TSTP Solution File: GRP775+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GRP775+1 : TPTP v5.0.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.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 : Sat Dec 25 11:33:29 EST 2010

% Result   : Theorem 0.52s
% Output   : CNFRefutation 0.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :    6
% Syntax   : Number of formulae    :  132 (  26 unt;   0 def)
%            Number of atoms       :  342 ( 158 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  365 ( 155   ~; 170   |;  35   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :  203 (   3 sgn  45   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2] :
      ( d(X1,X2)
    <=> ( product(X1,product(X2,X1)) = X1
        & product(X2,product(X1,X2)) = X2 ) ),
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',goals) ).

fof(2,axiom,
    ! [X3,X4] :
      ( r(X3,X4)
    <=> ( product(X3,X4) = X4
        & product(X4,X3) = X3 ) ),
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos04) ).

fof(3,axiom,
    ! [X5,X6] :
      ( d(X5,X6)
    <=> ? [X7] :
          ( r(X5,X7)
          & l(X7,X6) ) ),
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos05) ).

fof(4,axiom,
    ! [X8,X9,X10] : product(product(X10,X9),X8) = product(X10,product(X9,X8)),
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos01) ).

fof(5,axiom,
    ! [X10] : product(X10,X10) = X10,
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos02) ).

fof(6,axiom,
    ! [X11,X12] :
      ( l(X11,X12)
    <=> ( product(X11,X12) = X11
        & product(X12,X11) = X12 ) ),
    file('/tmp/tmpavXKju/sel_GRP775+1.p_1',sos03) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2] :
        ( d(X1,X2)
      <=> ( product(X1,product(X2,X1)) = X1
          & product(X2,product(X1,X2)) = X2 ) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(8,negated_conjecture,
    ? [X1,X2] :
      ( ( ~ d(X1,X2)
        | product(X1,product(X2,X1)) != X1
        | product(X2,product(X1,X2)) != X2 )
      & ( d(X1,X2)
        | ( product(X1,product(X2,X1)) = X1
          & product(X2,product(X1,X2)) = X2 ) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(9,negated_conjecture,
    ? [X3,X4] :
      ( ( ~ d(X3,X4)
        | product(X3,product(X4,X3)) != X3
        | product(X4,product(X3,X4)) != X4 )
      & ( d(X3,X4)
        | ( product(X3,product(X4,X3)) = X3
          & product(X4,product(X3,X4)) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[8]) ).

fof(10,negated_conjecture,
    ( ( ~ d(esk1_0,esk2_0)
      | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
      | product(esk2_0,product(esk1_0,esk2_0)) != esk2_0 )
    & ( d(esk1_0,esk2_0)
      | ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
        & product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ) ) ),
    inference(skolemize,[status(esa)],[9]) ).

fof(11,negated_conjecture,
    ( ( ~ d(esk1_0,esk2_0)
      | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
      | product(esk2_0,product(esk1_0,esk2_0)) != esk2_0 )
    & ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
      | d(esk1_0,esk2_0) )
    & ( product(esk2_0,product(esk1_0,esk2_0)) = esk2_0
      | d(esk1_0,esk2_0) ) ),
    inference(distribute,[status(thm)],[10]) ).

cnf(12,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(esk2_0,product(esk1_0,esk2_0)) = esk2_0 ),
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(13,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(esk1_0,product(esk2_0,esk1_0)) = esk1_0 ),
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(14,negated_conjecture,
    ( product(esk2_0,product(esk1_0,esk2_0)) != esk2_0
    | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | ~ d(esk1_0,esk2_0) ),
    inference(split_conjunct,[status(thm)],[11]) ).

fof(15,plain,
    ! [X3,X4] :
      ( ( ~ r(X3,X4)
        | ( product(X3,X4) = X4
          & product(X4,X3) = X3 ) )
      & ( product(X3,X4) != X4
        | product(X4,X3) != X3
        | r(X3,X4) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(16,plain,
    ! [X5,X6] :
      ( ( ~ r(X5,X6)
        | ( product(X5,X6) = X6
          & product(X6,X5) = X5 ) )
      & ( product(X5,X6) != X6
        | product(X6,X5) != X5
        | r(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[15]) ).

fof(17,plain,
    ! [X5,X6] :
      ( ( product(X5,X6) = X6
        | ~ r(X5,X6) )
      & ( product(X6,X5) = X5
        | ~ r(X5,X6) )
      & ( product(X5,X6) != X6
        | product(X6,X5) != X5
        | r(X5,X6) ) ),
    inference(distribute,[status(thm)],[16]) ).

cnf(18,plain,
    ( r(X1,X2)
    | product(X2,X1) != X1
    | product(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(19,plain,
    ( product(X2,X1) = X1
    | ~ r(X1,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

cnf(20,plain,
    ( product(X1,X2) = X2
    | ~ r(X1,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(21,plain,
    ! [X5,X6] :
      ( ( ~ d(X5,X6)
        | ? [X7] :
            ( r(X5,X7)
            & l(X7,X6) ) )
      & ( ! [X7] :
            ( ~ r(X5,X7)
            | ~ l(X7,X6) )
        | d(X5,X6) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(22,plain,
    ! [X8,X9] :
      ( ( ~ d(X8,X9)
        | ? [X10] :
            ( r(X8,X10)
            & l(X10,X9) ) )
      & ( ! [X11] :
            ( ~ r(X8,X11)
            | ~ l(X11,X9) )
        | d(X8,X9) ) ),
    inference(variable_rename,[status(thm)],[21]) ).

fof(23,plain,
    ! [X8,X9] :
      ( ( ~ d(X8,X9)
        | ( r(X8,esk3_2(X8,X9))
          & l(esk3_2(X8,X9),X9) ) )
      & ( ! [X11] :
            ( ~ r(X8,X11)
            | ~ l(X11,X9) )
        | d(X8,X9) ) ),
    inference(skolemize,[status(esa)],[22]) ).

fof(24,plain,
    ! [X8,X9,X11] :
      ( ( ~ r(X8,X11)
        | ~ l(X11,X9)
        | d(X8,X9) )
      & ( ~ d(X8,X9)
        | ( r(X8,esk3_2(X8,X9))
          & l(esk3_2(X8,X9),X9) ) ) ),
    inference(shift_quantors,[status(thm)],[23]) ).

fof(25,plain,
    ! [X8,X9,X11] :
      ( ( ~ r(X8,X11)
        | ~ l(X11,X9)
        | d(X8,X9) )
      & ( r(X8,esk3_2(X8,X9))
        | ~ d(X8,X9) )
      & ( l(esk3_2(X8,X9),X9)
        | ~ d(X8,X9) ) ),
    inference(distribute,[status(thm)],[24]) ).

cnf(26,plain,
    ( l(esk3_2(X1,X2),X2)
    | ~ d(X1,X2) ),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(27,plain,
    ( r(X1,esk3_2(X1,X2))
    | ~ d(X1,X2) ),
    inference(split_conjunct,[status(thm)],[25]) ).

cnf(28,plain,
    ( d(X1,X2)
    | ~ l(X3,X2)
    | ~ r(X1,X3) ),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(29,plain,
    ! [X11,X12,X13] : product(product(X13,X12),X11) = product(X13,product(X12,X11)),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(30,plain,
    product(product(X1,X2),X3) = product(X1,product(X2,X3)),
    inference(split_conjunct,[status(thm)],[29]) ).

fof(31,plain,
    ! [X11] : product(X11,X11) = X11,
    inference(variable_rename,[status(thm)],[5]) ).

cnf(32,plain,
    product(X1,X1) = X1,
    inference(split_conjunct,[status(thm)],[31]) ).

fof(33,plain,
    ! [X11,X12] :
      ( ( ~ l(X11,X12)
        | ( product(X11,X12) = X11
          & product(X12,X11) = X12 ) )
      & ( product(X11,X12) != X11
        | product(X12,X11) != X12
        | l(X11,X12) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(34,plain,
    ! [X13,X14] :
      ( ( ~ l(X13,X14)
        | ( product(X13,X14) = X13
          & product(X14,X13) = X14 ) )
      & ( product(X13,X14) != X13
        | product(X14,X13) != X14
        | l(X13,X14) ) ),
    inference(variable_rename,[status(thm)],[33]) ).

fof(35,plain,
    ! [X13,X14] :
      ( ( product(X13,X14) = X13
        | ~ l(X13,X14) )
      & ( product(X14,X13) = X14
        | ~ l(X13,X14) )
      & ( product(X13,X14) != X13
        | product(X14,X13) != X14
        | l(X13,X14) ) ),
    inference(distribute,[status(thm)],[34]) ).

cnf(36,plain,
    ( l(X1,X2)
    | product(X2,X1) != X2
    | product(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(37,plain,
    ( product(X2,X1) = X2
    | ~ l(X1,X2) ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(38,plain,
    ( product(X1,X2) = X1
    | ~ l(X1,X2) ),
    inference(split_conjunct,[status(thm)],[35]) ).

cnf(39,plain,
    ( product(esk3_2(X1,X2),X1) = X1
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[19,27,theory(equality)]) ).

cnf(40,plain,
    ( product(X1,esk3_2(X1,X2)) = esk3_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[20,27,theory(equality)]) ).

cnf(41,plain,
    product(X1,product(X2,product(X1,X2))) = product(X1,X2),
    inference(spm,[status(thm)],[32,30,theory(equality)]) ).

cnf(42,plain,
    product(X1,X2) = product(X1,product(X1,X2)),
    inference(spm,[status(thm)],[30,32,theory(equality)]) ).

cnf(48,plain,
    ( product(X1,esk3_2(X2,X1)) = X1
    | ~ d(X2,X1) ),
    inference(spm,[status(thm)],[37,26,theory(equality)]) ).

cnf(49,plain,
    ( product(esk3_2(X1,X2),X2) = esk3_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[38,26,theory(equality)]) ).

cnf(50,plain,
    ( d(X1,X2)
    | ~ r(X1,esk3_2(X3,X2))
    | ~ d(X3,X2) ),
    inference(spm,[status(thm)],[28,26,theory(equality)]) ).

cnf(55,plain,
    ( d(X1,X2)
    | ~ r(X1,X3)
    | product(X2,X3) != X2
    | product(X3,X2) != X3 ),
    inference(spm,[status(thm)],[28,36,theory(equality)]) ).

cnf(58,plain,
    product(product(X1,X2),X3) = product(X1,product(X2,product(product(X1,X2),X3))),
    inference(spm,[status(thm)],[30,42,theory(equality)]) ).

cnf(64,plain,
    product(X1,product(X2,X3)) = product(X1,product(X2,product(product(X1,X2),X3))),
    inference(rw,[status(thm)],[58,30,theory(equality)]) ).

cnf(65,plain,
    product(X1,product(X2,X3)) = product(X1,product(X2,product(X1,product(X2,X3)))),
    inference(rw,[status(thm)],[64,30,theory(equality)]) ).

cnf(68,plain,
    ( product(X1,X3) = product(esk3_2(X1,X2),product(X1,X3))
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[30,39,theory(equality)]) ).

cnf(127,plain,
    ( d(X1,X2)
    | ~ d(X3,X2)
    | product(esk3_2(X3,X2),X1) != X1
    | product(X1,esk3_2(X3,X2)) != esk3_2(X3,X2) ),
    inference(spm,[status(thm)],[50,18,theory(equality)]) ).

cnf(132,plain,
    ( product(esk3_2(X1,X2),product(X2,esk3_2(X1,X2))) = esk3_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[41,49,theory(equality)]) ).

cnf(162,plain,
    ( product(X1,X2) = esk3_2(X1,product(X1,X2))
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[49,68,theory(equality)]) ).

cnf(174,plain,
    ( d(X1,X2)
    | product(X2,X2) != X2
    | ~ r(X1,X2) ),
    inference(spm,[status(thm)],[55,32,theory(equality)]) ).

cnf(184,plain,
    ( d(X1,X2)
    | $false
    | ~ r(X1,X2) ),
    inference(rw,[status(thm)],[174,32,theory(equality)]) ).

cnf(185,plain,
    ( d(X1,X2)
    | ~ r(X1,X2) ),
    inference(cn,[status(thm)],[184,theory(equality)]) ).

cnf(192,plain,
    ( d(X1,X2)
    | product(X2,X1) != X1
    | product(X1,X2) != X2 ),
    inference(spm,[status(thm)],[185,18,theory(equality)]) ).

cnf(200,plain,
    ( r(X1,product(X1,X2))
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[27,162,theory(equality)]) ).

cnf(202,plain,
    ( product(product(X1,X2),X1) = X1
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[39,162,theory(equality)]) ).

cnf(213,plain,
    ( product(product(X1,X2),product(X1,X3)) = product(X1,X3)
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[68,162,theory(equality)]) ).

cnf(216,plain,
    ( product(X1,product(X2,X1)) = X1
    | ~ d(X1,product(X1,X2)) ),
    inference(rw,[status(thm)],[202,30,theory(equality)]) ).

cnf(221,plain,
    ( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
    | ~ d(X1,product(X1,X2)) ),
    inference(rw,[status(thm)],[213,30,theory(equality)]) ).

cnf(257,plain,
    ( product(X1,product(X2,product(X1,esk3_2(X2,X3)))) = product(X1,esk3_2(X2,X3))
    | ~ d(X2,X3) ),
    inference(spm,[status(thm)],[65,40,theory(equality)]) ).

cnf(264,plain,
    ( product(X1,product(esk3_2(X2,X3),product(X1,product(X2,X4)))) = product(X1,product(X2,X4))
    | ~ d(X2,X3) ),
    inference(spm,[status(thm)],[65,68,theory(equality)]) ).

cnf(300,plain,
    ( product(product(X1,X2),product(X3,product(X1,X2))) = product(X1,X2)
    | ~ d(product(X1,X2),product(X1,product(X2,X3))) ),
    inference(spm,[status(thm)],[216,30,theory(equality)]) ).

cnf(312,plain,
    ( product(X1,product(X2,product(X3,product(X1,X2)))) = product(X1,X2)
    | ~ d(product(X1,X2),product(X1,product(X2,X3))) ),
    inference(rw,[status(thm)],[300,30,theory(equality)]) ).

cnf(997,plain,
    ( d(esk3_2(X1,X2),X2)
    | product(esk3_2(X1,X2),esk3_2(X1,X2)) != esk3_2(X1,X2)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[127,32,theory(equality)]) ).

cnf(1016,plain,
    ( d(esk3_2(X1,X2),X2)
    | $false
    | ~ d(X1,X2) ),
    inference(rw,[status(thm)],[997,32,theory(equality)]) ).

cnf(1017,plain,
    ( d(esk3_2(X1,X2),X2)
    | ~ d(X1,X2) ),
    inference(cn,[status(thm)],[1016,theory(equality)]) ).

cnf(1032,plain,
    ( d(product(X1,X2),product(X1,X2))
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[1017,162,theory(equality)]) ).

cnf(1103,plain,
    ( d(X1,X1)
    | ~ d(esk3_2(X1,X2),X1)
    | ~ d(X1,X2) ),
    inference(spm,[status(thm)],[1032,39,theory(equality)]) ).

cnf(1117,plain,
    ( d(X1,X1)
    | ~ d(product(X1,X2),X1)
    | ~ d(X1,product(X1,X2)) ),
    inference(spm,[status(thm)],[1103,162,theory(equality)]) ).

cnf(1132,plain,
    ( d(X1,X1)
    | ~ d(X1,product(X1,X2))
    | product(X1,product(X1,X2)) != product(X1,X2)
    | product(product(X1,X2),X1) != X1 ),
    inference(spm,[status(thm)],[1117,192,theory(equality)]) ).

cnf(1138,plain,
    ( d(X1,X1)
    | ~ d(X1,product(X1,X2))
    | $false
    | product(product(X1,X2),X1) != X1 ),
    inference(rw,[status(thm)],[1132,42,theory(equality)]) ).

cnf(1139,plain,
    ( d(X1,X1)
    | ~ d(X1,product(X1,X2))
    | $false
    | product(X1,product(X2,X1)) != X1 ),
    inference(rw,[status(thm)],[1138,30,theory(equality)]) ).

cnf(1140,plain,
    ( d(X1,X1)
    | ~ d(X1,product(X1,X2))
    | product(X1,product(X2,X1)) != X1 ),
    inference(cn,[status(thm)],[1139,theory(equality)]) ).

cnf(1141,plain,
    ( d(X1,X1)
    | ~ d(X1,product(X1,X2)) ),
    inference(csr,[status(thm)],[1140,216]) ).

cnf(1154,plain,
    ( d(X1,X1)
    | product(product(X1,X2),X1) != X1
    | product(X1,product(X1,X2)) != product(X1,X2) ),
    inference(spm,[status(thm)],[1141,192,theory(equality)]) ).

cnf(1160,plain,
    ( d(X1,X1)
    | product(X1,product(X2,X1)) != X1
    | product(X1,product(X1,X2)) != product(X1,X2) ),
    inference(rw,[status(thm)],[1154,30,theory(equality)]) ).

cnf(1161,plain,
    ( d(X1,X1)
    | product(X1,product(X2,X1)) != X1
    | $false ),
    inference(rw,[status(thm)],[1160,42,theory(equality)]) ).

cnf(1162,plain,
    ( d(X1,X1)
    | product(X1,product(X2,X1)) != X1 ),
    inference(cn,[status(thm)],[1161,theory(equality)]) ).

cnf(1242,plain,
    ( d(X1,X1)
    | product(X1,X1) != X1 ),
    inference(spm,[status(thm)],[1162,32,theory(equality)]) ).

cnf(1268,plain,
    ( d(X1,X1)
    | $false ),
    inference(rw,[status(thm)],[1242,32,theory(equality)]) ).

cnf(1269,plain,
    d(X1,X1),
    inference(cn,[status(thm)],[1268,theory(equality)]) ).

cnf(4615,plain,
    ( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
    | product(product(X1,X2),X1) != X1
    | product(X1,product(X1,X2)) != product(X1,X2) ),
    inference(spm,[status(thm)],[221,192,theory(equality)]) ).

cnf(4652,plain,
    ( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
    | product(X1,product(X2,X1)) != X1
    | product(X1,product(X1,X2)) != product(X1,X2) ),
    inference(rw,[status(thm)],[4615,30,theory(equality)]) ).

cnf(4653,plain,
    ( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
    | product(X1,product(X2,X1)) != X1
    | $false ),
    inference(rw,[status(thm)],[4652,42,theory(equality)]) ).

cnf(4654,plain,
    ( product(X1,product(X2,product(X1,X3))) = product(X1,X3)
    | product(X1,product(X2,X1)) != X1 ),
    inference(cn,[status(thm)],[4653,theory(equality)]) ).

cnf(6511,plain,
    ( product(X1,product(X2,X1)) = X1
    | ~ d(X2,X1) ),
    inference(spm,[status(thm)],[257,48,theory(equality)]) ).

cnf(6685,negated_conjecture,
    product(esk2_0,product(esk1_0,esk2_0)) = esk2_0,
    inference(spm,[status(thm)],[6511,12,theory(equality)]) ).

cnf(6719,negated_conjecture,
    ( d(X1,esk2_0)
    | product(product(esk1_0,esk2_0),esk2_0) != product(esk1_0,esk2_0)
    | ~ r(X1,product(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[55,6685,theory(equality)]) ).

cnf(6764,negated_conjecture,
    ( product(esk2_0,product(product(esk1_0,esk2_0),product(esk2_0,X1))) = product(esk2_0,X1)
    | ~ d(esk2_0,esk2_0) ),
    inference(spm,[status(thm)],[221,6685,theory(equality)]) ).

cnf(6783,negated_conjecture,
    ( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | $false
    | ~ d(esk1_0,esk2_0) ),
    inference(rw,[status(thm)],[14,6685,theory(equality)]) ).

cnf(6784,negated_conjecture,
    ( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | ~ d(esk1_0,esk2_0) ),
    inference(cn,[status(thm)],[6783,theory(equality)]) ).

cnf(6794,negated_conjecture,
    ( d(X1,esk2_0)
    | $false
    | ~ r(X1,product(esk1_0,esk2_0)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[6719,30,theory(equality)]),32,theory(equality)]) ).

cnf(6795,negated_conjecture,
    ( d(X1,esk2_0)
    | ~ r(X1,product(esk1_0,esk2_0)) ),
    inference(cn,[status(thm)],[6794,theory(equality)]) ).

cnf(6855,negated_conjecture,
    ( product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1)
    | ~ d(esk2_0,esk2_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[6764,30,theory(equality)]),42,theory(equality)]) ).

cnf(6856,negated_conjecture,
    ( product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1)
    | $false ),
    inference(rw,[status(thm)],[6855,1269,theory(equality)]) ).

cnf(6857,negated_conjecture,
    product(esk2_0,product(esk1_0,product(esk2_0,X1))) = product(esk2_0,X1),
    inference(cn,[status(thm)],[6856,theory(equality)]) ).

cnf(7532,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | ~ d(esk1_0,product(esk1_0,esk2_0)) ),
    inference(spm,[status(thm)],[6795,200,theory(equality)]) ).

cnf(7546,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(product(esk1_0,esk2_0),esk1_0) != esk1_0
    | product(esk1_0,product(esk1_0,esk2_0)) != product(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[7532,192,theory(equality)]) ).

cnf(7548,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | product(esk1_0,product(esk1_0,esk2_0)) != product(esk1_0,esk2_0) ),
    inference(rw,[status(thm)],[7546,30,theory(equality)]) ).

cnf(7549,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | $false ),
    inference(rw,[status(thm)],[7548,42,theory(equality)]) ).

cnf(7550,negated_conjecture,
    ( d(esk1_0,esk2_0)
    | product(esk1_0,product(esk2_0,esk1_0)) != esk1_0 ),
    inference(cn,[status(thm)],[7549,theory(equality)]) ).

cnf(7551,negated_conjecture,
    d(esk1_0,esk2_0),
    inference(csr,[status(thm)],[7550,13]) ).

cnf(7554,negated_conjecture,
    ( product(esk1_0,product(esk2_0,esk1_0)) != esk1_0
    | $false ),
    inference(rw,[status(thm)],[6784,7551,theory(equality)]) ).

cnf(7555,negated_conjecture,
    product(esk1_0,product(esk2_0,esk1_0)) != esk1_0,
    inference(cn,[status(thm)],[7554,theory(equality)]) ).

cnf(7598,negated_conjecture,
    ( product(esk2_0,product(esk3_2(esk1_0,X1),esk2_0)) = esk2_0
    | ~ d(esk1_0,X1) ),
    inference(spm,[status(thm)],[264,6685,theory(equality)]) ).

cnf(8566,negated_conjecture,
    ( product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0
    | ~ d(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[7598,49,theory(equality)]) ).

cnf(8651,negated_conjecture,
    ( product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0
    | $false ),
    inference(rw,[status(thm)],[8566,7551,theory(equality)]) ).

cnf(8652,negated_conjecture,
    product(esk2_0,esk3_2(esk1_0,esk2_0)) = esk2_0,
    inference(cn,[status(thm)],[8651,theory(equality)]) ).

cnf(8767,negated_conjecture,
    ( product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0)
    | ~ d(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[132,8652,theory(equality)]) ).

cnf(8824,negated_conjecture,
    ( product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[8767,7551,theory(equality)]) ).

cnf(8825,negated_conjecture,
    product(esk3_2(esk1_0,esk2_0),esk2_0) = esk3_2(esk1_0,esk2_0),
    inference(cn,[status(thm)],[8824,theory(equality)]) ).

cnf(9087,negated_conjecture,
    ( product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0)
    | ~ d(product(X1,esk2_0),product(X1,esk2_0)) ),
    inference(spm,[status(thm)],[312,8652,theory(equality)]) ).

cnf(9225,negated_conjecture,
    ( product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[9087,1269,theory(equality)]) ).

cnf(9226,negated_conjecture,
    product(X1,product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(X1,esk2_0)))) = product(X1,esk2_0),
    inference(cn,[status(thm)],[9225,theory(equality)]) ).

cnf(10118,negated_conjecture,
    product(esk2_0,product(esk1_0,esk2_0)) = product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))),
    inference(spm,[status(thm)],[6857,9226,theory(equality)]) ).

cnf(10236,negated_conjecture,
    esk2_0 = product(esk2_0,product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))),
    inference(rw,[status(thm)],[10118,6685,theory(equality)]) ).

cnf(10395,negated_conjecture,
    ( product(esk3_2(esk1_0,esk2_0),esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
    | product(esk3_2(esk1_0,esk2_0),product(esk2_0,esk3_2(esk1_0,esk2_0))) != esk3_2(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[4654,10236,theory(equality)]) ).

cnf(10499,negated_conjecture,
    ( esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
    | product(esk3_2(esk1_0,esk2_0),product(esk2_0,esk3_2(esk1_0,esk2_0))) != esk3_2(esk1_0,esk2_0) ),
    inference(rw,[status(thm)],[10395,8825,theory(equality)]) ).

cnf(10500,negated_conjecture,
    ( esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0))
    | $false ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[10499,8652,theory(equality)]),8825,theory(equality)]) ).

cnf(10501,negated_conjecture,
    esk3_2(esk1_0,esk2_0) = product(esk3_2(esk1_0,esk2_0),product(esk1_0,esk2_0)),
    inference(cn,[status(thm)],[10500,theory(equality)]) ).

cnf(10788,negated_conjecture,
    ( esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0)
    | ~ d(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[68,10501,theory(equality)]) ).

cnf(10870,negated_conjecture,
    ( esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0)
    | $false ),
    inference(rw,[status(thm)],[10788,7551,theory(equality)]) ).

cnf(10871,negated_conjecture,
    esk3_2(esk1_0,esk2_0) = product(esk1_0,esk2_0),
    inference(cn,[status(thm)],[10870,theory(equality)]) ).

cnf(10988,negated_conjecture,
    ( product(product(esk1_0,esk2_0),esk1_0) = esk1_0
    | ~ d(esk1_0,esk2_0) ),
    inference(spm,[status(thm)],[39,10871,theory(equality)]) ).

cnf(11059,negated_conjecture,
    ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
    | ~ d(esk1_0,esk2_0) ),
    inference(rw,[status(thm)],[10988,30,theory(equality)]) ).

cnf(11060,negated_conjecture,
    ( product(esk1_0,product(esk2_0,esk1_0)) = esk1_0
    | $false ),
    inference(rw,[status(thm)],[11059,7551,theory(equality)]) ).

cnf(11061,negated_conjecture,
    product(esk1_0,product(esk2_0,esk1_0)) = esk1_0,
    inference(cn,[status(thm)],[11060,theory(equality)]) ).

cnf(11062,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[11061,7555,theory(equality)]) ).

cnf(11063,negated_conjecture,
    $false,
    11062,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/GRP/GRP775+1.p
% --creating new selector for []
% -running prover on /tmp/tmpavXKju/sel_GRP775+1.p_1 with time limit 29
% -prover status Theorem
% Problem GRP775+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GRP/GRP775+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GRP/GRP775+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
% 
%------------------------------------------------------------------------------