TSTP Solution File: SYN015-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SYN015-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n009.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 11:08:32 EDT 2023

% Result   : Unsatisfiable 3.94s 2.21s
% Output   : CNFRefutation 4.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  134 (  44 unt;   7 typ;   0 def)
%            Number of atoms       :  320 ( 194 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  296 ( 103   ~; 193   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :   55 (;  55   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ element > #nlpp > g > f > n > m > k > j

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(m,type,
    m: $i ).

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

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

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

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

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

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

tff(f_34,axiom,
    ! [Y] :
      ( ( Y = j )
      | ( Y != k )
      | element(Y,j) ),
    file(unknown,unknown) ).

tff(f_140,axiom,
    ! [Y] :
      ( ( Y = k )
      | ( Y != n )
      | element(Y,k) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    m != n,
    file(unknown,unknown) ).

tff(f_133,axiom,
    ! [Y] :
      ( ( Y = k )
      | ( Y != m )
      | element(Y,k) ),
    file(unknown,unknown) ).

tff(f_41,axiom,
    ! [Y] :
      ( ( Y = j )
      | ( Y = k )
      | ~ element(Y,j) ),
    file(unknown,unknown) ).

tff(f_85,axiom,
    ! [Y,V1] :
      ( ( Y = m )
      | element(Y,m)
      | ( V1 = m )
      | ( V1 = Y )
      | ~ element(Y,V1)
      | ~ element(V1,Y) ),
    file(unknown,unknown) ).

tff(f_99,axiom,
    ! [Y] :
      ( ( Y = n )
      | element(Y,n)
      | ( g(Y) != Y ) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ! [Y] :
      ( ( Y = n )
      | element(Y,n)
      | ( g(Y) != n ) ),
    file(unknown,unknown) ).

tff(f_111,axiom,
    ! [Y] :
      ( ( Y = n )
      | element(Y,n)
      | element(g(Y),Y) ),
    file(unknown,unknown) ).

tff(f_149,axiom,
    ! [Y] :
      ( ( Y = k )
      | ( Y = m )
      | ( Y = n )
      | ~ element(Y,k) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [Y] :
      ( ( Y = m )
      | ~ element(Y,m)
      | ( f(Y) != Y ) ),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [Y] :
      ( ( Y = m )
      | ~ element(Y,m)
      | ( f(Y) != m ) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [Y] :
      ( ( Y = m )
      | ~ element(Y,m)
      | element(f(Y),Y) ),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ! [Y] :
      ( ( Y = m )
      | ~ element(Y,m)
      | element(Y,f(Y)) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    ! [Y,V] :
      ( ( Y = n )
      | ~ element(Y,n)
      | ( V = n )
      | ( V = Y )
      | ~ element(Y,V)
      | ~ element(V,Y) ),
    file(unknown,unknown) ).

tff(f_105,axiom,
    ! [Y] :
      ( ( Y = n )
      | element(Y,n)
      | element(Y,g(Y)) ),
    file(unknown,unknown) ).

tff(c_4,plain,
    ( element(k,j)
    | ( k = j ) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_40,plain,
    k = j,
    inference(splitLeft,[status(thm)],[c_4]) ).

tff(c_30,plain,
    ( element(n,k)
    | ( n = k ) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_33,plain,
    n = k,
    inference(splitLeft,[status(thm)],[c_30]) ).

tff(c_2,plain,
    n != m,
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_34,plain,
    m != k,
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_2]) ).

tff(c_42,plain,
    m != j,
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_34]) ).

tff(c_28,plain,
    ( element(m,k)
    | ( m = k ) ),
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_39,plain,
    element(m,k),
    inference(negUnitSimplification,[status(thm)],[c_34,c_28]) ).

tff(c_41,plain,
    element(m,j),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_39]) ).

tff(c_6,plain,
    ! [Y_2] :
      ( ~ element(Y_2,j)
      | ( k = Y_2 )
      | ( j = Y_2 ) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_52,plain,
    ! [Y_2] :
      ( ~ element(Y_2,j)
      | ( j = Y_2 )
      | ( j = Y_2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_40,c_6]) ).

tff(c_56,plain,
    m = j,
    inference(resolution,[status(thm)],[c_41,c_52]) ).

tff(c_60,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_42,c_56]) ).

tff(c_62,plain,
    k != j,
    inference(splitRight,[status(thm)],[c_4]) ).

tff(c_61,plain,
    element(k,j),
    inference(splitRight,[status(thm)],[c_4]) ).

tff(c_153,plain,
    ! [V1_31,Y_32] :
      ( ~ element(V1_31,Y_32)
      | ~ element(Y_32,V1_31)
      | ( Y_32 = V1_31 )
      | ( m = V1_31 )
      | element(Y_32,m)
      | ( m = Y_32 ) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_167,plain,
    ( ~ element(j,k)
    | ( k = j )
    | ( m = k )
    | element(j,m)
    | ( m = j ) ),
    inference(resolution,[status(thm)],[c_61,c_153]) ).

tff(c_180,plain,
    ( ~ element(j,k)
    | element(j,m)
    | ( m = j ) ),
    inference(negUnitSimplification,[status(thm)],[c_34,c_62,c_167]) ).

tff(c_185,plain,
    ~ element(j,k),
    inference(splitLeft,[status(thm)],[c_180]) ).

tff(c_20,plain,
    ! [Y_10] :
      ( ( g(Y_10) != Y_10 )
      | element(Y_10,n)
      | ( n = Y_10 ) ),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_71,plain,
    ! [Y_10] :
      ( ( g(Y_10) != Y_10 )
      | element(Y_10,k)
      | ( k = Y_10 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_33,c_20]) ).

tff(c_191,plain,
    ( ( g(j) != j )
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_71,c_185]) ).

tff(c_197,plain,
    g(j) != j,
    inference(negUnitSimplification,[status(thm)],[c_62,c_191]) ).

tff(c_18,plain,
    ! [Y_9] :
      ( ( g(Y_9) != n )
      | element(Y_9,n)
      | ( n = Y_9 ) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_73,plain,
    ! [Y_9] :
      ( ( g(Y_9) != k )
      | element(Y_9,k)
      | ( k = Y_9 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_33,c_33,c_18]) ).

tff(c_188,plain,
    ( ( g(j) != k )
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_73,c_185]) ).

tff(c_194,plain,
    g(j) != k,
    inference(negUnitSimplification,[status(thm)],[c_62,c_188]) ).

tff(c_24,plain,
    ! [Y_12] :
      ( element(g(Y_12),Y_12)
      | element(Y_12,n)
      | ( n = Y_12 ) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_125,plain,
    ! [Y_30] :
      ( element(g(Y_30),Y_30)
      | element(Y_30,k)
      | ( k = Y_30 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_33,c_24]) ).

tff(c_141,plain,
    ( ( g(j) = k )
    | ( g(j) = j )
    | element(j,k)
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_125,c_6]) ).

tff(c_152,plain,
    ( ( g(j) = k )
    | ( g(j) = j )
    | element(j,k) ),
    inference(negUnitSimplification,[status(thm)],[c_62,c_141]) ).

tff(c_231,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_185,c_197,c_194,c_152]) ).

tff(c_233,plain,
    element(j,k),
    inference(splitRight,[status(thm)],[c_180]) ).

tff(c_32,plain,
    ! [Y_17] :
      ( ~ element(Y_17,k)
      | ( n = Y_17 )
      | ( m = Y_17 )
      | ( k = Y_17 ) ),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_77,plain,
    ! [Y_17] :
      ( ~ element(Y_17,k)
      | ( k = Y_17 )
      | ( m = Y_17 )
      | ( k = Y_17 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_33,c_32]) ).

tff(c_238,plain,
    ( ( m = j )
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_233,c_77]) ).

tff(c_245,plain,
    m = j,
    inference(negUnitSimplification,[status(thm)],[c_62,c_62,c_238]) ).

tff(c_10,plain,
    ! [Y_4] :
      ( ( f(Y_4) != Y_4 )
      | ~ element(Y_4,m)
      | ( m = Y_4 ) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_305,plain,
    ! [Y_37] :
      ( ( f(Y_37) != Y_37 )
      | ~ element(Y_37,j)
      | ( j = Y_37 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_245,c_245,c_10]) ).

tff(c_312,plain,
    ( ( f(k) != k )
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_61,c_305]) ).

tff(c_318,plain,
    f(k) != k,
    inference(negUnitSimplification,[status(thm)],[c_62,c_312]) ).

tff(c_8,plain,
    ! [Y_3] :
      ( ( f(Y_3) != m )
      | ~ element(Y_3,m)
      | ( m = Y_3 ) ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_321,plain,
    ! [Y_40] :
      ( ( f(Y_40) != j )
      | ~ element(Y_40,j)
      | ( j = Y_40 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_245,c_245,c_245,c_8]) ).

tff(c_328,plain,
    ( ( f(k) != j )
    | ( k = j ) ),
    inference(resolution,[status(thm)],[c_61,c_321]) ).

tff(c_334,plain,
    f(k) != j,
    inference(negUnitSimplification,[status(thm)],[c_62,c_328]) ).

tff(c_94,plain,
    ! [Y_25] :
      ( element(f(Y_25),Y_25)
      | ~ element(Y_25,m)
      | ( m = Y_25 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_98,plain,
    ( ( f(k) = m )
    | ( f(k) = k )
    | ~ element(k,m)
    | ( m = k ) ),
    inference(resolution,[status(thm)],[c_94,c_77]) ).

tff(c_113,plain,
    ( ( f(k) = m )
    | ( f(k) = k )
    | ~ element(k,m) ),
    inference(negUnitSimplification,[status(thm)],[c_34,c_98]) ).

tff(c_337,plain,
    ( ( f(k) = j )
    | ( f(k) = k ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_61,c_245,c_245,c_113]) ).

tff(c_338,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_318,c_334,c_337]) ).

tff(c_340,plain,
    n != k,
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_339,plain,
    element(n,k),
    inference(splitRight,[status(thm)],[c_30]) ).

tff(c_341,plain,
    m = k,
    inference(splitLeft,[status(thm)],[c_28]) ).

tff(c_379,plain,
    ! [Y_43] :
      ( ( f(Y_43) != k )
      | ~ element(Y_43,k)
      | ( k = Y_43 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_341,c_8]) ).

tff(c_382,plain,
    ( ( f(n) != k )
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_339,c_379]) ).

tff(c_385,plain,
    f(n) != k,
    inference(negUnitSimplification,[status(thm)],[c_340,c_382]) ).

tff(c_389,plain,
    ! [Y_46] :
      ( ( f(Y_46) != Y_46 )
      | ~ element(Y_46,k)
      | ( k = Y_46 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_10]) ).

tff(c_392,plain,
    ( ( f(n) != n )
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_339,c_389]) ).

tff(c_395,plain,
    f(n) != n,
    inference(negUnitSimplification,[status(thm)],[c_340,c_392]) ).

tff(c_14,plain,
    ! [Y_6] :
      ( element(f(Y_6),Y_6)
      | ~ element(Y_6,m)
      | ( m = Y_6 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_407,plain,
    ! [Y_6] :
      ( element(f(Y_6),Y_6)
      | ~ element(Y_6,k)
      | ( k = Y_6 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_14]) ).

tff(c_12,plain,
    ! [Y_5] :
      ( element(Y_5,f(Y_5))
      | ~ element(Y_5,m)
      | ( m = Y_5 ) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_405,plain,
    ! [Y_5] :
      ( element(Y_5,f(Y_5))
      | ~ element(Y_5,k)
      | ( k = Y_5 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_12]) ).

tff(c_16,plain,
    ! [V1_8,Y_7] :
      ( ~ element(V1_8,Y_7)
      | ~ element(Y_7,V1_8)
      | ( Y_7 = V1_8 )
      | ( m = V1_8 )
      | element(Y_7,m)
      | ( m = Y_7 ) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_465,plain,
    ! [V1_52,Y_53] :
      ( ~ element(V1_52,Y_53)
      | ~ element(Y_53,V1_52)
      | ( Y_53 = V1_52 )
      | ( k = V1_52 )
      | element(Y_53,k)
      | ( k = Y_53 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_341,c_341,c_16]) ).

tff(c_645,plain,
    ! [Y_61] :
      ( ~ element(f(Y_61),Y_61)
      | ( f(Y_61) = Y_61 )
      | element(f(Y_61),k)
      | ( f(Y_61) = k )
      | ~ element(Y_61,k)
      | ( k = Y_61 ) ),
    inference(resolution,[status(thm)],[c_405,c_465]) ).

tff(c_675,plain,
    ! [Y_63] :
      ( ( f(Y_63) = Y_63 )
      | element(f(Y_63),k)
      | ( f(Y_63) = k )
      | ~ element(Y_63,k)
      | ( k = Y_63 ) ),
    inference(resolution,[status(thm)],[c_407,c_645]) ).

tff(c_396,plain,
    ! [Y_17] :
      ( ~ element(Y_17,k)
      | ( n = Y_17 )
      | ( k = Y_17 )
      | ( k = Y_17 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_341,c_32]) ).

tff(c_698,plain,
    ! [Y_64] :
      ( ( f(Y_64) = n )
      | ( f(Y_64) = Y_64 )
      | ( f(Y_64) = k )
      | ~ element(Y_64,k)
      | ( k = Y_64 ) ),
    inference(resolution,[status(thm)],[c_675,c_396]) ).

tff(c_712,plain,
    ( ( f(n) = n )
    | ( f(n) = k )
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_339,c_698]) ).

tff(c_722,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_340,c_385,c_395,c_395,c_712]) ).

tff(c_724,plain,
    m != k,
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_723,plain,
    element(m,k),
    inference(splitRight,[status(thm)],[c_28]) ).

tff(c_829,plain,
    ! [V_76,Y_77] :
      ( ~ element(V_76,Y_77)
      | ~ element(Y_77,V_76)
      | ( Y_77 = V_76 )
      | ( n = V_76 )
      | ~ element(Y_77,n)
      | ( n = Y_77 ) ),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_845,plain,
    ( ~ element(k,m)
    | ( m = k )
    | ( n = m )
    | ~ element(k,n)
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_723,c_829]) ).

tff(c_861,plain,
    ( ~ element(k,m)
    | ~ element(k,n) ),
    inference(negUnitSimplification,[status(thm)],[c_340,c_2,c_724,c_845]) ).

tff(c_866,plain,
    ~ element(k,n),
    inference(splitLeft,[status(thm)],[c_861]) ).

tff(c_869,plain,
    ( ( g(k) != k )
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_20,c_866]) ).

tff(c_875,plain,
    g(k) != k,
    inference(negUnitSimplification,[status(thm)],[c_340,c_869]) ).

tff(c_872,plain,
    ( ( g(k) != n )
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_18,c_866]) ).

tff(c_878,plain,
    g(k) != n,
    inference(negUnitSimplification,[status(thm)],[c_340,c_872]) ).

tff(c_801,plain,
    ! [Y_74] :
      ( element(g(Y_74),Y_74)
      | element(Y_74,n)
      | ( n = Y_74 ) ),
    inference(cnfTransformation,[status(thm)],[f_111]) ).

tff(c_805,plain,
    ( ( g(k) = n )
    | ( g(k) = m )
    | ( g(k) = k )
    | element(k,n)
    | ( n = k ) ),
    inference(resolution,[status(thm)],[c_801,c_32]) ).

tff(c_820,plain,
    ( ( g(k) = n )
    | ( g(k) = m )
    | ( g(k) = k )
    | element(k,n) ),
    inference(negUnitSimplification,[status(thm)],[c_340,c_805]) ).

tff(c_1223,plain,
    g(k) = m,
    inference(negUnitSimplification,[status(thm)],[c_866,c_875,c_878,c_820]) ).

tff(c_22,plain,
    ! [Y_11] :
      ( element(Y_11,g(Y_11))
      | element(Y_11,n)
      | ( n = Y_11 ) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_1229,plain,
    ( element(k,m)
    | element(k,n)
    | ( n = k ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1223,c_22]) ).

tff(c_1235,plain,
    element(k,m),
    inference(negUnitSimplification,[status(thm)],[c_340,c_866,c_1229]) ).

tff(c_1273,plain,
    ( ( f(k) != m )
    | ( m = k ) ),
    inference(resolution,[status(thm)],[c_1235,c_8]) ).

tff(c_1288,plain,
    f(k) != m,
    inference(negUnitSimplification,[status(thm)],[c_724,c_1273]) ).

tff(c_776,plain,
    ! [Y_73] :
      ( element(f(Y_73),Y_73)
      | ~ element(Y_73,m)
      | ( m = Y_73 ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_780,plain,
    ( ( f(k) = n )
    | ( f(k) = m )
    | ( f(k) = k )
    | ~ element(k,m)
    | ( m = k ) ),
    inference(resolution,[status(thm)],[c_776,c_32]) ).

tff(c_795,plain,
    ( ( f(k) = n )
    | ( f(k) = m )
    | ( f(k) = k )
    | ~ element(k,m) ),
    inference(negUnitSimplification,[status(thm)],[c_724,c_780]) ).

tff(c_1302,plain,
    ( ( f(k) = n )
    | ( f(k) = m )
    | ( f(k) = k ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1235,c_795]) ).

tff(c_1303,plain,
    f(k) = k,
    inference(splitLeft,[status(thm)],[c_1302]) ).

tff(c_1270,plain,
    ( ( f(k) != k )
    | ( m = k ) ),
    inference(resolution,[status(thm)],[c_1235,c_10]) ).

tff(c_1285,plain,
    f(k) != k,
    inference(negUnitSimplification,[status(thm)],[c_724,c_1270]) ).

tff(c_1322,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1303,c_1285]) ).

tff(c_1323,plain,
    ( ( f(k) = m )
    | ( f(k) = n ) ),
    inference(splitRight,[status(thm)],[c_1302]) ).

tff(c_1325,plain,
    f(k) = n,
    inference(negUnitSimplification,[status(thm)],[c_1288,c_1323]) ).

tff(c_1334,plain,
    ( element(k,n)
    | ~ element(k,m)
    | ( m = k ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1325,c_12]) ).

tff(c_1341,plain,
    ( element(k,n)
    | ( m = k ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1235,c_1334]) ).

tff(c_1343,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_724,c_866,c_1341]) ).

tff(c_1344,plain,
    ~ element(k,m),
    inference(splitRight,[status(thm)],[c_861]) ).

tff(c_1345,plain,
    element(k,n),
    inference(splitRight,[status(thm)],[c_861]) ).

tff(c_1346,plain,
    ! [V1_87,Y_88] :
      ( ~ element(V1_87,Y_88)
      | ~ element(Y_88,V1_87)
      | ( Y_88 = V1_87 )
      | ( m = V1_87 )
      | element(Y_88,m)
      | ( m = Y_88 ) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_1364,plain,
    ( ~ element(k,n)
    | ( n = k )
    | ( n = m )
    | element(k,m)
    | ( m = k ) ),
    inference(resolution,[status(thm)],[c_339,c_1346]) ).

tff(c_1384,plain,
    ( ~ element(k,n)
    | element(k,m) ),
    inference(negUnitSimplification,[status(thm)],[c_724,c_2,c_340,c_1364]) ).

tff(c_1423,plain,
    element(k,m),
    inference(demodulation,[status(thm),theory(equality)],[c_1345,c_1384]) ).

tff(c_1424,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1344,c_1423]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYN015-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % 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
% 0.13/0.34  % Computer : n009.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 17:17:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.94/2.21  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.63/2.23  
% 4.63/2.23  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.80/2.27  
% 4.80/2.27  Inference rules
% 4.80/2.27  ----------------------
% 4.80/2.27  #Ref     : 0
% 4.80/2.27  #Sup     : 237
% 4.80/2.27  #Fact    : 0
% 4.80/2.27  #Define  : 0
% 4.80/2.27  #Split   : 31
% 4.80/2.27  #Chain   : 0
% 4.80/2.27  #Close   : 0
% 4.80/2.27  
% 4.80/2.27  Ordering : KBO
% 4.80/2.27  
% 4.80/2.27  Simplification rules
% 4.80/2.27  ----------------------
% 4.80/2.27  #Subsume      : 30
% 4.80/2.27  #Demod        : 249
% 4.80/2.27  #Tautology    : 118
% 4.80/2.27  #SimpNegUnit  : 130
% 4.80/2.27  #BackRed      : 86
% 4.80/2.27  
% 4.80/2.27  #Partial instantiations: 0
% 4.80/2.27  #Strategies tried      : 1
% 4.80/2.27  
% 4.80/2.27  Timing (in seconds)
% 4.80/2.27  ----------------------
% 4.80/2.27  Preprocessing        : 0.49
% 4.80/2.27  Parsing              : 0.26
% 4.80/2.27  CNF conversion       : 0.02
% 4.80/2.27  Main loop            : 0.57
% 4.80/2.27  Inferencing          : 0.20
% 4.80/2.27  Reduction            : 0.16
% 4.80/2.27  Demodulation         : 0.10
% 4.80/2.27  BG Simplification    : 0.03
% 4.80/2.27  Subsumption          : 0.12
% 4.80/2.27  Abstraction          : 0.03
% 4.80/2.27  MUC search           : 0.00
% 4.80/2.27  Cooper               : 0.00
% 4.80/2.27  Total                : 1.12
% 4.80/2.27  Index Insertion      : 0.00
% 4.80/2.27  Index Deletion       : 0.00
% 4.80/2.27  Index Matching       : 0.00
% 4.80/2.27  BG Taut test         : 0.00
%------------------------------------------------------------------------------