TSTP Solution File: SWW198+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n018.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  : 600s
% DateTime : Thu Jul 21 00:10:16 EDT 2022

% Result   : Theorem 0.33s 1.52s
% Output   : CNFRefutation 0.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   66 (  60 unt;   0 def)
%            Number of atoms       :   74 (  63 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   21 (  13   ~;   6   |;   1   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   4 con; 0-3 aty)
%            Number of variables   :   77 (   4 sgn  43   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(conj_0,conjecture,
    ? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',conj_0) ).

fof(fact_Bit0__def,axiom,
    ! [X8] : c_Int_OBit0(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,X8),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit0__def) ).

fof(fact_Bit1__def,axiom,
    ! [X8] : c_Int_OBit1(X8) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X8),X8),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Bit1__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_nat__1__add__1,axiom,
    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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_add__Pls__right,axiom,
    ! [X8] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X8,c_Int_OPls) = X8,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Pls__def) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X13] : c_Nat_OSuc(X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_mult__Suc,axiom,
    ! [X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X10),X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X13)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_mult__Suc) ).

fof(fact_odd__Suc__mult__two__ex,axiom,
    ! [X3] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X3)
    <=> ? [X23] : X3 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_odd__Suc__mult__two__ex) ).

fof(fact_semiring__norm_I115_J,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('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_One__nat__def) ).

fof(fact_nat__mult__1,axiom,
    ! [X13] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X13) = X13,
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__mult__1) ).

fof(fact_add__mult__distrib,axiom,
    ! [X8,X13,X10] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X10,X8),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X13,X8)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_nat__add__assoc,axiom,
    ! [X8,X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13),X8) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X8)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_nat__add__commute,axiom,
    ! [X13,X10] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X10,X13) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X13,X10),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X21,X17,X18] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X21)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_o,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',fact_o) ).

fof(c_0_18,negated_conjecture,
    ~ ? [X23] : v_na____ = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X23)),
    inference(assume_negation,[status(cth)],[conj_0]) ).

fof(c_0_19,plain,
    ! [X9] : c_Int_OBit0(X9) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,X9),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(c_0_20,plain,
    ! [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),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(c_0_21,negated_conjecture,
    ! [X24] : v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X24)),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])]) ).

fof(c_0_22,plain,
    ! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

cnf(c_0_23,plain,
    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_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    inference(split_conjunct,[status(thm)],[fact_nat__1__add__1]) ).

cnf(c_0_24,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,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)],[c_0_20]) ).

fof(c_0_26,plain,
    ! [X9] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X9,c_Int_OPls) = X9,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

cnf(c_0_27,negated_conjecture,
    v_na____ != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X1)),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_28,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)],[c_0_22]) ).

cnf(c_0_29,plain,
    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_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))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_25]) ).

cnf(c_0_30,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]) ).

fof(c_0_31,plain,
    ! [X14] : c_Nat_OSuc(X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(c_0_32,plain,
    ! [X14,X15] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).

fof(c_0_33,plain,
    ! [X24,X24,X26] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24)
        | X24 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk6_1(X24))) )
      & ( X24 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),X26))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X24) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_odd__Suc__mult__two__ex])])])])])])]) ).

cnf(c_0_34,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)],[fact_semiring__norm_I115_J]) ).

cnf(c_0_35,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_36,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)],[fact_One__nat__def]) ).

cnf(c_0_37,negated_conjecture,
    v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,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))),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_28]),c_0_25]),c_0_25]) ).

cnf(c_0_38,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_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(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_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_30]),c_0_30]),c_0_30]) ).

cnf(c_0_39,plain,
    c_Nat_OSuc(X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(X1),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

fof(c_0_41,plain,
    ! [X14] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X14) = X14,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

cnf(c_0_42,plain,
    ( X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),esk6_1(X1)))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_43,plain,
    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)) = 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))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_24]),c_0_28]),c_0_28]),c_0_25]),c_0_25]) ).

cnf(c_0_44,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X1,
    inference(rw,[status(thm)],[c_0_35,c_0_30]) ).

cnf(c_0_45,plain,
    c_Groups_Oone__class_Oone(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)),
    inference(rw,[status(thm)],[c_0_36,c_0_28]) ).

fof(c_0_46,plain,
    ! [X14,X15,X16] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X16,X14),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X15,X14)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

fof(c_0_47,plain,
    ! [X14,X15,X16] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(c_0_48,plain,
    ! [X14,X15] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X14,X15),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(c_0_49,plain,
    ! [X22,X23,X24] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,X22)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X23,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X24,X22)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

cnf(c_0_50,negated_conjecture,
    v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_30]),c_0_30]),c_0_30]),c_0_30]),c_0_38]) ).

cnf(c_0_51,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1),
    inference(rw,[status(thm)],[c_0_39,c_0_28]) ).

cnf(c_0_52,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X2)),
    inference(rw,[status(thm)],[c_0_40,c_0_28]) ).

cnf(c_0_53,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_54,plain,
    ( X1 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,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))),esk6_1(X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_24]),c_0_28]),c_0_25]),c_0_25]) ).

cnf(c_0_55,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)],[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)],[c_0_43,c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_45]) ).

cnf(c_0_56,plain,
    c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X1,X3),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_46]) ).

cnf(c_0_57,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2),X3) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_47]) ).

cnf(c_0_58,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_48]) ).

cnf(c_0_59,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_60,negated_conjecture,
    v_na____ != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]),c_0_53]) ).

cnf(c_0_61,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,esk6_1(X1),esk6_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_30]),c_0_44]),c_0_55]),c_0_56]),c_0_53]),c_0_53]),c_0_57]),c_0_58]),c_0_59]) ).

fof(c_0_62,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(fof_simplification,[status(thm)],[fact_o]) ).

cnf(c_0_63,negated_conjecture,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | v_na____ != X1 ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_64,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_65,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.12  % Command  : run_ET %s %d
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jun  5 04:12:03 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.33/1.52  # Running protocol protocol_eprover_2d86bd69119e7e9cc4417c0ee581499eaf828bb2 for 23 seconds:
% 0.33/1.52  # SinE strategy is GSinE(CountFormulas,,1.1,,02,500,1.0)
% 0.33/1.52  # Preprocessing time       : 0.072 s
% 0.33/1.52  
% 0.33/1.52  # Proof found!
% 0.33/1.52  # SZS status Theorem
% 0.33/1.52  # SZS output start CNFRefutation
% See solution above
% 0.33/1.52  # Proof object total steps             : 66
% 0.33/1.52  # Proof object clause steps            : 33
% 0.33/1.52  # Proof object formula steps           : 33
% 0.33/1.52  # Proof object conjectures             : 9
% 0.33/1.52  # Proof object clause conjectures      : 6
% 0.33/1.52  # Proof object formula conjectures     : 3
% 0.33/1.52  # Proof object initial clauses used    : 18
% 0.33/1.52  # Proof object initial formulas used   : 18
% 0.33/1.52  # Proof object generating inferences   : 2
% 0.33/1.52  # Proof object simplifying inferences  : 57
% 0.33/1.52  # Training examples: 0 positive, 0 negative
% 0.33/1.52  # Parsed axioms                        : 1186
% 0.33/1.52  # Removed by relevancy pruning/SinE    : 839
% 0.33/1.52  # Initial clauses                      : 564
% 0.33/1.52  # Removed in clause preprocessing      : 24
% 0.33/1.52  # Initial clauses in saturation        : 540
% 0.33/1.52  # Processed clauses                    : 755
% 0.33/1.52  # ...of these trivial                  : 45
% 0.33/1.52  # ...subsumed                          : 250
% 0.33/1.52  # ...remaining for further processing  : 460
% 0.33/1.52  # Other redundant clauses eliminated   : 21
% 0.33/1.52  # Clauses deleted for lack of memory   : 0
% 0.33/1.52  # Backward-subsumed                    : 11
% 0.33/1.52  # Backward-rewritten                   : 38
% 0.33/1.52  # Generated clauses                    : 4029
% 0.33/1.52  # ...of the previous two non-trivial   : 3431
% 0.33/1.52  # Contextual simplify-reflections      : 7
% 0.33/1.52  # Paramodulations                      : 3958
% 0.33/1.52  # Factorizations                       : 10
% 0.33/1.52  # Equation resolutions                 : 61
% 0.33/1.52  # Current number of processed clauses  : 396
% 0.33/1.52  #    Positive orientable unit clauses  : 66
% 0.33/1.52  #    Positive unorientable unit clauses: 9
% 0.33/1.52  #    Negative unit clauses             : 39
% 0.33/1.52  #    Non-unit-clauses                  : 282
% 0.33/1.52  # Current number of unprocessed clauses: 2621
% 0.33/1.52  # ...number of literals in the above   : 6106
% 0.33/1.52  # Current number of archived formulas  : 0
% 0.33/1.52  # Current number of archived clauses   : 52
% 0.33/1.52  # Clause-clause subsumption calls (NU) : 10463
% 0.33/1.52  # Rec. Clause-clause subsumption calls : 8469
% 0.33/1.52  # Non-unit clause-clause subsumptions  : 179
% 0.33/1.52  # Unit Clause-clause subsumption calls : 1079
% 0.33/1.52  # Rewrite failures with RHS unbound    : 0
% 0.33/1.52  # BW rewrite match attempts            : 785
% 0.33/1.52  # BW rewrite match successes           : 112
% 0.33/1.52  # Condensation attempts                : 0
% 0.33/1.52  # Condensation successes               : 0
% 0.33/1.52  # Termbank termtop insertions          : 123427
% 0.33/1.52  
% 0.33/1.52  # -------------------------------------------------
% 0.33/1.52  # User time                : 0.138 s
% 0.33/1.52  # System time              : 0.006 s
% 0.33/1.52  # Total time               : 0.144 s
% 0.33/1.52  # Maximum resident set size: 7848 pages
% 0.33/23.50  eprover: CPU time limit exceeded, terminating
% 0.33/23.52  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.52  eprover: No such file or directory
% 0.33/23.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.53  eprover: No such file or directory
% 0.33/23.53  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.53  eprover: No such file or directory
% 0.33/23.53  eprover: CPU time limit exceeded, terminating
% 0.33/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54  eprover: No such file or directory
% 0.33/23.54  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.54  eprover: No such file or directory
% 0.33/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55  eprover: No such file or directory
% 0.33/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55  eprover: No such file or directory
% 0.33/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55  eprover: No such file or directory
% 0.33/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55  eprover: No such file or directory
% 0.33/23.55  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.55  eprover: No such file or directory
% 0.33/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56  eprover: No such file or directory
% 0.33/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56  eprover: No such file or directory
% 0.33/23.56  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.56  eprover: No such file or directory
% 0.33/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57  eprover: No such file or directory
% 0.33/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57  eprover: No such file or directory
% 0.33/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57  eprover: No such file or directory
% 0.33/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57  eprover: No such file or directory
% 0.33/23.57  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.57  eprover: No such file or directory
% 0.33/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58  eprover: No such file or directory
% 0.33/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58  eprover: No such file or directory
% 0.33/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58  eprover: No such file or directory
% 0.33/23.58  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.33/23.58  eprover: No such file or directory
%------------------------------------------------------------------------------