TSTP Solution File: SWW198+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n015.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  : 300s
% DateTime : Tue Aug 22 11:06:50 EDT 2023

% Result   : Theorem 50.08s 27.30s
% Output   : CNFRefutation 50.08s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  121
% Syntax   : Number of formulae    :  132 (  14 unt; 115 typ;   0 def)
%            Number of atoms       :   20 (  13 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    9 (   6   ~;   2   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  142 ( 103   >;  39   *;   0   +;   0  <<)
%            Number of predicates  :   69 (  67 usr;   1 prp; 0-3 aty)
%            Number of functors    :   48 (  48 usr;  12 con; 0-4 aty)
%            Number of variables   :    9 (;   7   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Orderings_Oord__class_Oless__eq > c_Orderings_Oord__class_Oless > c_Parity_Oeven__odd__class_Oeven > hBOOL > class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct > class_Rings_Ozero__neq__one > class_Rings_Osemiring__1 > class_Rings_Osemiring__0 > class_Rings_Osemiring > class_Rings_Oring__no__zero__divisors > class_Rings_Oring__1__no__zero__divisors > class_Rings_Oordered__semiring > class_Rings_Oordered__ring__abs > class_Rings_Oordered__ring > class_Rings_Oordered__comm__semiring > class_Rings_Oordered__cancel__semiring > class_Rings_Ono__zero__divisors > class_Rings_Omult__zero > class_Rings_Olinordered__semiring__strict > class_Rings_Olinordered__semiring__1__strict > class_Rings_Olinordered__semiring__1 > class_Rings_Olinordered__semiring > class_Rings_Olinordered__semidom > class_Rings_Olinordered__ring__strict > class_Rings_Olinordered__ring > class_Rings_Olinordered__idom > class_Rings_Olinordered__comm__semiring__strict > class_Rings_Odivision__ring__inverse__zero > class_Rings_Odivision__ring > class_Rings_Ocomm__semiring__1 > class_Rings_Ocomm__semiring > class_RealVector_Oreal__normed__vector > class_RealVector_Oreal__normed__field > class_RealVector_Oreal__normed__div__algebra > class_RealVector_Oreal__normed__algebra__1 > class_RealVector_Oreal__normed__algebra > class_RealVector_Oreal__field > class_RealVector_Oreal__algebra__1 > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_Int_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > class_Groups_Ozero > class_Groups_Oordered__comm__monoid__add > class_Groups_Oordered__cancel__ab__semigroup__add > class_Groups_Oordered__ab__semigroup__add__imp__le > class_Groups_Oordered__ab__semigroup__add > class_Groups_Oordered__ab__group__add__abs > class_Groups_Oone > class_Groups_Omonoid__mult > class_Groups_Omonoid__add > class_Groups_Olinordered__ab__group__add > class_Groups_Ocomm__monoid__mult > class_Groups_Ocomm__monoid__add > class_Groups_Ocancel__semigroup__add > class_Groups_Ocancel__ab__semigroup__add > class_Groups_Oab__semigroup__mult > class_Groups_Oab__semigroup__add > class_Fields_Olinordered__field__inverse__zero > class_Fields_Olinordered__field > class_Fields_Ofield__inverse__zero > class_Fields_Ofield > class_Divides_Osemiring__div > c_Rings_Oinverse__class_Odivide > c_Power_Opower__class_Opower > c_Groups_Otimes__class_Otimes > c_Groups_Oplus__class_Oplus > c_Groups_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > tc_fun > hAPP > c_RealVector_Oof__real > c_RealVector_Onorm__class_Onorm > c_Int_Onumber__class_Onumber__of > c_Groups_Oabs__class_Oabs > #nlpp > c_Transcendental_Oarctan > c_NthRoot_Osqrt > c_Nat_OSuc > c_Int_OBit1 > c_Int_OBit0 > c_Groups_Ozero__class_Ozero > c_Groups_Oone__class_Oone > c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt > v_na____ > v_n > v_b > tc_RealDef_Oreal > tc_Nat_Onat > tc_Int_Oint > tc_HOL_Obool > tc_Complex_Ocomplex > c_Int_OPls > c_Int_OMin > c_Complex_Oii > #skF_7 > #skF_6 > #skF_17 > #skF_2 > #skF_4 > #skF_1 > #skF_9 > #skF_13 > #skF_10 > #skF_8 > #skF_15 > #skF_14 > #skF_3 > #skF_11 > #skF_5 > #skF_12 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_Groups_Olinordered__ab__group__add,type,
    class_Groups_Olinordered__ab__group__add: $i > $o ).

tff(class_Rings_Ocomm__semiring__1,type,
    class_Rings_Ocomm__semiring__1: $i > $o ).

tff(c_Orderings_Oord__class_Oless__eq,type,
    c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).

tff(class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $i > $o ).

tff(class_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $i > $o ).

tff('#skF_7',type,
    '#skF_7': $i > $i ).

tff(class_Groups_Omonoid__add,type,
    class_Groups_Omonoid__add: $i > $o ).

tff(class_Rings_Oordered__ring,type,
    class_Rings_Oordered__ring: $i > $o ).

tff(class_Rings_Olinordered__semiring__strict,type,
    class_Rings_Olinordered__semiring__strict: $i > $o ).

tff(class_Int_Onumber__ring,type,
    class_Int_Onumber__ring: $i > $o ).

tff(class_Rings_Osemiring,type,
    class_Rings_Osemiring: $i > $o ).

tff(tc_HOL_Obool,type,
    tc_HOL_Obool: $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

tff(c_Parity_Oeven__odd__class_Oeven,type,
    c_Parity_Oeven__odd__class_Oeven: ( $i * $i ) > $o ).

tff('#skF_2',type,
    '#skF_2': $i > $i ).

tff('#skF_4',type,
    '#skF_4': $i > $i ).

tff(class_Groups_Oordered__ab__semigroup__add__imp__le,type,
    class_Groups_Oordered__ab__semigroup__add__imp__le: $i > $o ).

tff(tc_Nat_Onat,type,
    tc_Nat_Onat: $i ).

tff(class_Groups_Oone,type,
    class_Groups_Oone: $i > $o ).

tff(class_Rings_Olinordered__semiring,type,
    class_Rings_Olinordered__semiring: $i > $o ).

tff(c_Int_Onumber__class_Onumber__of,type,
    c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).

tff(class_RealVector_Oreal__normed__algebra__1,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

tff(class_Groups_Ocomm__monoid__add,type,
    class_Groups_Ocomm__monoid__add: $i > $o ).

tff(v_na____,type,
    v_na____: $i ).

tff(class_RealVector_Oreal__normed__field,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

tff(class_Groups_Omonoid__mult,type,
    class_Groups_Omonoid__mult: $i > $o ).

tff('#skF_1',type,
    '#skF_1': $i > $i ).

tff(class_Rings_Olinordered__comm__semiring__strict,type,
    class_Rings_Olinordered__comm__semiring__strict: $i > $o ).

tff(v_n,type,
    v_n: $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i * $i ) > $i ).

tff(c_Groups_Oone__class_Oone,type,
    c_Groups_Oone__class_Oone: $i > $i ).

tff(tc_Int_Oint,type,
    tc_Int_Oint: $i ).

tff(class_Fields_Ofield__inverse__zero,type,
    class_Fields_Ofield__inverse__zero: $i > $o ).

tff(class_Orderings_Oorder,type,
    class_Orderings_Oorder: $i > $o ).

tff(class_Orderings_Opreorder,type,
    class_Orderings_Opreorder: $i > $o ).

tff(class_Rings_Olinordered__ring,type,
    class_Rings_Olinordered__ring: $i > $o ).

tff(v_b,type,
    v_b: $i ).

tff(tc_RealDef_Oreal,type,
    tc_RealDef_Oreal: $i ).

tff(class_Int_Onumber,type,
    class_Int_Onumber: $i > $o ).

tff(class_Groups_Ocomm__monoid__mult,type,
    class_Groups_Ocomm__monoid__mult: $i > $o ).

tff(class_Rings_Oordered__comm__semiring,type,
    class_Rings_Oordered__comm__semiring: $i > $o ).

tff(class_Rings_Olinordered__semidom,type,
    class_Rings_Olinordered__semidom: $i > $o ).

tff(c_Int_OPls,type,
    c_Int_OPls: $i ).

tff('#skF_13',type,
    '#skF_13': ( $i * $i ) > $i ).

tff(c_Complex_Oii,type,
    c_Complex_Oii: $i ).

tff(c_Int_OBit0,type,
    c_Int_OBit0: $i > $i ).

tff(class_Rings_Odivision__ring,type,
    class_Rings_Odivision__ring: $i > $o ).

tff(class_Rings_Ocomm__semiring,type,
    class_Rings_Ocomm__semiring: $i > $o ).

tff(class_Groups_Oordered__ab__group__add__abs,type,
    class_Groups_Oordered__ab__group__add__abs: $i > $o ).

tff(class_Groups_Ocancel__semigroup__add,type,
    class_Groups_Ocancel__semigroup__add: $i > $o ).

tff(class_Rings_Oordered__cancel__semiring,type,
    class_Rings_Oordered__cancel__semiring: $i > $o ).

tff(c_Rings_Oinverse__class_Odivide,type,
    c_Rings_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).

tff(c_Int_OBit1,type,
    c_Int_OBit1: $i > $i ).

tff(class_Fields_Ofield,type,
    class_Fields_Ofield: $i > $o ).

tff(c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt: $i > $i ).

tff(class_Rings_Olinordered__semiring__1,type,
    class_Rings_Olinordered__semiring__1: $i > $o ).

tff(class_Rings_Oordered__ring__abs,type,
    class_Rings_Oordered__ring__abs: $i > $o ).

tff(class_Groups_Oordered__comm__monoid__add,type,
    class_Groups_Oordered__comm__monoid__add: $i > $o ).

tff(c_Groups_Ominus__class_Ominus,type,
    c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).

tff(c_Orderings_Oord__class_Oless,type,
    c_Orderings_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_Divides_Odiv__class_Omod,type,
    c_Divides_Odiv__class_Omod: ( $i * $i * $i ) > $i ).

tff(c_Groups_Ozero__class_Ozero,type,
    c_Groups_Ozero__class_Ozero: $i > $i ).

tff(class_RealVector_Oreal__normed__algebra,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

tff(class_RealVector_Oreal__normed__div__algebra,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

tff(class_Rings_Odivision__ring__inverse__zero,type,
    class_Rings_Odivision__ring__inverse__zero: $i > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff(class_Power_Opower,type,
    class_Power_Opower: $i > $o ).

tff(tc_fun,type,
    tc_fun: ( $i * $i ) > $i ).

tff(c_NthRoot_Osqrt,type,
    c_NthRoot_Osqrt: $i > $i ).

tff(class_Rings_Osemiring__0,type,
    class_Rings_Osemiring__0: $i > $o ).

tff(class_Rings_Omult__zero,type,
    class_Rings_Omult__zero: $i > $o ).

tff(c_Groups_Oplus__class_Oplus,type,
    c_Groups_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).

tff(class_Orderings_Oord,type,
    class_Orderings_Oord: $i > $o ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(class_RealVector_Oreal__normed__vector,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

tff(class_Groups_Oab__semigroup__add,type,
    class_Groups_Oab__semigroup__add: $i > $o ).

tff(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
    class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct: $i > $o ).

tff(class_Fields_Olinordered__field,type,
    class_Fields_Olinordered__field: $i > $o ).

tff(c_Groups_Oabs__class_Oabs,type,
    c_Groups_Oabs__class_Oabs: ( $i * $i ) > $i ).

tff(class_RealVector_Oreal__algebra__1,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

tff(c_Power_Opower__class_Opower,type,
    c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).

tff(tc_Complex_Ocomplex,type,
    tc_Complex_Ocomplex: $i ).

tff(class_Groups_Ocancel__ab__semigroup__add,type,
    class_Groups_Ocancel__ab__semigroup__add: $i > $o ).

tff(c_Groups_Otimes__class_Otimes,type,
    c_Groups_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(class_Groups_Ozero,type,
    class_Groups_Ozero: $i > $o ).

tff(class_Rings_Oring__no__zero__divisors,type,
    class_Rings_Oring__no__zero__divisors: $i > $o ).

tff(class_Rings_Osemiring__1,type,
    class_Rings_Osemiring__1: $i > $o ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff(class_Rings_Olinordered__semiring__1__strict,type,
    class_Rings_Olinordered__semiring__1__strict: $i > $o ).

tff(c_Nat_OSuc,type,
    c_Nat_OSuc: $i > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

tff(c_RealVector_Onorm__class_Onorm,type,
    c_RealVector_Onorm__class_Onorm: ( $i * $i ) > $i ).

tff(hAPP,type,
    hAPP: ( $i * $i ) > $i ).

tff(class_Groups_Oab__semigroup__mult,type,
    class_Groups_Oab__semigroup__mult: $i > $o ).

tff(class_Groups_Oordered__cancel__ab__semigroup__add,type,
    class_Groups_Oordered__cancel__ab__semigroup__add: $i > $o ).

tff('#skF_3',type,
    '#skF_3': $i > $i ).

tff('#skF_11',type,
    '#skF_11': $i > $i ).

tff(class_Rings_Ozero__neq__one,type,
    class_Rings_Ozero__neq__one: $i > $o ).

tff(class_Rings_Ono__zero__divisors,type,
    class_Rings_Ono__zero__divisors: $i > $o ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff(class_Divides_Osemiring__div,type,
    class_Divides_Osemiring__div: $i > $o ).

tff(c_RealVector_Oof__real,type,
    c_RealVector_Oof__real: ( $i * $i ) > $i ).

tff(class_Rings_Oordered__semiring,type,
    class_Rings_Oordered__semiring: $i > $o ).

tff(class_RealVector_Oreal__field,type,
    class_RealVector_Oreal__field: $i > $o ).

tff(class_Rings_Olinordered__idom,type,
    class_Rings_Olinordered__idom: $i > $o ).

tff(class_Fields_Olinordered__field__inverse__zero,type,
    class_Fields_Olinordered__field__inverse__zero: $i > $o ).

tff(c_Transcendental_Oarctan,type,
    c_Transcendental_Oarctan: $i > $i ).

tff(class_Rings_Olinordered__ring__strict,type,
    class_Rings_Olinordered__ring__strict: $i > $o ).

tff(class_Rings_Oring__1__no__zero__divisors,type,
    class_Rings_Oring__1__no__zero__divisors: $i > $o ).

tff(class_Groups_Oordered__ab__semigroup__add,type,
    class_Groups_Oordered__ab__semigroup__add: $i > $o ).

tff(c_Int_OMin,type,
    c_Int_OMin: $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_3920,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

tff(f_199,axiom,
    ! [V_x_2] :
      ( ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2)
    <=> ? [B_y] : ( V_x_2 = 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))),B_y)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nat__equiv__def2) ).

tff(f_3924,axiom,
    ! [V_n] : ( c_Nat_OSuc(V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

tff(f_4596,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/benchmark/theBenchmark.p',fact_nat__1__add__1) ).

tff(f_5907,negated_conjecture,
    ~ ? [B_m] : ( 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))),B_m)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

tff(f_29,axiom,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o) ).

tff(c_2193,plain,
    c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    inference(cnfTransformation,[status(thm)],[f_3920]) ).

tff(c_147,plain,
    ! [V_x_2_78] :
      ( ( 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))),'#skF_3'(V_x_2_78))) = V_x_2_78 )
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2_78) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_91443,plain,
    ! [V_x_2_4019] :
      ( ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),'#skF_3'(V_x_2_4019))) = V_x_2_4019 )
      | c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,V_x_2_4019) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2193,c_147]) ).

tff(c_2197,plain,
    ! [V_n_1799] : ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_1799,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_OSuc(V_n_1799) ),
    inference(cnfTransformation,[status(thm)],[f_3924]) ).

tff(c_2655,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(cnfTransformation,[status(thm)],[f_4596]) ).

tff(c_3714,plain,
    c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(demodulation,[status(thm),theory(equality)],[c_2197,c_2655]) ).

tff(c_3706,plain,
    ! [B_m_2524] : ( 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))),B_m_2524)) != v_na____ ),
    inference(cnfTransformation,[status(thm)],[f_5907]) ).

tff(c_3718,plain,
    ! [B_m_2524] : ( c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)),B_m_2524)) != v_na____ ),
    inference(demodulation,[status(thm),theory(equality)],[c_3714,c_3706]) ).

tff(c_91959,plain,
    c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(superposition,[status(thm),theory(equality)],[c_91443,c_3718]) ).

tff(c_2,plain,
    ~ c_Parity_Oeven__odd__class_Oeven(tc_Nat_Onat,v_na____),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_91962,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_91959,c_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW198+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 19:39:59 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 50.08/27.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.08/27.30  
% 50.08/27.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 50.08/27.33  
% 50.08/27.33  Inference rules
% 50.08/27.33  ----------------------
% 50.08/27.33  #Ref     : 43
% 50.08/27.33  #Sup     : 18547
% 50.08/27.33  #Fact    : 20
% 50.08/27.33  #Define  : 0
% 50.08/27.33  #Split   : 9
% 50.08/27.33  #Chain   : 0
% 50.08/27.33  #Close   : 0
% 50.08/27.33  
% 50.08/27.33  Ordering : KBO
% 50.08/27.33  
% 50.08/27.33  Simplification rules
% 50.08/27.33  ----------------------
% 50.08/27.33  #Subsume      : 6643
% 50.08/27.33  #Demod        : 14613
% 50.08/27.33  #Tautology    : 6987
% 50.08/27.33  #SimpNegUnit  : 1110
% 50.08/27.33  #BackRed      : 33
% 50.08/27.33  
% 50.08/27.33  #Partial instantiations: 0
% 50.08/27.33  #Strategies tried      : 1
% 50.08/27.33  
% 50.08/27.33  Timing (in seconds)
% 50.08/27.33  ----------------------
% 50.23/27.33  Preprocessing        : 2.21
% 50.23/27.34  Parsing              : 1.28
% 50.23/27.34  CNF conversion       : 0.17
% 50.23/27.34  Main loop            : 24.06
% 50.23/27.34  Inferencing          : 2.90
% 50.23/27.34  Reduction            : 13.62
% 50.23/27.34  Demodulation         : 10.50
% 50.23/27.34  BG Simplification    : 0.28
% 50.23/27.34  Subsumption          : 5.96
% 50.23/27.34  Abstraction          : 0.22
% 50.23/27.34  MUC search           : 0.00
% 50.23/27.34  Cooper               : 0.00
% 50.23/27.34  Total                : 26.33
% 50.23/27.34  Index Insertion      : 0.00
% 50.23/27.34  Index Deletion       : 0.00
% 50.23/27.34  Index Matching       : 0.00
% 50.23/27.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------