TSTP Solution File: SWW198+1 by Enigma---0.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Enigma---0.5.1
% Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : enigmatic-eprover.py %s %d 1

% Computer : n020.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 00:01:43 EDT 2022

% Result   : Theorem 11.32s 3.23s
% Output   : CNFRefutation 11.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   42 (  37 unt;   0 def)
%            Number of atoms       :   49 (  39 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  12   ~;   5   |;   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   :   40 (   4 sgn  21   !;   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/sandbox/benchmark/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/sandbox/benchmark/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/sandbox/benchmark/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/sandbox/benchmark/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/sandbox/benchmark/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/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).

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/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_odd__nat__equiv__def2,axiom,
    ! [X15] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X15)
    <=> ? [X24] : X15 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_odd__nat__equiv__def2) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X13] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X13) = X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

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/sandbox/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_o,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o) ).

fof(c_0_11,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_12,plain,
    ! [X590] : c_Int_OBit0(X590) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X590,X590),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(c_0_13,plain,
    ! [X1883] : c_Int_OBit1(X1883) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1883),X1883),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(c_0_14,negated_conjecture,
    ! [X2596] : 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))),X2596)),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_15,plain,
    ! [X1880] : c_Nat_OSuc(X1880) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1880,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

cnf(c_0_16,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_17,plain,
    c_Int_OBit0(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X1),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_18,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_13]) ).

fof(c_0_19,plain,
    ! [X589] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X589,c_Int_OPls) = X589,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

cnf(c_0_20,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_14]) ).

cnf(c_0_21,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_15]) ).

cnf(c_0_22,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_16,c_0_17]),c_0_18]),c_0_18]) ).

cnf(c_0_23,plain,
    c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

fof(c_0_24,plain,
    ! [X1879] : c_Nat_OSuc(X1879) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X1879),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(c_0_25,plain,
    ! [X157,X159,X160] :
      ( ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X157)
        | X157 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk3_1(X157))) )
      & ( X159 != c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X160))
        | ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X159) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_odd__nat__equiv__def2])])])])])]) ).

cnf(c_0_26,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_20,c_0_17]),c_0_21]),c_0_18]),c_0_18]) ).

cnf(c_0_27,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)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).

cnf(c_0_28,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_24]) ).

cnf(c_0_29,plain,
    ( c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1)
    | X1 = c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),esk3_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_30,plain,
    ! [X585] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X585) = X585,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(c_0_31,plain,
    ! [X1100,X1101] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1101,X1100) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1100,X1101),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

cnf(c_0_32,negated_conjecture,
    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)) != v_na____,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_23]),c_0_23]),c_0_23]),c_0_23]),c_0_27]) ).

cnf(c_0_33,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_28,c_0_21]) ).

cnf(c_0_34,plain,
    ( X1 = 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_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)),esk3_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)],[c_0_29,c_0_21]),c_0_21]),c_0_21]) ).

cnf(c_0_35,plain,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_36,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_31]) ).

fof(c_0_37,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(fof_simplification,[status(thm)],[fact_o]) ).

cnf(c_0_38,negated_conjecture,
    c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(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)) != v_na____,
    inference(rw,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_39,plain,
    ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(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)),esk3_1(X1))) = X1
    | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,X1) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).

cnf(c_0_40,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(split_conjunct,[status(thm)],[c_0_37]) ).

cnf(c_0_41,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39])]),c_0_40]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW198+1 : TPTP v8.1.0. Released v5.2.0.
% 0.11/0.13  % Command  : enigmatic-eprover.py %s %d 1
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun  5 04:13:39 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.46  # ENIGMATIC: Selected SinE mode:
% 0.19/0.51  # Parsing /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51  # Filter: axfilter_auto   0 goes into file theBenchmark_axfilter_auto   0.p
% 0.19/0.51  # Filter: axfilter_auto   1 goes into file theBenchmark_axfilter_auto   1.p
% 0.19/0.51  # Filter: axfilter_auto   2 goes into file theBenchmark_axfilter_auto   2.p
% 11.32/3.23  # ENIGMATIC: Solved by autoschedule:
% 11.32/3.23  # No SInE strategy applied
% 11.32/3.23  # Trying AutoSched0 for 150 seconds
% 11.32/3.23  # AutoSched0-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 11.32/3.23  # and selection function SelectComplexExceptUniqMaxHorn.
% 11.32/3.23  #
% 11.32/3.23  # Preprocessing time       : 0.096 s
% 11.32/3.23  # Presaturation interreduction done
% 11.32/3.23  
% 11.32/3.23  # Proof found!
% 11.32/3.23  # SZS status Theorem
% 11.32/3.23  # SZS output start CNFRefutation
% See solution above
% 11.32/3.23  # Training examples: 0 positive, 0 negative
% 11.32/3.23  
% 11.32/3.23  # -------------------------------------------------
% 11.32/3.23  # User time                : 0.393 s
% 11.32/3.23  # System time              : 0.013 s
% 11.32/3.23  # Total time               : 0.406 s
% 11.32/3.23  # Maximum resident set size: 7412 pages
% 11.32/3.23  
%------------------------------------------------------------------------------