TSTP Solution File: SYN415+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SYN415+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n001.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 11:10:48 EDT 2023

% Result   : Theorem 3.24s 1.80s
% Output   : CNFRefutation 3.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  175 (  91 unt;   6 typ;   0 def)
%            Number of atoms       :  308 ( 100 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :  300 ( 161   ~; 133   |;   3   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :  126 (; 124   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ f > #nlpp > #skF_2 > #skF_5 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(f_44,negated_conjecture,
    ~ ( ( ? [X] : f(X)
        & ! [Y,Z] :
            ( ( f(Y)
              & f(Z) )
           => ( Y = Z ) ) )
    <=> ? [U] :
          ( f(U)
          & ! [V] :
              ( f(V)
             => ( U = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish317) ).

tff(c_20,plain,
    ! [X_7] :
      ( f('#skF_1')
      | f('#skF_4')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_42,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_20]) ).

tff(c_36,plain,
    ( f('#skF_1')
    | f('#skF_3') ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_41,plain,
    f('#skF_3'),
    inference(splitLeft,[status(thm)],[c_36]) ).

tff(c_44,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_41]) ).

tff(c_45,plain,
    ( f('#skF_4')
    | f('#skF_1') ),
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_46,plain,
    f('#skF_1'),
    inference(splitLeft,[status(thm)],[c_45]) ).

tff(c_30,plain,
    ! [U_3,V_6] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_351,plain,
    ! [U_24] :
      ( ( '#skF_2'(U_24) != U_24 )
      | ~ f(U_24) ),
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_362,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_351]) ).

tff(c_24,plain,
    ! [U_3,X_7] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | f('#skF_4')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_82,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_24]) ).

tff(c_16,plain,
    ! [U_3,X_7] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | f('#skF_5')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_71,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_16]) ).

tff(c_73,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_71,c_46]) ).

tff(c_74,plain,
    ! [U_3] :
      ( f('#skF_5')
      | f('#skF_2'(U_3))
      | ~ f(U_3) ),
    inference(splitRight,[status(thm)],[c_16]) ).

tff(c_81,plain,
    f('#skF_5'),
    inference(splitLeft,[status(thm)],[c_74]) ).

tff(c_89,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_82,c_81]) ).

tff(c_90,plain,
    ! [U_3] :
      ( f('#skF_4')
      | f('#skF_2'(U_3))
      | ~ f(U_3) ),
    inference(splitRight,[status(thm)],[c_24]) ).

tff(c_101,plain,
    f('#skF_4'),
    inference(splitLeft,[status(thm)],[c_90]) ).

tff(c_32,plain,
    ! [U_3,V_6] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_54,plain,
    ! [V_8] :
      ( ( V_8 = '#skF_3' )
      | ~ f(V_8) ),
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_61,plain,
    '#skF_3' = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_54]) ).

tff(c_53,plain,
    ! [V_6] :
      ( ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(splitLeft,[status(thm)],[c_32]) ).

tff(c_64,plain,
    ! [V_6] :
      ( ( V_6 = '#skF_1' )
      | ~ f(V_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_61,c_53]) ).

tff(c_105,plain,
    '#skF_1' = '#skF_4',
    inference(resolution,[status(thm)],[c_101,c_64]) ).

tff(c_94,plain,
    '#skF_5' = '#skF_1',
    inference(resolution,[status(thm)],[c_81,c_64]) ).

tff(c_106,plain,
    '#skF_5' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_94]) ).

tff(c_8,plain,
    ! [U_3,X_7] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | ( '#skF_5' != '#skF_4' )
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_124,plain,
    ! [U_3,X_7] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | ~ f(X_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_8]) ).

tff(c_125,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_124]) ).

tff(c_127,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_125,c_101]) ).

tff(c_135,plain,
    ! [U_11] :
      ( f('#skF_2'(U_11))
      | ~ f(U_11) ),
    inference(splitRight,[status(thm)],[c_124]) ).

tff(c_107,plain,
    ! [V_6] :
      ( ( V_6 = '#skF_4' )
      | ~ f(V_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_64]) ).

tff(c_140,plain,
    ! [U_12] :
      ( ( '#skF_2'(U_12) = '#skF_4' )
      | ~ f(U_12) ),
    inference(resolution,[status(thm)],[c_135,c_107]) ).

tff(c_148,plain,
    '#skF_2'('#skF_4') = '#skF_4',
    inference(resolution,[status(thm)],[c_101,c_140]) ).

tff(c_6,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ( '#skF_5' != '#skF_4' )
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_187,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ~ f(X_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_6]) ).

tff(c_188,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_187]) ).

tff(c_192,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_188,c_101]) ).

tff(c_194,plain,
    ! [U_14] :
      ( ( '#skF_2'(U_14) != U_14 )
      | ~ f(U_14) ),
    inference(splitRight,[status(thm)],[c_187]) ).

tff(c_200,plain,
    '#skF_2'('#skF_4') != '#skF_4',
    inference(resolution,[status(thm)],[c_101,c_194]) ).

tff(c_205,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_148,c_200]) ).

tff(c_208,plain,
    ! [U_15] :
      ( f('#skF_2'(U_15))
      | ~ f(U_15) ),
    inference(splitRight,[status(thm)],[c_90]) ).

tff(c_213,plain,
    ! [U_16] :
      ( ( '#skF_2'(U_16) = '#skF_1' )
      | ~ f(U_16) ),
    inference(resolution,[status(thm)],[c_208,c_64]) ).

tff(c_221,plain,
    '#skF_2'('#skF_1') = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_213]) ).

tff(c_207,plain,
    ~ f('#skF_4'),
    inference(splitRight,[status(thm)],[c_90]) ).

tff(c_22,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | f('#skF_4')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_259,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ~ f(X_7) ),
    inference(negUnitSimplification,[status(thm)],[c_207,c_22]) ).

tff(c_260,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_259]) ).

tff(c_263,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_260,c_46]) ).

tff(c_265,plain,
    ! [U_18] :
      ( ( '#skF_2'(U_18) != U_18 )
      | ~ f(U_18) ),
    inference(splitRight,[status(thm)],[c_259]) ).

tff(c_271,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_265]) ).

tff(c_276,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_221,c_271]) ).

tff(c_279,plain,
    ! [U_19] :
      ( f('#skF_2'(U_19))
      | ~ f(U_19) ),
    inference(splitRight,[status(thm)],[c_74]) ).

tff(c_284,plain,
    ! [U_20] :
      ( ( '#skF_2'(U_20) = '#skF_1' )
      | ~ f(U_20) ),
    inference(resolution,[status(thm)],[c_279,c_64]) ).

tff(c_292,plain,
    '#skF_2'('#skF_1') = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_284]) ).

tff(c_278,plain,
    ~ f('#skF_5'),
    inference(splitRight,[status(thm)],[c_74]) ).

tff(c_14,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | f('#skF_5')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_329,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ~ f(X_7) ),
    inference(negUnitSimplification,[status(thm)],[c_278,c_14]) ).

tff(c_330,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_329]) ).

tff(c_334,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_330,c_46]) ).

tff(c_336,plain,
    ! [U_22] :
      ( ( '#skF_2'(U_22) != U_22 )
      | ~ f(U_22) ),
    inference(splitRight,[status(thm)],[c_329]) ).

tff(c_342,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_336]) ).

tff(c_347,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_292,c_342]) ).

tff(c_348,plain,
    ! [U_3] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3) ),
    inference(splitRight,[status(thm)],[c_32]) ).

tff(c_18,plain,
    ! [Z_2,Y_1,X_7] :
      ( ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1)
      | f('#skF_4')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_365,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_18]) ).

tff(c_369,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_365,c_46]) ).

tff(c_370,plain,
    ! [Z_2,Y_1] :
      ( f('#skF_4')
      | ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1) ),
    inference(splitRight,[status(thm)],[c_18]) ).

tff(c_371,plain,
    f('#skF_4'),
    inference(splitLeft,[status(thm)],[c_370]) ).

tff(c_350,plain,
    ! [U_3] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3) ),
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_375,plain,
    '#skF_2'('#skF_4') != '#skF_4',
    inference(resolution,[status(thm)],[c_371,c_350]) ).

tff(c_2,plain,
    ! [Z_2,Y_1,X_7] :
      ( ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1)
      | ( '#skF_5' != '#skF_4' )
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_376,plain,
    '#skF_5' != '#skF_4',
    inference(splitLeft,[status(thm)],[c_2]) ).

tff(c_10,plain,
    ! [Z_2,Y_1,X_7] :
      ( ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1)
      | f('#skF_5')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_377,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_10]) ).

tff(c_382,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_377,c_371]) ).

tff(c_383,plain,
    ! [Z_2,Y_1] :
      ( f('#skF_5')
      | ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1) ),
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_384,plain,
    f('#skF_5'),
    inference(splitLeft,[status(thm)],[c_383]) ).

tff(c_26,plain,
    ! [Z_2,Y_1,V_6] :
      ( ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1)
      | ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_390,plain,
    ! [V_26] :
      ( ( V_26 = '#skF_3' )
      | ~ f(V_26) ),
    inference(splitLeft,[status(thm)],[c_26]) ).

tff(c_407,plain,
    '#skF_3' = '#skF_4',
    inference(resolution,[status(thm)],[c_371,c_390]) ).

tff(c_406,plain,
    '#skF_5' = '#skF_3',
    inference(resolution,[status(thm)],[c_384,c_390]) ).

tff(c_414,plain,
    '#skF_3' != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_406,c_376]) ).

tff(c_435,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_414]) ).

tff(c_437,plain,
    ! [Z_27,Y_28] :
      ( ( Z_27 = Y_28 )
      | ~ f(Z_27)
      | ~ f(Y_28) ),
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_453,plain,
    ! [Y_29] :
      ( ( Y_29 = '#skF_5' )
      | ~ f(Y_29) ),
    inference(resolution,[status(thm)],[c_384,c_437]) ).

tff(c_459,plain,
    '#skF_5' = '#skF_4',
    inference(resolution,[status(thm)],[c_371,c_453]) ).

tff(c_474,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_376,c_459]) ).

tff(c_477,plain,
    ! [Z_30,Y_31] :
      ( ( Z_30 = Y_31 )
      | ~ f(Z_30)
      | ~ f(Y_31) ),
    inference(splitRight,[status(thm)],[c_383]) ).

tff(c_490,plain,
    ! [Y_32] :
      ( ( Y_32 = '#skF_4' )
      | ~ f(Y_32) ),
    inference(resolution,[status(thm)],[c_371,c_477]) ).

tff(c_524,plain,
    ! [U_33] :
      ( ( '#skF_2'(U_33) = '#skF_4' )
      | ~ f(U_33) ),
    inference(resolution,[status(thm)],[c_348,c_490]) ).

tff(c_527,plain,
    '#skF_2'('#skF_4') = '#skF_4',
    inference(resolution,[status(thm)],[c_371,c_524]) ).

tff(c_534,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_375,c_527]) ).

tff(c_535,plain,
    ! [X_7,Z_2,Y_1] :
      ( ~ f(X_7)
      | ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1) ),
    inference(splitRight,[status(thm)],[c_2]) ).

tff(c_541,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_535]) ).

tff(c_546,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_541,c_371]) ).

tff(c_548,plain,
    ! [Z_34,Y_35] :
      ( ( Z_34 = Y_35 )
      | ~ f(Z_34)
      | ~ f(Y_35) ),
    inference(splitRight,[status(thm)],[c_535]) ).

tff(c_561,plain,
    ! [Y_36] :
      ( ( Y_36 = '#skF_4' )
      | ~ f(Y_36) ),
    inference(resolution,[status(thm)],[c_371,c_548]) ).

tff(c_595,plain,
    ! [U_37] :
      ( ( '#skF_2'(U_37) = '#skF_4' )
      | ~ f(U_37) ),
    inference(resolution,[status(thm)],[c_348,c_561]) ).

tff(c_598,plain,
    '#skF_2'('#skF_4') = '#skF_4',
    inference(resolution,[status(thm)],[c_371,c_595]) ).

tff(c_605,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_375,c_598]) ).

tff(c_608,plain,
    ! [Z_38,Y_39] :
      ( ( Z_38 = Y_39 )
      | ~ f(Z_38)
      | ~ f(Y_39) ),
    inference(splitRight,[status(thm)],[c_370]) ).

tff(c_618,plain,
    ! [Y_40] :
      ( ( Y_40 = '#skF_1' )
      | ~ f(Y_40) ),
    inference(resolution,[status(thm)],[c_46,c_608]) ).

tff(c_640,plain,
    ! [U_41] :
      ( ( '#skF_2'(U_41) = '#skF_1' )
      | ~ f(U_41) ),
    inference(resolution,[status(thm)],[c_348,c_618]) ).

tff(c_646,plain,
    '#skF_2'('#skF_1') = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_640]) ).

tff(c_651,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_362,c_646]) ).

tff(c_653,plain,
    ! [V_42] :
      ( ( V_42 = '#skF_3' )
      | ~ f(V_42) ),
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_664,plain,
    '#skF_3' = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_653]) ).

tff(c_663,plain,
    ! [U_3] :
      ( ( '#skF_2'(U_3) = '#skF_3' )
      | ~ f(U_3) ),
    inference(resolution,[status(thm)],[c_348,c_653]) ).

tff(c_690,plain,
    ! [U_44] :
      ( ( '#skF_2'(U_44) = '#skF_1' )
      | ~ f(U_44) ),
    inference(demodulation,[status(thm),theory(equality)],[c_664,c_663]) ).

tff(c_698,plain,
    '#skF_2'('#skF_1') = '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_690]) ).

tff(c_763,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_22]) ).

tff(c_767,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_763,c_46]) ).

tff(c_768,plain,
    ! [U_3] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | f('#skF_4') ),
    inference(splitRight,[status(thm)],[c_22]) ).

tff(c_770,plain,
    ! [U_47] :
      ( ( '#skF_2'(U_47) != U_47 )
      | ~ f(U_47) ),
    inference(splitLeft,[status(thm)],[c_768]) ).

tff(c_776,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_770]) ).

tff(c_781,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_698,c_776]) ).

tff(c_782,plain,
    f('#skF_4'),
    inference(splitRight,[status(thm)],[c_768]) ).

tff(c_652,plain,
    ! [V_6] :
      ( ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_667,plain,
    ! [V_6] :
      ( ( V_6 = '#skF_1' )
      | ~ f(V_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_664,c_652]) ).

tff(c_790,plain,
    '#skF_1' = '#skF_4',
    inference(resolution,[status(thm)],[c_782,c_667]) ).

tff(c_793,plain,
    '#skF_2'('#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_790,c_790,c_698]) ).

tff(c_684,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_14]) ).

tff(c_687,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_684,c_46]) ).

tff(c_688,plain,
    ! [U_3] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | f('#skF_5') ),
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_735,plain,
    ! [U_46] :
      ( ( '#skF_2'(U_46) != U_46 )
      | ~ f(U_46) ),
    inference(splitLeft,[status(thm)],[c_688]) ).

tff(c_741,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_46,c_735]) ).

tff(c_746,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_698,c_741]) ).

tff(c_747,plain,
    f('#skF_5'),
    inference(splitRight,[status(thm)],[c_688]) ).

tff(c_755,plain,
    '#skF_5' = '#skF_1',
    inference(resolution,[status(thm)],[c_747,c_667]) ).

tff(c_791,plain,
    '#skF_5' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_790,c_755]) ).

tff(c_821,plain,
    ! [U_3,X_7] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | ~ f(X_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_791,c_6]) ).

tff(c_822,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_821]) ).

tff(c_825,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_822,c_782]) ).

tff(c_838,plain,
    ! [U_49] :
      ( ( '#skF_2'(U_49) != U_49 )
      | ~ f(U_49) ),
    inference(splitRight,[status(thm)],[c_821]) ).

tff(c_841,plain,
    '#skF_2'('#skF_4') != '#skF_4',
    inference(resolution,[status(thm)],[c_782,c_838]) ).

tff(c_848,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_793,c_841]) ).

tff(c_850,plain,
    ~ f('#skF_1'),
    inference(splitRight,[status(thm)],[c_45]) ).

tff(c_849,plain,
    f('#skF_4'),
    inference(splitRight,[status(thm)],[c_45]) ).

tff(c_28,plain,
    ! [V_6] :
      ( f('#skF_1')
      | ( V_6 = '#skF_3' )
      | ~ f(V_6) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_858,plain,
    ! [V_50] :
      ( ( V_50 = '#skF_3' )
      | ~ f(V_50) ),
    inference(negUnitSimplification,[status(thm)],[c_850,c_28]) ).

tff(c_869,plain,
    '#skF_3' = '#skF_4',
    inference(resolution,[status(thm)],[c_849,c_858]) ).

tff(c_12,plain,
    ! [X_7] :
      ( f('#skF_1')
      | f('#skF_5')
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_851,plain,
    ! [X_7] :
      ( f('#skF_5')
      | ~ f(X_7) ),
    inference(negUnitSimplification,[status(thm)],[c_850,c_12]) ).

tff(c_852,plain,
    ! [X_7] : ~ f(X_7),
    inference(splitLeft,[status(thm)],[c_851]) ).

tff(c_855,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_852,c_849]) ).

tff(c_856,plain,
    f('#skF_5'),
    inference(splitRight,[status(thm)],[c_851]) ).

tff(c_868,plain,
    '#skF_5' = '#skF_3',
    inference(resolution,[status(thm)],[c_856,c_858]) ).

tff(c_878,plain,
    '#skF_5' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_869,c_868]) ).

tff(c_4,plain,
    ! [X_7] :
      ( f('#skF_1')
      | ( '#skF_5' != '#skF_4' )
      | ~ f(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_897,plain,
    ! [X_7] :
      ( f('#skF_1')
      | ~ f(X_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_878,c_4]) ).

tff(c_898,plain,
    ! [X_7] : ~ f(X_7),
    inference(negUnitSimplification,[status(thm)],[c_850,c_897]) ).

tff(c_900,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_898,c_849]) ).

tff(c_901,plain,
    f('#skF_1'),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_902,plain,
    ~ f('#skF_3'),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_38,plain,
    ! [U_3] :
      ( ( '#skF_2'(U_3) != U_3 )
      | ~ f(U_3)
      | f('#skF_3') ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_908,plain,
    ! [U_52] :
      ( ( '#skF_2'(U_52) != U_52 )
      | ~ f(U_52) ),
    inference(negUnitSimplification,[status(thm)],[c_902,c_38]) ).

tff(c_912,plain,
    '#skF_2'('#skF_1') != '#skF_1',
    inference(resolution,[status(thm)],[c_901,c_908]) ).

tff(c_40,plain,
    ! [U_3] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3)
      | f('#skF_3') ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_913,plain,
    ! [U_3] :
      ( f('#skF_2'(U_3))
      | ~ f(U_3) ),
    inference(negUnitSimplification,[status(thm)],[c_902,c_40]) ).

tff(c_34,plain,
    ! [Z_2,Y_1] :
      ( ( Z_2 = Y_1 )
      | ~ f(Z_2)
      | ~ f(Y_1)
      | f('#skF_3') ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_921,plain,
    ! [Z_55,Y_56] :
      ( ( Z_55 = Y_56 )
      | ~ f(Z_55)
      | ~ f(Y_56) ),
    inference(negUnitSimplification,[status(thm)],[c_902,c_34]) ).

tff(c_928,plain,
    ! [Y_57] :
      ( ( Y_57 = '#skF_1' )
      | ~ f(Y_57) ),
    inference(resolution,[status(thm)],[c_901,c_921]) ).

tff(c_938,plain,
    ! [U_58] :
      ( ( '#skF_2'(U_58) = '#skF_1' )
      | ~ f(U_58) ),
    inference(resolution,[status(thm)],[c_913,c_928]) ).

tff(c_944,plain,
    '#skF_2'('#skF_1') = '#skF_1',
    inference(resolution,[status(thm)],[c_901,c_938]) ).

tff(c_949,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_912,c_944]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN415+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.12  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.12/0.33  % Computer : n001.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu Aug  3 18:01:40 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 3.24/1.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.24/1.82  
% 3.24/1.82  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/1.86  
% 3.51/1.86  Inference rules
% 3.51/1.86  ----------------------
% 3.51/1.86  #Ref     : 0
% 3.51/1.86  #Sup     : 184
% 3.51/1.86  #Fact    : 0
% 3.51/1.86  #Define  : 0
% 3.51/1.86  #Split   : 27
% 3.51/1.86  #Chain   : 0
% 3.51/1.86  #Close   : 0
% 3.51/1.86  
% 3.51/1.86  Ordering : KBO
% 3.51/1.86  
% 3.51/1.86  Simplification rules
% 3.51/1.86  ----------------------
% 3.51/1.86  #Subsume      : 64
% 3.51/1.86  #Demod        : 132
% 3.51/1.86  #Tautology    : 126
% 3.51/1.86  #SimpNegUnit  : 44
% 3.51/1.86  #BackRed      : 61
% 3.51/1.86  
% 3.51/1.86  #Partial instantiations: 0
% 3.51/1.86  #Strategies tried      : 1
% 3.51/1.86  
% 3.51/1.86  Timing (in seconds)
% 3.51/1.86  ----------------------
% 3.51/1.86  Preprocessing        : 0.41
% 3.51/1.86  Parsing              : 0.21
% 3.51/1.86  CNF conversion       : 0.03
% 3.51/1.87  Main loop            : 0.40
% 3.51/1.87  Inferencing          : 0.14
% 3.51/1.87  Reduction            : 0.10
% 3.51/1.87  Demodulation         : 0.06
% 3.51/1.87  BG Simplification    : 0.02
% 3.51/1.87  Subsumption          : 0.08
% 3.51/1.87  Abstraction          : 0.02
% 3.51/1.87  MUC search           : 0.00
% 3.51/1.87  Cooper               : 0.00
% 3.51/1.87  Total                : 0.89
% 3.51/1.87  Index Insertion      : 0.00
% 3.51/1.87  Index Deletion       : 0.00
% 3.51/1.87  Index Matching       : 0.00
% 3.51/1.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------