TSTP Solution File: GRP026-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP026-1 : TPTP v8.1.2. Bugfixed 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 : n004.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 10:39:39 EDT 2023

% Result   : Unsatisfiable 9.32s 3.40s
% Output   : CNFRefutation 10.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   48
% Syntax   : Number of formulae    :  275 ( 205 unt;  17 typ;   0 def)
%            Number of atoms       :  327 ( 165 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  145 (  76   ~;  69   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   13 (   6   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-4 aty)
%            Number of functors    :   15 (  15 usr;  11 con; 0-3 aty)
%            Number of variables   :   67 (;  67   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > group_member > multiply > inverse > #nlpp > identity_for > an_isomorphism > h > g2 > g1 > g > f > d3 > d2 > d1 > c > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

tff(g2,type,
    g2: $i ).

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

tff(g1,type,
    g1: $i ).

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

tff(d2,type,
    d2: $i ).

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

tff(d1,type,
    d1: $i ).

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

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

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

tff(d3,type,
    d3: $i ).

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

tff(f_163,axiom,
    product(g2,h,h,g),
    file(unknown,unknown) ).

tff(f_166,axiom,
    an_isomorphism(b) = g,
    file(unknown,unknown) ).

tff(f_156,axiom,
    product(g2,f,g,g),
    file(unknown,unknown) ).

tff(f_158,axiom,
    product(g2,f,h,h),
    file(unknown,unknown) ).

tff(f_167,axiom,
    an_isomorphism(c) = h,
    file(unknown,unknown) ).

tff(f_155,axiom,
    product(g2,f,f,f),
    file(unknown,unknown) ).

tff(f_165,axiom,
    an_isomorphism(a) = f,
    file(unknown,unknown) ).

tff(f_171,axiom,
    group_member(d3,g1),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [X] :
      ( ~ group_member(X,g1)
      | ( X = a )
      | ( X = b )
      | ( X = c ) ),
    file(unknown,unknown) ).

tff(f_170,axiom,
    group_member(d2,g1),
    file(unknown,unknown) ).

tff(f_169,axiom,
    group_member(d1,g1),
    file(unknown,unknown) ).

tff(f_174,axiom,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    file(unknown,unknown) ).

tff(f_172,axiom,
    product(g1,d1,d2,d3),
    file(unknown,unknown) ).

tff(f_146,axiom,
    product(g1,a,a,a),
    file(unknown,unknown) ).

tff(f_96,axiom,
    ! [Xg,W,Z,X,Y] :
      ( ~ product(Xg,X,Y,Z)
      | ~ product(Xg,X,Y,W)
      | ( W = Z ) ),
    file(unknown,unknown) ).

tff(f_149,axiom,
    product(g1,a,c,c),
    file(unknown,unknown) ).

tff(f_147,axiom,
    product(g1,a,b,b),
    file(unknown,unknown) ).

tff(f_150,axiom,
    product(g1,c,a,c),
    file(unknown,unknown) ).

tff(f_159,axiom,
    product(g2,h,f,h),
    file(unknown,unknown) ).

tff(f_154,axiom,
    product(g1,c,c,b),
    file(unknown,unknown) ).

tff(f_153,axiom,
    product(g1,c,b,a),
    file(unknown,unknown) ).

tff(f_152,axiom,
    product(g1,b,c,a),
    file(unknown,unknown) ).

tff(f_151,axiom,
    product(g1,b,b,c),
    file(unknown,unknown) ).

tff(f_162,axiom,
    product(g2,h,g,f),
    file(unknown,unknown) ).

tff(f_157,axiom,
    product(g2,g,f,g),
    file(unknown,unknown) ).

tff(f_160,axiom,
    product(g2,g,g,h),
    file(unknown,unknown) ).

tff(f_122,axiom,
    group_member(a,g1),
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [X,Xg,Y] :
      ( ~ group_member(X,Xg)
      | ~ group_member(Y,Xg)
      | product(Xg,X,Y,multiply(Xg,X,Y)) ),
    file(unknown,unknown) ).

tff(f_161,axiom,
    product(g2,g,h,f),
    file(unknown,unknown) ).

tff(f_148,axiom,
    product(g1,b,a,b),
    file(unknown,unknown) ).

tff(f_124,axiom,
    group_member(c,g1),
    file(unknown,unknown) ).

tff(c_74,plain,
    product(g2,h,h,g),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_78,plain,
    an_isomorphism(b) = g,
    inference(cnfTransformation,[status(thm)],[f_166]) ).

tff(c_60,plain,
    product(g2,f,g,g),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_64,plain,
    product(g2,f,h,h),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_80,plain,
    an_isomorphism(c) = h,
    inference(cnfTransformation,[status(thm)],[f_167]) ).

tff(c_58,plain,
    product(g2,f,f,f),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_76,plain,
    an_isomorphism(a) = f,
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_86,plain,
    group_member(d3,g1),
    inference(cnfTransformation,[status(thm)],[f_171]) ).

tff(c_109,plain,
    ! [X_50] :
      ( ( c = X_50 )
      | ( b = X_50 )
      | ( a = X_50 )
      | ~ group_member(X_50,g1) ),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_146,plain,
    ( ( d3 = c )
    | ( d3 = b )
    | ( d3 = a ) ),
    inference(resolution,[status(thm)],[c_86,c_109]) ).

tff(c_261,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_84,plain,
    group_member(d2,g1),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_145,plain,
    ( ( d2 = c )
    | ( d2 = b )
    | ( d2 = a ) ),
    inference(resolution,[status(thm)],[c_84,c_109]) ).

tff(c_183,plain,
    d2 = a,
    inference(splitLeft,[status(thm)],[c_145]) ).

tff(c_82,plain,
    group_member(d1,g1),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_138,plain,
    ( ( d1 = c )
    | ( d1 = b )
    | ( d1 = a ) ),
    inference(resolution,[status(thm)],[c_82,c_109]) ).

tff(c_173,plain,
    d1 = a,
    inference(splitLeft,[status(thm)],[c_138]) ).

tff(c_90,plain,
    ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
    inference(cnfTransformation,[status(thm)],[f_174]) ).

tff(c_174,plain,
    ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_173,c_90]) ).

tff(c_177,plain,
    ~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_174]) ).

tff(c_913,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_76,c_261,c_76,c_183,c_177]) ).

tff(c_914,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_916,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_914]) ).

tff(c_915,plain,
    d3 != a,
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_917,plain,
    c != a,
    inference(demodulation,[status(thm),theory(equality)],[c_916,c_915]) ).

tff(c_88,plain,
    product(g1,d1,d2,d3),
    inference(cnfTransformation,[status(thm)],[f_172]) ).

tff(c_175,plain,
    product(g1,a,d2,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_173,c_88]) ).

tff(c_184,plain,
    product(g1,a,a,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_183,c_175]) ).

tff(c_918,plain,
    product(g1,a,a,c),
    inference(demodulation,[status(thm),theory(equality)],[c_916,c_184]) ).

tff(c_40,plain,
    product(g1,a,a,a),
    inference(cnfTransformation,[status(thm)],[f_146]) ).

tff(c_191,plain,
    ! [X_54,Z_53,Xg_55,W_52,Y_56] :
      ( ( Z_53 = W_52 )
      | ~ product(Xg_55,X_54,Y_56,W_52)
      | ~ product(Xg_55,X_54,Y_56,Z_53) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_1480,plain,
    ! [Z_130] :
      ( ( a = Z_130 )
      | ~ product(g1,a,a,Z_130) ),
    inference(resolution,[status(thm)],[c_40,c_191]) ).

tff(c_1487,plain,
    c = a,
    inference(resolution,[status(thm)],[c_918,c_1480]) ).

tff(c_1497,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_917,c_1487]) ).

tff(c_1498,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_914]) ).

tff(c_1500,plain,
    b != a,
    inference(demodulation,[status(thm),theory(equality)],[c_1498,c_915]) ).

tff(c_1501,plain,
    product(g1,a,a,b),
    inference(demodulation,[status(thm),theory(equality)],[c_1498,c_184]) ).

tff(c_1943,plain,
    ! [Z_161] :
      ( ( a = Z_161 )
      | ~ product(g1,a,a,Z_161) ),
    inference(resolution,[status(thm)],[c_40,c_191]) ).

tff(c_1950,plain,
    b = a,
    inference(resolution,[status(thm)],[c_1501,c_1943]) ).

tff(c_1960,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1500,c_1950]) ).

tff(c_1961,plain,
    ( ( d2 = b )
    | ( d2 = c ) ),
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_2033,plain,
    d2 = c,
    inference(splitLeft,[status(thm)],[c_1961]) ).

tff(c_1962,plain,
    d2 != a,
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_2034,plain,
    c != a,
    inference(demodulation,[status(thm),theory(equality)],[c_2033,c_1962]) ).

tff(c_2056,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_2035,plain,
    product(g1,a,c,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_2033,c_175]) ).

tff(c_2057,plain,
    product(g1,a,c,a),
    inference(demodulation,[status(thm),theory(equality)],[c_2056,c_2035]) ).

tff(c_46,plain,
    product(g1,a,c,c),
    inference(cnfTransformation,[status(thm)],[f_149]) ).

tff(c_1963,plain,
    ! [Z_163,W_162,Xg_165,Y_166,X_164] :
      ( ( Z_163 = W_162 )
      | ~ product(Xg_165,X_164,Y_166,W_162)
      | ~ product(Xg_165,X_164,Y_166,Z_163) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_2433,plain,
    ! [Z_195] :
      ( ( c = Z_195 )
      | ~ product(g1,a,c,Z_195) ),
    inference(resolution,[status(thm)],[c_46,c_1963]) ).

tff(c_2440,plain,
    c = a,
    inference(resolution,[status(thm)],[c_2057,c_2433]) ).

tff(c_2450,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2034,c_2440]) ).

tff(c_2451,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_2457,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_2451]) ).

tff(c_3094,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_64,c_80,c_2457,c_80,c_2033,c_177]) ).

tff(c_3095,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_2451]) ).

tff(c_3096,plain,
    d3 != c,
    inference(splitRight,[status(thm)],[c_2451]) ).

tff(c_3105,plain,
    c != b,
    inference(demodulation,[status(thm),theory(equality)],[c_3095,c_3096]) ).

tff(c_3098,plain,
    product(g1,a,c,b),
    inference(demodulation,[status(thm),theory(equality)],[c_3095,c_2035]) ).

tff(c_3619,plain,
    ! [Z_259] :
      ( ( c = Z_259 )
      | ~ product(g1,a,c,Z_259) ),
    inference(resolution,[status(thm)],[c_46,c_1963]) ).

tff(c_3622,plain,
    c = b,
    inference(resolution,[status(thm)],[c_3098,c_3619]) ).

tff(c_3633,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3105,c_3622]) ).

tff(c_3634,plain,
    d2 = b,
    inference(splitRight,[status(thm)],[c_1961]) ).

tff(c_3635,plain,
    d2 != c,
    inference(splitRight,[status(thm)],[c_1961]) ).

tff(c_3644,plain,
    c != b,
    inference(demodulation,[status(thm),theory(equality)],[c_3634,c_3635]) ).

tff(c_3636,plain,
    b != a,
    inference(demodulation,[status(thm),theory(equality)],[c_3634,c_1962]) ).

tff(c_3659,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_3637,plain,
    product(g1,a,b,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_3634,c_175]) ).

tff(c_3660,plain,
    product(g1,a,b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_3659,c_3637]) ).

tff(c_42,plain,
    product(g1,a,b,b),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_4279,plain,
    ! [Z_297] :
      ( ( b = Z_297 )
      | ~ product(g1,a,b,Z_297) ),
    inference(resolution,[status(thm)],[c_42,c_1963]) ).

tff(c_4286,plain,
    b = a,
    inference(resolution,[status(thm)],[c_3660,c_4279]) ).

tff(c_4296,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3636,c_4286]) ).

tff(c_4297,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_4299,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_4297]) ).

tff(c_4301,plain,
    product(g1,a,b,c),
    inference(demodulation,[status(thm),theory(equality)],[c_4299,c_3637]) ).

tff(c_4785,plain,
    ! [Z_327] :
      ( ( b = Z_327 )
      | ~ product(g1,a,b,Z_327) ),
    inference(resolution,[status(thm)],[c_42,c_1963]) ).

tff(c_4788,plain,
    c = b,
    inference(resolution,[status(thm)],[c_4301,c_4785]) ).

tff(c_4799,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3644,c_4788]) ).

tff(c_4800,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_4297]) ).

tff(c_5429,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_78,c_4800,c_78,c_3634,c_177]) ).

tff(c_5430,plain,
    ( ( d1 = b )
    | ( d1 = c ) ),
    inference(splitRight,[status(thm)],[c_138]) ).

tff(c_5432,plain,
    d1 = c,
    inference(splitLeft,[status(thm)],[c_5430]) ).

tff(c_5431,plain,
    d1 != a,
    inference(splitRight,[status(thm)],[c_138]) ).

tff(c_5433,plain,
    c != a,
    inference(demodulation,[status(thm),theory(equality)],[c_5432,c_5431]) ).

tff(c_48,plain,
    product(g1,c,a,c),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_7304,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_66,plain,
    product(g2,h,f,h),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_5535,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_5513,plain,
    d2 = a,
    inference(splitLeft,[status(thm)],[c_145]) ).

tff(c_5435,plain,
    product(g1,c,d2,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_5432,c_88]) ).

tff(c_5514,plain,
    product(g1,c,a,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_5513,c_5435]) ).

tff(c_5536,plain,
    product(g1,c,a,a),
    inference(demodulation,[status(thm),theory(equality)],[c_5535,c_5514]) ).

tff(c_5443,plain,
    ! [Xg_366,Z_364,Y_367,X_365,W_363] :
      ( ( Z_364 = W_363 )
      | ~ product(Xg_366,X_365,Y_367,W_363)
      | ~ product(Xg_366,X_365,Y_367,Z_364) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_6006,plain,
    ! [Z_400] :
      ( ( c = Z_400 )
      | ~ product(g1,c,a,Z_400) ),
    inference(resolution,[status(thm)],[c_48,c_5443]) ).

tff(c_6013,plain,
    c = a,
    inference(resolution,[status(thm)],[c_5536,c_6006]) ).

tff(c_6023,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5433,c_6013]) ).

tff(c_6024,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_6026,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_6024]) ).

tff(c_5434,plain,
    ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_5432,c_90]) ).

tff(c_5437,plain,
    ~ product(g2,h,an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_5434]) ).

tff(c_6667,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_80,c_6026,c_76,c_5513,c_5437]) ).

tff(c_6668,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_6024]) ).

tff(c_6669,plain,
    d3 != c,
    inference(splitRight,[status(thm)],[c_6024]) ).

tff(c_6682,plain,
    c != b,
    inference(demodulation,[status(thm),theory(equality)],[c_6668,c_6669]) ).

tff(c_6675,plain,
    product(g1,c,a,b),
    inference(demodulation,[status(thm),theory(equality)],[c_6668,c_5514]) ).

tff(c_7264,plain,
    ! [Z_469] :
      ( ( c = Z_469 )
      | ~ product(g1,c,a,Z_469) ),
    inference(resolution,[status(thm)],[c_48,c_5443]) ).

tff(c_7267,plain,
    c = b,
    inference(resolution,[status(thm)],[c_6675,c_7264]) ).

tff(c_7278,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6682,c_7267]) ).

tff(c_7279,plain,
    ( ( d2 = b )
    | ( d2 = c ) ),
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_7292,plain,
    d2 = c,
    inference(splitLeft,[status(thm)],[c_7279]) ).

tff(c_7294,plain,
    product(g1,c,c,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_7292,c_5435]) ).

tff(c_7309,plain,
    product(g1,c,c,a),
    inference(demodulation,[status(thm),theory(equality)],[c_7304,c_7294]) ).

tff(c_56,plain,
    product(g1,c,c,b),
    inference(cnfTransformation,[status(thm)],[f_154]) ).

tff(c_7319,plain,
    ! [Z_476] :
      ( ( b = Z_476 )
      | ~ product(g1,c,c,Z_476) ),
    inference(resolution,[status(thm)],[c_56,c_5443]) ).

tff(c_7330,plain,
    b = a,
    inference(resolution,[status(thm)],[c_7309,c_7319]) ).

tff(c_54,plain,
    product(g1,c,b,a),
    inference(cnfTransformation,[status(thm)],[f_153]) ).

tff(c_5504,plain,
    ! [Z_364] :
      ( ( a = Z_364 )
      | ~ product(g1,c,b,Z_364) ),
    inference(resolution,[status(thm)],[c_54,c_5443]) ).

tff(c_7559,plain,
    ! [Z_491] :
      ( ( a = Z_491 )
      | ~ product(g1,c,a,Z_491) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7330,c_5504]) ).

tff(c_7569,plain,
    c = a,
    inference(resolution,[status(thm)],[c_48,c_7559]) ).

tff(c_7578,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5433,c_7569]) ).

tff(c_7579,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_7581,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_7579]) ).

tff(c_7583,plain,
    product(g1,c,c,c),
    inference(demodulation,[status(thm),theory(equality)],[c_7581,c_7294]) ).

tff(c_7697,plain,
    ! [Z_503] :
      ( ( b = Z_503 )
      | ~ product(g1,c,c,Z_503) ),
    inference(resolution,[status(thm)],[c_56,c_5443]) ).

tff(c_7708,plain,
    c = b,
    inference(resolution,[status(thm)],[c_7583,c_7697]) ).

tff(c_7718,plain,
    b != a,
    inference(demodulation,[status(thm),theory(equality)],[c_7708,c_5433]) ).

tff(c_52,plain,
    product(g1,b,c,a),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_7722,plain,
    product(g1,b,b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_7708,c_52]) ).

tff(c_50,plain,
    product(g1,b,b,c),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_5494,plain,
    ! [Z_364] :
      ( ( c = Z_364 )
      | ~ product(g1,b,b,Z_364) ),
    inference(resolution,[status(thm)],[c_50,c_5443]) ).

tff(c_7945,plain,
    ! [Z_514] :
      ( ( b = Z_514 )
      | ~ product(g1,b,b,Z_514) ),
    inference(demodulation,[status(thm),theory(equality)],[c_7708,c_5494]) ).

tff(c_7948,plain,
    b = a,
    inference(resolution,[status(thm)],[c_7722,c_7945]) ).

tff(c_7959,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_7718,c_7948]) ).

tff(c_7960,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_7579]) ).

tff(c_8603,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_74,c_78,c_7960,c_80,c_7292,c_5437]) ).

tff(c_8604,plain,
    d2 = b,
    inference(splitRight,[status(thm)],[c_7279]) ).

tff(c_7280,plain,
    d2 != a,
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_8610,plain,
    b != a,
    inference(demodulation,[status(thm),theory(equality)],[c_8604,c_7280]) ).

tff(c_72,plain,
    product(g2,h,g,f),
    inference(cnfTransformation,[status(thm)],[f_162]) ).

tff(c_8622,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_9261,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_76,c_8622,c_78,c_8604,c_5437]) ).

tff(c_9262,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_9337,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_9262]) ).

tff(c_8611,plain,
    product(g1,c,b,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_8604,c_5435]) ).

tff(c_9339,plain,
    product(g1,c,b,c),
    inference(demodulation,[status(thm),theory(equality)],[c_9337,c_8611]) ).

tff(c_9425,plain,
    ! [Z_599] :
      ( ( a = Z_599 )
      | ~ product(g1,c,b,Z_599) ),
    inference(resolution,[status(thm)],[c_54,c_5443]) ).

tff(c_9428,plain,
    c = a,
    inference(resolution,[status(thm)],[c_9339,c_9425]) ).

tff(c_9439,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_5433,c_9428]) ).

tff(c_9440,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_9262]) ).

tff(c_9443,plain,
    product(g1,c,b,b),
    inference(demodulation,[status(thm),theory(equality)],[c_9440,c_8611]) ).

tff(c_9705,plain,
    ! [Z_614] :
      ( ( a = Z_614 )
      | ~ product(g1,c,b,Z_614) ),
    inference(resolution,[status(thm)],[c_54,c_5443]) ).

tff(c_9708,plain,
    b = a,
    inference(resolution,[status(thm)],[c_9443,c_9705]) ).

tff(c_9719,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8610,c_9708]) ).

tff(c_9720,plain,
    d1 = b,
    inference(splitRight,[status(thm)],[c_5430]) ).

tff(c_9721,plain,
    d1 != c,
    inference(splitRight,[status(thm)],[c_5430]) ).

tff(c_9732,plain,
    c != b,
    inference(demodulation,[status(thm),theory(equality)],[c_9720,c_9721]) ).

tff(c_9722,plain,
    b != a,
    inference(demodulation,[status(thm),theory(equality)],[c_9720,c_5431]) ).

tff(c_62,plain,
    product(g2,g,f,g),
    inference(cnfTransformation,[status(thm)],[f_157]) ).

tff(c_12414,plain,
    d2 = a,
    inference(splitLeft,[status(thm)],[c_145]) ).

tff(c_68,plain,
    product(g2,g,g,h),
    inference(cnfTransformation,[status(thm)],[f_160]) ).

tff(c_24,plain,
    group_member(a,g1),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_14,plain,
    ! [Xg_13,X_12,Y_14] :
      ( product(Xg_13,X_12,Y_14,multiply(Xg_13,X_12,Y_14))
      | ~ group_member(Y_14,Xg_13)
      | ~ group_member(X_12,Xg_13) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_9734,plain,
    ! [X_617,Xg_618,Z_616,W_615,Y_619] :
      ( ( Z_616 = W_615 )
      | ~ product(Xg_618,X_617,Y_619,W_615)
      | ~ product(Xg_618,X_617,Y_619,Z_616) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_11112,plain,
    ! [Z_706] :
      ( ( a = Z_706 )
      | ~ product(g1,a,a,Z_706) ),
    inference(resolution,[status(thm)],[c_40,c_9734]) ).

tff(c_11116,plain,
    ( ( multiply(g1,a,a) = a )
    | ~ group_member(a,g1) ),
    inference(resolution,[status(thm)],[c_14,c_11112]) ).

tff(c_11122,plain,
    multiply(g1,a,a) = a,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_11116]) ).

tff(c_70,plain,
    product(g2,g,h,f),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_9814,plain,
    d2 = a,
    inference(splitLeft,[status(thm)],[c_145]) ).

tff(c_9733,plain,
    d3 = a,
    inference(splitLeft,[status(thm)],[c_146]) ).

tff(c_9724,plain,
    product(g1,b,d2,d3),
    inference(demodulation,[status(thm),theory(equality)],[c_9720,c_88]) ).

tff(c_9804,plain,
    product(g1,b,d2,a),
    inference(demodulation,[status(thm),theory(equality)],[c_9733,c_9724]) ).

tff(c_9826,plain,
    product(g1,b,a,a),
    inference(demodulation,[status(thm),theory(equality)],[c_9814,c_9804]) ).

tff(c_44,plain,
    product(g1,b,a,b),
    inference(cnfTransformation,[status(thm)],[f_148]) ).

tff(c_10378,plain,
    ! [Z_655] :
      ( ( b = Z_655 )
      | ~ product(g1,b,a,Z_655) ),
    inference(resolution,[status(thm)],[c_44,c_9734]) ).

tff(c_10385,plain,
    b = a,
    inference(resolution,[status(thm)],[c_9826,c_10378]) ).

tff(c_10395,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9722,c_10385]) ).

tff(c_10396,plain,
    ( ( d2 = b )
    | ( d2 = c ) ),
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_10398,plain,
    d2 = c,
    inference(splitLeft,[status(thm)],[c_10396]) ).

tff(c_9723,plain,
    ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_9720,c_90]) ).

tff(c_9726,plain,
    ~ product(g2,g,an_isomorphism(d2),an_isomorphism(d3)),
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_9723]) ).

tff(c_10847,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_80,c_10398,c_76,c_9733,c_9726]) ).

tff(c_10848,plain,
    d2 = b,
    inference(splitRight,[status(thm)],[c_10396]) ).

tff(c_10851,plain,
    product(g1,b,b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_10848,c_9804]) ).

tff(c_11239,plain,
    ! [Z_715] :
      ( ( c = Z_715 )
      | ~ product(g1,b,b,Z_715) ),
    inference(resolution,[status(thm)],[c_50,c_9734]) ).

tff(c_11253,plain,
    c = a,
    inference(resolution,[status(thm)],[c_10851,c_11239]) ).

tff(c_28,plain,
    group_member(c,g1),
    inference(cnfTransformation,[status(thm)],[f_124]) ).

tff(c_11212,plain,
    ! [Z_714] :
      ( ( b = Z_714 )
      | ~ product(g1,c,c,Z_714) ),
    inference(resolution,[status(thm)],[c_56,c_9734]) ).

tff(c_11216,plain,
    ( ( multiply(g1,c,c) = b )
    | ~ group_member(c,g1) ),
    inference(resolution,[status(thm)],[c_14,c_11212]) ).

tff(c_11222,plain,
    multiply(g1,c,c) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_11216]) ).

tff(c_11257,plain,
    multiply(g1,a,a) = b,
    inference(demodulation,[status(thm),theory(equality)],[c_11253,c_11253,c_11222]) ).

tff(c_11273,plain,
    b = a,
    inference(demodulation,[status(thm),theory(equality)],[c_11122,c_11257]) ).

tff(c_11275,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9722,c_11273]) ).

tff(c_11276,plain,
    ( ( d3 = b )
    | ( d3 = c ) ),
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_11278,plain,
    d3 = c,
    inference(splitLeft,[status(thm)],[c_11276]) ).

tff(c_11277,plain,
    d3 != a,
    inference(splitRight,[status(thm)],[c_146]) ).

tff(c_11279,plain,
    c != a,
    inference(demodulation,[status(thm),theory(equality)],[c_11278,c_11277]) ).

tff(c_11357,plain,
    d2 = a,
    inference(splitLeft,[status(thm)],[c_145]) ).

tff(c_11280,plain,
    product(g1,b,d2,c),
    inference(demodulation,[status(thm),theory(equality)],[c_11278,c_9724]) ).

tff(c_11358,plain,
    product(g1,b,a,c),
    inference(demodulation,[status(thm),theory(equality)],[c_11357,c_11280]) ).

tff(c_11287,plain,
    ! [X_718,Xg_719,Y_720,Z_717,W_716] :
      ( ( Z_717 = W_716 )
      | ~ product(Xg_719,X_718,Y_720,W_716)
      | ~ product(Xg_719,X_718,Y_720,Z_717) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_11391,plain,
    ! [Z_726] :
      ( ( b = Z_726 )
      | ~ product(g1,b,a,Z_726) ),
    inference(resolution,[status(thm)],[c_44,c_11287]) ).

tff(c_11394,plain,
    c = b,
    inference(resolution,[status(thm)],[c_11358,c_11391]) ).

tff(c_11401,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9732,c_11394]) ).

tff(c_11402,plain,
    ( ( d2 = b )
    | ( d2 = c ) ),
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_11415,plain,
    d2 = c,
    inference(splitLeft,[status(thm)],[c_11402]) ).

tff(c_11417,plain,
    product(g1,b,c,c),
    inference(demodulation,[status(thm),theory(equality)],[c_11415,c_11280]) ).

tff(c_11941,plain,
    ! [Z_761] :
      ( ( a = Z_761 )
      | ~ product(g1,b,c,Z_761) ),
    inference(resolution,[status(thm)],[c_52,c_11287]) ).

tff(c_11948,plain,
    c = a,
    inference(resolution,[status(thm)],[c_11417,c_11941]) ).

tff(c_11958,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_11279,c_11948]) ).

tff(c_11959,plain,
    d2 = b,
    inference(splitRight,[status(thm)],[c_11402]) ).

tff(c_12332,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_68,c_78,c_11959,c_80,c_11278,c_9726]) ).

tff(c_12333,plain,
    d3 = b,
    inference(splitRight,[status(thm)],[c_11276]) ).

tff(c_12465,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_76,c_12414,c_78,c_12333,c_9726]) ).

tff(c_12466,plain,
    ( ( d2 = b )
    | ( d2 = c ) ),
    inference(splitRight,[status(thm)],[c_145]) ).

tff(c_12479,plain,
    d2 = c,
    inference(splitLeft,[status(thm)],[c_12466]) ).

tff(c_12336,plain,
    product(g1,b,d2,b),
    inference(demodulation,[status(thm),theory(equality)],[c_12333,c_9724]) ).

tff(c_12481,plain,
    product(g1,b,c,b),
    inference(demodulation,[status(thm),theory(equality)],[c_12479,c_12336]) ).

tff(c_12344,plain,
    ! [Xg_790,Z_788,Y_791,X_789,W_787] :
      ( ( Z_788 = W_787 )
      | ~ product(Xg_790,X_789,Y_791,W_787)
      | ~ product(Xg_790,X_789,Y_791,Z_788) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_12885,plain,
    ! [Z_829] :
      ( ( a = Z_829 )
      | ~ product(g1,b,c,Z_829) ),
    inference(resolution,[status(thm)],[c_52,c_12344]) ).

tff(c_12888,plain,
    b = a,
    inference(resolution,[status(thm)],[c_12481,c_12885]) ).

tff(c_12899,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9722,c_12888]) ).

tff(c_12900,plain,
    d2 = b,
    inference(splitRight,[status(thm)],[c_12466]) ).

tff(c_12903,plain,
    product(g1,b,b,b),
    inference(demodulation,[status(thm),theory(equality)],[c_12900,c_12336]) ).

tff(c_13145,plain,
    ! [Z_850] :
      ( ( c = Z_850 )
      | ~ product(g1,b,b,Z_850) ),
    inference(resolution,[status(thm)],[c_50,c_12344]) ).

tff(c_13148,plain,
    c = b,
    inference(resolution,[status(thm)],[c_12903,c_13145]) ).

tff(c_13159,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_9732,c_13148]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP026-1 : TPTP v8.1.2. Bugfixed v2.0.0.
% 0.13/0.13  % 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
% 0.13/0.34  % Computer : n004.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  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 22:01:26 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 9.32/3.40  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.32/3.43  
% 9.32/3.43  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.17/3.50  
% 10.17/3.50  Inference rules
% 10.17/3.50  ----------------------
% 10.17/3.50  #Ref     : 0
% 10.17/3.50  #Sup     : 3283
% 10.17/3.50  #Fact    : 0
% 10.17/3.50  #Define  : 0
% 10.17/3.50  #Split   : 26
% 10.17/3.50  #Chain   : 0
% 10.17/3.50  #Close   : 0
% 10.17/3.50  
% 10.17/3.50  Ordering : KBO
% 10.17/3.50  
% 10.17/3.50  Simplification rules
% 10.17/3.50  ----------------------
% 10.17/3.50  #Subsume      : 19
% 10.17/3.50  #Demod        : 2550
% 10.17/3.50  #Tautology    : 1612
% 10.17/3.50  #SimpNegUnit  : 18
% 10.17/3.50  #BackRed      : 168
% 10.17/3.50  
% 10.17/3.50  #Partial instantiations: 0
% 10.17/3.50  #Strategies tried      : 1
% 10.17/3.50  
% 10.17/3.50  Timing (in seconds)
% 10.17/3.50  ----------------------
% 10.17/3.50  Preprocessing        : 0.52
% 10.17/3.50  Parsing              : 0.25
% 10.17/3.50  CNF conversion       : 0.03
% 10.17/3.51  Main loop            : 1.85
% 10.17/3.51  Inferencing          : 0.66
% 10.17/3.51  Reduction            : 0.60
% 10.17/3.51  Demodulation         : 0.46
% 10.17/3.51  BG Simplification    : 0.06
% 10.17/3.51  Subsumption          : 0.38
% 10.17/3.51  Abstraction          : 0.05
% 10.17/3.51  MUC search           : 0.00
% 10.17/3.51  Cooper               : 0.00
% 10.17/3.51  Total                : 2.49
% 10.17/3.51  Index Insertion      : 0.00
% 10.17/3.51  Index Deletion       : 0.00
% 10.17/3.51  Index Matching       : 0.00
% 10.17/3.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------