TSTP Solution File: SWW186+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW186+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Mar  6 14:50:40 EST 2011

% Result   : Theorem 5.14s
% Output   : CNFRefutation 5.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   59 (  15 unt;   0 def)
%            Number of atoms       :  129 (  80 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  122 (  52   ~;  52   |;   9   &)
%                                         (   1 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   70 (  10 sgn  42   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(272,axiom,
    ! [X52] :
      ( class_Rings_Ocomm__semiring__0(X52)
     => class_Groups_Ocomm__monoid__add(X52) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',clrel_Rings_Ocomm__semiring__0__Groups_Ocomm__monoid__add) ).

fof(281,axiom,
    ! [X3,X2,X14,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X14,X2),c_Polynomial_OpCons(X4,X3,X2)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
       => X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_offset__poly__eq__0__lemma) ).

fof(450,axiom,
    ! [X52] :
      ( class_Rings_Ocomm__semiring__0(X52)
     => class_Groups_Ozero(X52) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',clrel_Rings_Ocomm__semiring__0__Groups_Ozero) ).

fof(585,axiom,
    ! [X3,X4] :
      ( class_Rings_Ocomm__semiring__0(X4)
     => c_Polynomial_Osmult(X4,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_smult__0__right) ).

fof(603,axiom,
    ! [X28,X18,X19] :
      ( class_Groups_Ozero(X19)
     => ( c_Polynomial_OpCons(X19,X18,X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
      <=> ( X18 = c_Groups_Ozero__class_Ozero(X19)
          & X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_pCons__eq__0__iff) ).

fof(719,axiom,
    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)),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_1) ).

fof(722,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('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_0) ).

fof(788,axiom,
    ! [X1,X4] :
      ( class_Groups_Ocomm__monoid__add(X4)
     => c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X1) = X1 ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',fact_add__poly__code_I1_J) ).

fof(1105,conjecture,
    ( v_a = c_Groups_Ozero__class_Ozero(t_a)
    & v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',conj_2) ).

fof(1148,axiom,
    class_Rings_Ocomm__semiring__0(t_a),
    file('/tmp/tmp_ggpwJ/sel_SWW186+1.p_1',tfree_0) ).

fof(1183,negated_conjecture,
    ~ ( v_a = c_Groups_Ozero__class_Ozero(t_a)
      & v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(assume_negation,[status(cth)],[1105]) ).

fof(2149,plain,
    ! [X52] :
      ( ~ class_Rings_Ocomm__semiring__0(X52)
      | class_Groups_Ocomm__monoid__add(X52) ),
    inference(fof_nnf,[status(thm)],[272]) ).

fof(2150,plain,
    ! [X53] :
      ( ~ class_Rings_Ocomm__semiring__0(X53)
      | class_Groups_Ocomm__monoid__add(X53) ),
    inference(variable_rename,[status(thm)],[2149]) ).

cnf(2151,plain,
    ( class_Groups_Ocomm__monoid__add(X1)
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[2150]) ).

fof(2181,plain,
    ! [X3,X2,X14,X4] :
      ( ~ class_Rings_Ocomm__semiring__0(X4)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Polynomial_Osmult(X4,X14,X2),c_Polynomial_OpCons(X4,X3,X2)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))
      | X2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
    inference(fof_nnf,[status(thm)],[281]) ).

fof(2182,plain,
    ! [X15,X16,X17,X18] :
      ( ~ class_Rings_Ocomm__semiring__0(X18)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X18),c_Polynomial_Osmult(X18,X17,X16),c_Polynomial_OpCons(X18,X15,X16)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X18))
      | X16 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X18)) ),
    inference(variable_rename,[status(thm)],[2181]) ).

cnf(2183,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X2),c_Polynomial_Osmult(X2,X3,X1),c_Polynomial_OpCons(X2,X4,X1)) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X2))
    | ~ class_Rings_Ocomm__semiring__0(X2) ),
    inference(split_conjunct,[status(thm)],[2182]) ).

fof(2697,plain,
    ! [X52] :
      ( ~ class_Rings_Ocomm__semiring__0(X52)
      | class_Groups_Ozero(X52) ),
    inference(fof_nnf,[status(thm)],[450]) ).

fof(2698,plain,
    ! [X53] :
      ( ~ class_Rings_Ocomm__semiring__0(X53)
      | class_Groups_Ozero(X53) ),
    inference(variable_rename,[status(thm)],[2697]) ).

cnf(2699,plain,
    ( class_Groups_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[2698]) ).

fof(3121,plain,
    ! [X3,X4] :
      ( ~ class_Rings_Ocomm__semiring__0(X4)
      | c_Polynomial_Osmult(X4,X3,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) ),
    inference(fof_nnf,[status(thm)],[585]) ).

fof(3122,plain,
    ! [X5,X6] :
      ( ~ class_Rings_Ocomm__semiring__0(X6)
      | c_Polynomial_Osmult(X6,X5,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)) ),
    inference(variable_rename,[status(thm)],[3121]) ).

cnf(3123,plain,
    ( c_Polynomial_Osmult(X1,X2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[3122]) ).

fof(3181,plain,
    ! [X28,X18,X19] :
      ( ~ class_Groups_Ozero(X19)
      | ( ( c_Polynomial_OpCons(X19,X18,X28) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
          | ( X18 = c_Groups_Ozero__class_Ozero(X19)
            & X28 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) )
        & ( X18 != c_Groups_Ozero__class_Ozero(X19)
          | X28 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19))
          | c_Polynomial_OpCons(X19,X18,X28) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X19)) ) ) ),
    inference(fof_nnf,[status(thm)],[603]) ).

fof(3182,plain,
    ! [X29,X30,X31] :
      ( ~ class_Groups_Ozero(X31)
      | ( ( c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
          | ( X30 = c_Groups_Ozero__class_Ozero(X31)
            & X29 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31)) ) )
        & ( X30 != c_Groups_Ozero__class_Ozero(X31)
          | X29 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
          | c_Polynomial_OpCons(X31,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31)) ) ) ),
    inference(variable_rename,[status(thm)],[3181]) ).

fof(3183,plain,
    ! [X29,X30,X31] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(X31)
        | c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
        | ~ class_Groups_Ozero(X31) )
      & ( X29 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
        | c_Polynomial_OpCons(X31,X30,X29) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
        | ~ class_Groups_Ozero(X31) )
      & ( X30 != c_Groups_Ozero__class_Ozero(X31)
        | X29 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
        | c_Polynomial_OpCons(X31,X30,X29) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X31))
        | ~ class_Groups_Ozero(X31) ) ),
    inference(distribute,[status(thm)],[3182]) ).

cnf(3186,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Groups_Ozero(X1)
    | c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) ),
    inference(split_conjunct,[status(thm)],[3183]) ).

cnf(3549,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(split_conjunct,[status(thm)],[719]) ).

fof(3556,plain,
    ( 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)) ),
    inference(fof_nnf,[status(thm)],[722]) ).

cnf(3557,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(split_conjunct,[status(thm)],[3556]) ).

fof(3786,plain,
    ! [X1,X4] :
      ( ~ class_Groups_Ocomm__monoid__add(X4)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X4),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)),X1) = X1 ),
    inference(fof_nnf,[status(thm)],[788]) ).

fof(3787,plain,
    ! [X5,X6] :
      ( ~ class_Groups_Ocomm__monoid__add(X6)
      | c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X6),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X6)),X5) = X5 ),
    inference(variable_rename,[status(thm)],[3786]) ).

cnf(3788,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
    | ~ class_Groups_Ocomm__monoid__add(X1) ),
    inference(split_conjunct,[status(thm)],[3787]) ).

fof(4851,negated_conjecture,
    ( v_a != c_Groups_Ozero__class_Ozero(t_a)
    | v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(fof_nnf,[status(thm)],[1183]) ).

cnf(4852,negated_conjecture,
    ( v_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))
    | v_a != c_Groups_Ozero__class_Ozero(t_a) ),
    inference(split_conjunct,[status(thm)],[4851]) ).

cnf(4985,plain,
    class_Rings_Ocomm__semiring__0(t_a),
    inference(split_conjunct,[status(thm)],[1148]) ).

cnf(5376,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(X1),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2) = X2
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(spm,[status(thm)],[3788,2151,theory(equality)]) ).

cnf(5415,plain,
    ( c_Groups_Ozero__class_Ozero(X1) = X2
    | c_Polynomial_OpCons(X1,X2,X3) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))
    | ~ class_Rings_Ocomm__semiring__0(X1) ),
    inference(spm,[status(thm)],[3186,2699,theory(equality)]) ).

cnf(7217,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[2183,3549,theory(equality)]) ).

cnf(7220,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h)
    | $false ),
    inference(rw,[status(thm)],[7217,4985,theory(equality)]) ).

cnf(7221,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(t_a,v_p,v_h),
    inference(cn,[status(thm)],[7220,theory(equality)]) ).

cnf(55320,plain,
    c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),c_Polynomial_Osmult(t_a,v_h,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))),c_Polynomial_OpCons(t_a,v_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[3549,7221,theory(equality)]),7221,theory(equality)]) ).

cnf(55321,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p
    | $false ),
    inference(rw,[status(thm)],[3557,7221,theory(equality)]) ).

cnf(55322,plain,
    c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = v_p,
    inference(cn,[status(thm)],[55321,theory(equality)]) ).

cnf(55333,plain,
    ( c_Polynomial_Osmult(t_a,X1,v_p) = v_p
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[3123,55322,theory(equality)]) ).

cnf(55418,negated_conjecture,
    ( $false
    | c_Groups_Ozero__class_Ozero(t_a) != v_a ),
    inference(rw,[status(thm)],[4852,55322,theory(equality)]) ).

cnf(55419,negated_conjecture,
    c_Groups_Ozero__class_Ozero(t_a) != v_a,
    inference(cn,[status(thm)],[55418,theory(equality)]) ).

cnf(55420,plain,
    ( c_Polynomial_Osmult(t_a,X1,v_p) = v_p
    | $false ),
    inference(rw,[status(thm)],[55333,4985,theory(equality)]) ).

cnf(55421,plain,
    c_Polynomial_Osmult(t_a,X1,v_p) = v_p,
    inference(cn,[status(thm)],[55420,theory(equality)]) ).

cnf(58883,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1
    | ~ class_Rings_Ocomm__semiring__0(t_a) ),
    inference(spm,[status(thm)],[5376,55322,theory(equality)]) ).

cnf(58916,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1
    | $false ),
    inference(rw,[status(thm)],[58883,4985,theory(equality)]) ).

cnf(58917,plain,
    c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(t_a),v_p,X1) = X1,
    inference(cn,[status(thm)],[58916,theory(equality)]) ).

cnf(60778,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = X1
    | c_Polynomial_OpCons(t_a,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ),
    inference(spm,[status(thm)],[5415,4985,theory(equality)]) ).

cnf(60782,plain,
    ( c_Groups_Ozero__class_Ozero(t_a) = X1
    | c_Polynomial_OpCons(t_a,X1,X2) != v_p ),
    inference(rw,[status(thm)],[60778,55322,theory(equality)]) ).

cnf(64791,plain,
    c_Polynomial_OpCons(t_a,v_a,v_p) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[55320,55322,theory(equality)]),55421,theory(equality)]),55322,theory(equality)]),58917,theory(equality)]) ).

cnf(64792,plain,
    c_Polynomial_OpCons(t_a,v_a,v_p) = v_p,
    inference(rw,[status(thm)],[64791,55322,theory(equality)]) ).

cnf(64811,plain,
    c_Groups_Ozero__class_Ozero(t_a) = v_a,
    inference(spm,[status(thm)],[60782,64792,theory(equality)]) ).

cnf(64842,plain,
    $false,
    inference(sr,[status(thm)],[64811,55419,theory(equality)]) ).

cnf(64843,plain,
    $false,
    64842,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW186+1.p
% --creating new selector for []
% -running prover on /tmp/tmp_ggpwJ/sel_SWW186+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW186+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW186+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW186+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------