  ------ Proving...
% 97.37/13.84  
% 97.37/13.84  
% 97.37/13.84  % SZS status Theorem for theBenchmark.p
% 97.37/13.84  
% 97.37/13.84  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 97.37/13.84  
% 97.37/13.84  
%------------------------------------------------------------------------------