TSTP Solution File: SWW174+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWW174+1 : TPTP v5.2.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 14:43:44 EST 2011

% Result   : Theorem 5.79s
% Output   : CNFRefutation 5.79s
% Verified : 
% SZS Type : None (Could not find formula named the7)
% Syntax   : Number of formulae    : 72

% Comments : 
%------------------------------------------------------------------------------
fof(42,axiom,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_semiring__norm_I115_J) ).

fof(62,conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',conj_0) ).

fof(160,axiom,
    ! [X9] : c_Int_OBit1(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X9),X9),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_Bit1__def) ).

fof(222,axiom,
    ! [X4] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X4) = X4,
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_real__mult__1) ).

fof(314,axiom,
    ! [X3] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X3,X3)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_real__sqrt__abs2) ).

fof(393,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_One__nat__def) ).

fof(413,axiom,
    ! [X6] : c_Nat_OSuc(X6) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_Suc__eq__plus1) ).

fof(446,axiom,
    ! [X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OPls) = X9,
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_add__Pls__right) ).

fof(473,axiom,
    ! [X67,X25,X26] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,X25),X67) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X26,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X67)),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_zadd__assoc) ).

fof(575,axiom,
    ! [X9] : c_Int_OBit0(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X9),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_Bit0__def) ).

fof(692,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',arity_RealDef__Oreal__Int_Onumber__ring) ).

fof(742,axiom,
    ! [X4,X1] :
      ( class_Int_Onumber__ring(X1)
     => c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X4,X4) ),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_mult__2__right) ).

fof(804,axiom,
    ! [X3] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X3,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_real__sqrt__abs) ).

fof(1083,axiom,
    ! [X2,X1] :
      ( class_Int_Onumber__ring(X1)
     => c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) ),
    file('/tmp/tmpmMaBBL/sel_SWW174+1.p_1',fact_double__number__of__Bit0) ).

fof(1201,negated_conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(assume_negation,[status(cth)],[62]) ).

fof(1207,negated_conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(fof_simplification,[status(thm)],[1201,theory(equality)]) ).

cnf(1373,plain,
    c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[42]) ).

cnf(1448,negated_conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(split_conjunct,[status(thm)],[1207]) ).

fof(1766,plain,
    ! [X10] : c_Int_OBit1(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X10),X10),
    inference(variable_rename,[status(thm)],[160]) ).

cnf(1767,plain,
    c_Int_OBit1(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[1766]) ).

fof(1964,plain,
    ! [X5] : c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X5) = X5,
    inference(variable_rename,[status(thm)],[222]) ).

cnf(1965,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X1) = X1,
    inference(split_conjunct,[status(thm)],[1964]) ).

fof(2285,plain,
    ! [X4] : c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X4,X4)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4),
    inference(variable_rename,[status(thm)],[314]) ).

cnf(2286,plain,
    c_NthRoot_Osqrt(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,X1,X1)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[2285]) ).

cnf(2544,plain,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[393]) ).

fof(2601,plain,
    ! [X7] : c_Nat_OSuc(X7) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[413]) ).

cnf(2602,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(split_conjunct,[status(thm)],[2601]) ).

fof(2689,plain,
    ! [X10] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,c_Int_OPls) = X10,
    inference(variable_rename,[status(thm)],[446]) ).

cnf(2690,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[2689]) ).

fof(2760,plain,
    ! [X68,X69,X70] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,X69),X68) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X70,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X69,X68)),
    inference(variable_rename,[status(thm)],[473]) ).

cnf(2761,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X3)),
    inference(split_conjunct,[status(thm)],[2760]) ).

fof(3061,plain,
    ! [X10] : c_Int_OBit0(X10) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X10,X10),
    inference(variable_rename,[status(thm)],[575]) ).

cnf(3062,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[3061]) ).

cnf(3430,plain,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    inference(split_conjunct,[status(thm)],[692]) ).

fof(3567,plain,
    ! [X4,X1] :
      ( ~ class_Int_Onumber__ring(X1)
      | c_Groups_Otimes__class_Otimes(X1,X4,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X4,X4) ),
    inference(fof_nnf,[status(thm)],[742]) ).

fof(3568,plain,
    ! [X5,X6] :
      ( ~ class_Int_Onumber__ring(X6)
      | c_Groups_Otimes__class_Otimes(X6,X5,c_Int_Onumber__class_Onumber__of(X6,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X6,X5,X5) ),
    inference(variable_rename,[status(thm)],[3567]) ).

cnf(3569,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[3568]) ).

fof(3768,plain,
    ! [X4] : c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X4,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X4),
    inference(variable_rename,[status(thm)],[804]) ).

cnf(3769,plain,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(split_conjunct,[status(thm)],[3768]) ).

fof(4645,plain,
    ! [X2,X1] :
      ( ~ class_Int_Onumber__ring(X1)
      | c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2)) ),
    inference(fof_nnf,[status(thm)],[1083]) ).

fof(4646,plain,
    ! [X3,X4] :
      ( ~ class_Int_Onumber__ring(X4)
      | c_Groups_Otimes__class_Otimes(X4,c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4)),c_Int_Onumber__class_Onumber__of(X4,X3)) = c_Int_Onumber__class_Onumber__of(X4,c_Int_OBit0(X3)) ),
    inference(variable_rename,[status(thm)],[4645]) ).

cnf(4647,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Int_OBit0(X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[4646]) ).

cnf(5002,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(rw,[status(thm)],[1373,3062,theory(equality)]),
    [unfolding] ).

cnf(5017,plain,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(rw,[status(thm)],[3769,3062,theory(equality)]),
    [unfolding] ).

cnf(5084,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[3569,3062,theory(equality)]),
    [unfolding] ).

cnf(5093,plain,
    ( c_Groups_Otimes__class_Otimes(X1,c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Groups_Oone__class_Oone(X1)),c_Int_Onumber__class_Onumber__of(X1,X2)) = c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X2,X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[4647,3062,theory(equality)]),
    [unfolding] ).

cnf(5150,negated_conjecture,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[1448,3062,theory(equality)]),3062,theory(equality)]),3062,theory(equality)]),3062,theory(equality)]),
    [unfolding] ).

cnf(5155,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(rw,[status(thm)],[2544,2602,theory(equality)]),
    [unfolding] ).

cnf(5169,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),c_Int_OBit1(c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[5002,2602,theory(equality)]),2602,theory(equality)]),
    [unfolding] ).

cnf(5297,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[5169,1767,theory(equality)]),1767,theory(equality)]),
    [unfolding] ).

cnf(5313,plain,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[5017,1767,theory(equality)]),1767,theory(equality)]),
    [unfolding] ).

cnf(5380,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[5084,1767,theory(equality)]),1767,theory(equality)]),
    [unfolding] ).

cnf(5461,negated_conjecture,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5150,1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),1767,theory(equality)]),
    [unfolding] ).

cnf(5491,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5297,2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]) ).

cnf(5492,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[5491,5155,theory(equality)]) ).

cnf(5495,negated_conjecture,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5461,2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),5492,theory(equality)]) ).

cnf(5496,negated_conjecture,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5495,2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]) ).

cnf(5797,plain,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(tc_RealDef_Oreal,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5313,2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),5492,theory(equality)]) ).

cnf(5807,negated_conjecture,
    c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) != c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
    inference(rw,[status(thm)],[5496,5797,theory(equality)]) ).

cnf(15251,plain,
    ( c_Groups_Otimes__class_Otimes(X1,X2,c_Int_Onumber__class_Onumber__of(X1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = c_Groups_Oplus__class_Oplus(X1,X2,X2)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[5380,2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]),2690,theory(equality)]) ).

cnf(15257,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[1965,15251,theory(equality)]) ).

cnf(15461,plain,
    ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | $false ),
    inference(rw,[status(thm)],[15257,3430,theory(equality)]) ).

cnf(15462,plain,
    c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(cn,[status(thm)],[15461,theory(equality)]) ).

cnf(89915,plain,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    inference(spm,[status(thm)],[5093,15462,theory(equality)]) ).

cnf(90030,plain,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | ~ class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    inference(rw,[status(thm)],[89915,2761,theory(equality)]) ).

cnf(90031,plain,
    ( c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
    | $false ),
    inference(rw,[status(thm)],[90030,3430,theory(equality)]) ).

cnf(90032,plain,
    c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
    inference(cn,[status(thm)],[90031,theory(equality)]) ).

cnf(93063,negated_conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(rw,[status(thm)],[5807,2761,theory(equality)]) ).

cnf(93064,negated_conjecture,
    c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) != c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
    inference(rw,[status(thm)],[93063,15462,theory(equality)]) ).

cnf(102582,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[93064,90032,theory(equality)]),2286,theory(equality)]) ).

cnf(102583,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[102582,theory(equality)]) ).

cnf(102584,negated_conjecture,
    $false,
    102583,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWW/SWW174+1.p
% --creating new selector for []
% -running prover on /tmp/tmpmMaBBL/sel_SWW174+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWW174+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWW/SWW174+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWW/SWW174+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
% 
%------------------------------------------------------------------------------