TSTP Solution File: GRP129-2.004 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP129-2.004 : TPTP v8.1.2. Released v1.2.0.
% 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 : 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 10:40:12 EDT 2023

% Result   : Unsatisfiable 14.63s 6.32s
% Output   : CNFRefutation 15.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   34
% Syntax   : Number of formulae    :  555 ( 281 unt;   9 typ;   0 def)
%            Number of atoms       : 1355 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 1194 ( 385   ~; 809   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   5   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :  238 (; 238   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > next > greater > equalish > group_element > #nlpp > e_4 > e_3 > e_2 > e_1

%Foreground sorts:

%Background operators:

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

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

tff(e_2,type,
    e_2: $i ).

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

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

tff(e_4,type,
    e_4: $i ).

tff(e_3,type,
    e_3: $i ).

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

tff(e_1,type,
    e_1: $i ).

tff(f_65,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(f_31,axiom,
    next(e_2,e_3),
    file(unknown,unknown) ).

tff(f_48,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_50,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3)
      | product(X,Y,e_4) ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    greater(e_4,e_3),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [X,Y,X1] :
      ( ~ product(X,e_1,Y)
      | ~ next(X,X1)
      | ~ greater(Y,X1) ),
    file(unknown,unknown) ).

tff(f_121,axiom,
    ! [Y,X,Z1,Z2] :
      ( ~ product(Y,X,Z1)
      | ~ product(X,Z1,Z2)
      | product(Z1,Y,Z2) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    next(e_1,e_2),
    file(unknown,unknown) ).

tff(f_37,axiom,
    greater(e_4,e_2),
    file(unknown,unknown) ).

tff(f_36,axiom,
    greater(e_3,e_2),
    file(unknown,unknown) ).

tff(f_113,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_105,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_49,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ~ equalish(e_4,e_3),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ~ equalish(e_3,e_4),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ~ equalish(e_4,e_1),
    file(unknown,unknown) ).

tff(f_51,axiom,
    group_element(e_4),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ~ equalish(e_4,e_2),
    file(unknown,unknown) ).

tff(f_97,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ~ equalish(e_1,e_2),
    file(unknown,unknown) ).

tff(c_42,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_36,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_4,plain,
    next(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_22,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_26,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_92,plain,
    ! [X_47,Y_48] :
      ( product(X_47,Y_48,e_4)
      | product(X_47,Y_48,e_3)
      | product(X_47,Y_48,e_2)
      | product(X_47,Y_48,e_1)
      | ~ group_element(Y_48)
      | ~ group_element(X_47) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_18,plain,
    greater(e_4,e_3),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_63,plain,
    ! [Y_22,X1_23,X_24] :
      ( ~ greater(Y_22,X1_23)
      | ~ next(X_24,X1_23)
      | ~ product(X_24,e_1,Y_22) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_79,plain,
    ! [X_24] :
      ( ~ next(X_24,e_3)
      | ~ product(X_24,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_18,c_63]) ).

tff(c_106,plain,
    ! [X_47] :
      ( ~ next(X_47,e_3)
      | product(X_47,e_1,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(e_1)
      | ~ group_element(X_47) ),
    inference(resolution,[status(thm)],[c_92,c_79]) ).

tff(c_121,plain,
    ! [X_47] :
      ( ~ next(X_47,e_3)
      | product(X_47,e_1,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_106]) ).

tff(c_62,plain,
    ! [Z1_20,Y_18,Z2_21,X_19] :
      ( product(Z1_20,Y_18,Z2_21)
      | ~ product(X_19,Z1_20,Z2_21)
      | ~ product(Y_18,X_19,Z1_20) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_338,plain,
    ! [Y_80,Y_81,X_82] :
      ( product(Y_80,Y_81,e_4)
      | ~ product(Y_81,X_82,Y_80)
      | product(X_82,Y_80,e_3)
      | product(X_82,Y_80,e_2)
      | product(X_82,Y_80,e_1)
      | ~ group_element(Y_80)
      | ~ group_element(X_82) ),
    inference(resolution,[status(thm)],[c_92,c_62]) ).

tff(c_342,plain,
    ! [X_47] :
      ( product(e_3,X_47,e_4)
      | product(e_1,e_3,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(e_1)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(resolution,[status(thm)],[c_121,c_338]) ).

tff(c_350,plain,
    ! [X_47] :
      ( product(e_3,X_47,e_4)
      | product(e_1,e_3,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_342]) ).

tff(c_3369,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_350]) ).

tff(c_2,plain,
    next(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_16,plain,
    greater(e_4,e_2),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_76,plain,
    ! [X_24] :
      ( ~ next(X_24,e_2)
      | ~ product(X_24,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_16,c_63]) ).

tff(c_112,plain,
    ! [X_47] :
      ( ~ next(X_47,e_2)
      | product(X_47,e_1,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(e_1)
      | ~ group_element(X_47) ),
    inference(resolution,[status(thm)],[c_92,c_76]) ).

tff(c_237,plain,
    ! [X_62] :
      ( ~ next(X_62,e_2)
      | product(X_62,e_1,e_3)
      | product(X_62,e_1,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_112]) ).

tff(c_14,plain,
    greater(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_80,plain,
    ! [X_24] :
      ( ~ next(X_24,e_2)
      | ~ product(X_24,e_1,e_3) ),
    inference(resolution,[status(thm)],[c_14,c_63]) ).

tff(c_255,plain,
    ! [X_62] :
      ( ~ next(X_62,e_2)
      | product(X_62,e_1,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(resolution,[status(thm)],[c_237,c_80]) ).

tff(c_262,plain,
    ! [X_66] :
      ( ~ next(X_66,e_2)
      | product(X_66,e_1,e_2)
      | product(X_66,e_1,e_1)
      | ~ group_element(X_66) ),
    inference(resolution,[status(thm)],[c_237,c_80]) ).

tff(c_60,plain,
    ! [W_14,Z_17,Y_15,X_16] :
      ( equalish(W_14,Z_17)
      | ~ product(Z_17,Y_15,X_16)
      | ~ product(W_14,Y_15,X_16) ),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_284,plain,
    ! [W_69,X_70] :
      ( equalish(W_69,X_70)
      | ~ product(W_69,e_1,e_2)
      | ~ next(X_70,e_2)
      | product(X_70,e_1,e_1)
      | ~ group_element(X_70) ),
    inference(resolution,[status(thm)],[c_262,c_60]) ).

tff(c_287,plain,
    ! [X_62,X_70] :
      ( equalish(X_62,X_70)
      | ~ next(X_70,e_2)
      | product(X_70,e_1,e_1)
      | ~ group_element(X_70)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(resolution,[status(thm)],[c_255,c_284]) ).

tff(c_825,plain,
    ! [X_98] :
      ( equalish(X_98,X_98)
      | ~ next(X_98,e_2)
      | ~ group_element(X_98)
      | product(X_98,e_1,e_1) ),
    inference(factorization,[status(thm),theory(equality)],[c_287]) ).

tff(c_274,plain,
    ! [Y_18,X_66] :
      ( product(e_1,Y_18,e_2)
      | ~ product(Y_18,X_66,e_1)
      | ~ next(X_66,e_2)
      | product(X_66,e_1,e_1)
      | ~ group_element(X_66) ),
    inference(resolution,[status(thm)],[c_262,c_62]) ).

tff(c_833,plain,
    ! [X_98] :
      ( product(e_1,X_98,e_2)
      | ~ next(e_1,e_2)
      | product(e_1,e_1,e_1)
      | ~ group_element(e_1)
      | equalish(X_98,X_98)
      | ~ next(X_98,e_2)
      | ~ group_element(X_98) ),
    inference(resolution,[status(thm)],[c_825,c_274]) ).

tff(c_856,plain,
    ! [X_98] :
      ( product(e_1,X_98,e_2)
      | product(e_1,e_1,e_1)
      | equalish(X_98,X_98)
      | ~ next(X_98,e_2)
      | ~ group_element(X_98) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_833]) ).

tff(c_1124,plain,
    product(e_1,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_856]) ).

tff(c_58,plain,
    ! [W_11,Z_13,X_10,Y_12] :
      ( equalish(W_11,Z_13)
      | ~ product(X_10,Z_13,Y_12)
      | ~ product(X_10,W_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_1185,plain,
    ! [W_11] :
      ( equalish(W_11,e_1)
      | ~ product(e_1,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_1124,c_58]) ).

tff(c_3386,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_3369,c_1185]) ).

tff(c_3431,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_3386]) ).

tff(c_3433,plain,
    ~ product(e_1,e_3,e_1),
    inference(splitRight,[status(thm)],[c_350]) ).

tff(c_38,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_24,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_44,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_32,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_3432,plain,
    ! [X_47] :
      ( product(e_1,e_3,e_2)
      | product(e_1,e_3,e_3)
      | product(e_3,X_47,e_4)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(splitRight,[status(thm)],[c_350]) ).

tff(c_3538,plain,
    product(e_1,e_3,e_3),
    inference(splitLeft,[status(thm)],[c_3432]) ).

tff(c_52,plain,
    ~ equalish(e_4,e_3),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_46,plain,
    ~ equalish(e_3,e_4),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_48,plain,
    ~ equalish(e_4,e_1),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_28,plain,
    group_element(e_4),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_113,plain,
    ! [Y_48,Y_18,X_47] :
      ( product(Y_48,Y_18,e_4)
      | ~ product(Y_18,X_47,Y_48)
      | product(X_47,Y_48,e_3)
      | product(X_47,Y_48,e_2)
      | product(X_47,Y_48,e_1)
      | ~ group_element(Y_48)
      | ~ group_element(X_47) ),
    inference(resolution,[status(thm)],[c_92,c_62]) ).

tff(c_3560,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_3538,c_113]) ).

tff(c_3607,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_3560]) ).

tff(c_3902,plain,
    product(e_3,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_3607]) ).

tff(c_4155,plain,
    ! [Y_179] :
      ( product(e_3,Y_179,e_1)
      | ~ product(Y_179,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_3902,c_62]) ).

tff(c_4179,plain,
    product(e_3,e_1,e_1),
    inference(resolution,[status(thm)],[c_3538,c_4155]) ).

tff(c_3979,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_3,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_3902,c_58]) ).

tff(c_4203,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_4179,c_3979]) ).

tff(c_4254,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_4203]) ).

tff(c_4255,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_3607]) ).

tff(c_4257,plain,
    product(e_3,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_4255]) ).

tff(c_4271,plain,
    ( product(e_4,e_3,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_4257,c_113]) ).

tff(c_4322,plain,
    ( product(e_4,e_3,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_28,c_4271]) ).

tff(c_4726,plain,
    product(e_1,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_4322]) ).

tff(c_4745,plain,
    equalish(e_4,e_1),
    inference(resolution,[status(thm)],[c_4726,c_1185]) ).

tff(c_4794,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_48,c_4745]) ).

tff(c_4795,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_4,e_3,e_4) ),
    inference(splitRight,[status(thm)],[c_4322]) ).

tff(c_4997,plain,
    product(e_4,e_3,e_4),
    inference(splitLeft,[status(thm)],[c_4795]) ).

tff(c_5007,plain,
    ( product(e_4,e_4,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_4997,c_113]) ).

tff(c_5038,plain,
    ( product(e_4,e_4,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_5007]) ).

tff(c_5486,plain,
    product(e_3,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_5038]) ).

tff(c_5773,plain,
    ! [Y_205] :
      ( product(e_4,Y_205,e_1)
      | ~ product(Y_205,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_5486,c_62]) ).

tff(c_5782,plain,
    product(e_4,e_4,e_1),
    inference(resolution,[status(thm)],[c_4997,c_5773]) ).

tff(c_5564,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_4,e_1) ),
    inference(resolution,[status(thm)],[c_5486,c_60]) ).

tff(c_5791,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_5782,c_5564]) ).

tff(c_5827,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_5791]) ).

tff(c_5828,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_4,e_4,e_4) ),
    inference(splitRight,[status(thm)],[c_5038]) ).

tff(c_5977,plain,
    product(e_4,e_4,e_4),
    inference(splitLeft,[status(thm)],[c_5828]) ).

tff(c_5049,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_4,W_11,e_4) ),
    inference(resolution,[status(thm)],[c_4997,c_58]) ).

tff(c_5980,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_5977,c_5049]) ).

tff(c_6008,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_5980]) ).

tff(c_6009,plain,
    ( product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_5828]) ).

tff(c_6023,plain,
    product(e_3,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_6009]) ).

tff(c_6329,plain,
    ! [Y_214] :
      ( product(e_4,Y_214,e_2)
      | ~ product(Y_214,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_6023,c_62]) ).

tff(c_6338,plain,
    product(e_4,e_4,e_2),
    inference(resolution,[status(thm)],[c_4997,c_6329]) ).

tff(c_6209,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_4,e_2) ),
    inference(resolution,[status(thm)],[c_6023,c_60]) ).

tff(c_6347,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_6338,c_6209]) ).

tff(c_6377,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_6347]) ).

tff(c_6378,plain,
    product(e_3,e_4,e_3),
    inference(splitRight,[status(thm)],[c_6009]) ).

tff(c_5048,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_4)
      | ~ product(Y_18,e_4,e_3) ),
    inference(resolution,[status(thm)],[c_4997,c_62]) ).

tff(c_6414,plain,
    product(e_3,e_3,e_4),
    inference(resolution,[status(thm)],[c_6378,c_5048]) ).

tff(c_5050,plain,
    ! [W_14] :
      ( equalish(W_14,e_4)
      | ~ product(W_14,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_4997,c_60]) ).

tff(c_6461,plain,
    equalish(e_3,e_4),
    inference(resolution,[status(thm)],[c_6414,c_5050]) ).

tff(c_6496,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_6461]) ).

tff(c_6497,plain,
    ( product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_4795]) ).

tff(c_6557,plain,
    product(e_1,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_6497]) ).

tff(c_6571,plain,
    ( product(e_2,e_1,e_4)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_4) ),
    inference(resolution,[status(thm)],[c_6557,c_113]) ).

tff(c_6608,plain,
    ( product(e_2,e_1,e_4)
    | product(e_4,e_2,e_3)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_24,c_6571]) ).

tff(c_8620,plain,
    product(e_4,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_6608]) ).

tff(c_9148,plain,
    ! [Y_252] :
      ( product(e_2,Y_252,e_1)
      | ~ product(Y_252,e_4,e_2) ),
    inference(resolution,[status(thm)],[c_8620,c_62]) ).

tff(c_9161,plain,
    product(e_2,e_1,e_1),
    inference(resolution,[status(thm)],[c_6557,c_9148]) ).

tff(c_1186,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_1,e_1) ),
    inference(resolution,[status(thm)],[c_1124,c_60]) ).

tff(c_9188,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_9161,c_1186]) ).

tff(c_9253,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_9188]) ).

tff(c_9254,plain,
    ( product(e_4,e_2,e_2)
    | product(e_4,e_2,e_3)
    | product(e_2,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_6608]) ).

tff(c_9256,plain,
    product(e_2,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_9254]) ).

tff(c_4342,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_4257,c_60]) ).

tff(c_9261,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_9256,c_4342]) ).

tff(c_9307,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38,c_9261]) ).

tff(c_9308,plain,
    ( product(e_4,e_2,e_3)
    | product(e_4,e_2,e_2) ),
    inference(splitRight,[status(thm)],[c_9254]) ).

tff(c_9534,plain,
    product(e_4,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_9308]) ).

tff(c_6791,plain,
    ! [Y_221] :
      ( product(e_4,Y_221,e_2)
      | ~ product(Y_221,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_6557,c_62]) ).

tff(c_6800,plain,
    product(e_4,e_3,e_2),
    inference(resolution,[status(thm)],[c_4257,c_6791]) ).

tff(c_6855,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_4,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_6800,c_58]) ).

tff(c_9543,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_9534,c_6855]) ).

tff(c_9581,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38,c_9543]) ).

tff(c_9582,plain,
    product(e_4,e_2,e_3),
    inference(splitRight,[status(thm)],[c_9308]) ).

tff(c_10076,plain,
    ! [Y_261] :
      ( product(e_2,Y_261,e_3)
      | ~ product(Y_261,e_4,e_2) ),
    inference(resolution,[status(thm)],[c_9582,c_62]) ).

tff(c_10089,plain,
    product(e_2,e_1,e_3),
    inference(resolution,[status(thm)],[c_6557,c_10076]) ).

tff(c_3612,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_3)
      | ~ product(Y_18,e_1,e_3) ),
    inference(resolution,[status(thm)],[c_3538,c_62]) ).

tff(c_10163,plain,
    product(e_3,e_2,e_3),
    inference(resolution,[status(thm)],[c_10089,c_3612]) ).

tff(c_9876,plain,
    ! [W_14] :
      ( equalish(W_14,e_4)
      | ~ product(W_14,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_9582,c_60]) ).

tff(c_10224,plain,
    equalish(e_3,e_4),
    inference(resolution,[status(thm)],[c_10163,c_9876]) ).

tff(c_10262,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_10224]) ).

tff(c_10263,plain,
    product(e_1,e_4,e_3),
    inference(splitRight,[status(thm)],[c_6497]) ).

tff(c_3613,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_1,W_11,e_3) ),
    inference(resolution,[status(thm)],[c_3538,c_58]) ).

tff(c_10271,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_10263,c_3613]) ).

tff(c_10312,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_10271]) ).

tff(c_10313,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2) ),
    inference(splitRight,[status(thm)],[c_4255]) ).

tff(c_10321,plain,
    product(e_3,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_10313]) ).

tff(c_10458,plain,
    ! [Y_268] :
      ( product(e_3,Y_268,e_2)
      | ~ product(Y_268,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_10321,c_62]) ).

tff(c_10482,plain,
    product(e_3,e_1,e_2),
    inference(resolution,[status(thm)],[c_3538,c_10458]) ).

tff(c_10370,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_3,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_10321,c_58]) ).

tff(c_10506,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_10482,c_10370]) ).

tff(c_10545,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_10506]) ).

tff(c_10546,plain,
    product(e_3,e_3,e_3),
    inference(splitRight,[status(thm)],[c_10313]) ).

tff(c_3614,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_3538,c_60]) ).

tff(c_10550,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_10546,c_3614]) ).

tff(c_10584,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_10550]) ).

tff(c_10585,plain,
    ! [X_47] :
      ( product(e_1,e_3,e_2)
      | product(e_3,X_47,e_4)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(splitRight,[status(thm)],[c_3432]) ).

tff(c_10630,plain,
    product(e_1,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_10585]) ).

tff(c_10642,plain,
    ( product(e_2,e_1,e_4)
    | product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_10630,c_113]) ).

tff(c_10675,plain,
    ( product(e_2,e_1,e_4)
    | product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2)
    | product(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_10642]) ).

tff(c_10874,plain,
    product(e_3,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_10675]) ).

tff(c_11130,plain,
    ! [Y_276] :
      ( product(e_2,Y_276,e_1)
      | ~ product(Y_276,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_10874,c_62]) ).

tff(c_11133,plain,
    product(e_2,e_1,e_1),
    inference(resolution,[status(thm)],[c_10630,c_11130]) ).

tff(c_11152,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_11133,c_1186]) ).

tff(c_11209,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_11152]) ).

tff(c_11210,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3)
    | product(e_2,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_10675]) ).

tff(c_11212,plain,
    product(e_2,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_11210]) ).

tff(c_11248,plain,
    ~ next(e_2,e_3),
    inference(resolution,[status(thm)],[c_11212,c_79]) ).

tff(c_11302,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_11248]) ).

tff(c_11303,plain,
    ( product(e_3,e_2,e_3)
    | product(e_3,e_2,e_2) ),
    inference(splitRight,[status(thm)],[c_11210]) ).

tff(c_11312,plain,
    product(e_3,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_11303]) ).

tff(c_11322,plain,
    ( product(e_2,e_3,e_4)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_11312,c_113]) ).

tff(c_11351,plain,
    ( product(e_2,e_3,e_4)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_11322]) ).

tff(c_14162,plain,
    product(e_2,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_11351]) ).

tff(c_11448,plain,
    ! [Y_280] :
      ( product(e_2,Y_280,e_2)
      | ~ product(Y_280,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_11312,c_62]) ).

tff(c_11451,plain,
    product(e_2,e_1,e_2),
    inference(resolution,[status(thm)],[c_10630,c_11448]) ).

tff(c_11526,plain,
    ! [Y_18] :
      ( product(e_1,Y_18,e_2)
      | ~ product(Y_18,e_2,e_1) ),
    inference(resolution,[status(thm)],[c_11451,c_62]) ).

tff(c_14225,plain,
    product(e_1,e_2,e_2),
    inference(resolution,[status(thm)],[c_14162,c_11526]) ).

tff(c_11362,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_11312,c_60]) ).

tff(c_14311,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_14225,c_11362]) ).

tff(c_14350,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_14311]) ).

tff(c_14351,plain,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_3,e_4) ),
    inference(splitRight,[status(thm)],[c_11351]) ).

tff(c_14353,plain,
    product(e_2,e_3,e_4),
    inference(splitLeft,[status(thm)],[c_14351]) ).

tff(c_50,plain,
    ~ equalish(e_4,e_2),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_14448,plain,
    ( product(e_4,e_2,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_14353,c_113]) ).

tff(c_14479,plain,
    ( product(e_4,e_2,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_14448]) ).

tff(c_14679,plain,
    product(e_3,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_14479]) ).

tff(c_15008,plain,
    ! [Y_341] :
      ( product(e_4,Y_341,e_1)
      | ~ product(Y_341,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_14679,c_62]) ).

tff(c_15017,plain,
    product(e_4,e_2,e_1),
    inference(resolution,[status(thm)],[c_14353,c_15008]) ).

tff(c_15097,plain,
    product(e_1,e_4,e_2),
    inference(resolution,[status(thm)],[c_15017,c_11526]) ).

tff(c_10685,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_1,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_10630,c_58]) ).

tff(c_15154,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_15097,c_10685]) ).

tff(c_15194,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_15154]) ).

tff(c_15195,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_4,e_2,e_4) ),
    inference(splitRight,[status(thm)],[c_14479]) ).

tff(c_15228,plain,
    product(e_4,e_2,e_4),
    inference(splitLeft,[status(thm)],[c_15195]) ).

tff(c_15240,plain,
    ( product(e_4,e_4,e_4)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_15228,c_113]) ).

tff(c_15274,plain,
    ( product(e_4,e_4,e_4)
    | product(e_2,e_4,e_3)
    | product(e_2,e_4,e_2)
    | product(e_2,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_28,c_15240]) ).

tff(c_15396,plain,
    product(e_2,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_15274]) ).

tff(c_15740,plain,
    ! [Y_355] :
      ( product(e_4,Y_355,e_1)
      | ~ product(Y_355,e_2,e_4) ),
    inference(resolution,[status(thm)],[c_15396,c_62]) ).

tff(c_15749,plain,
    product(e_4,e_4,e_1),
    inference(resolution,[status(thm)],[c_15228,c_15740]) ).

tff(c_15513,plain,
    ! [W_14] :
      ( equalish(W_14,e_2)
      | ~ product(W_14,e_4,e_1) ),
    inference(resolution,[status(thm)],[c_15396,c_60]) ).

tff(c_15851,plain,
    equalish(e_4,e_2),
    inference(resolution,[status(thm)],[c_15749,c_15513]) ).

tff(c_15909,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_15851]) ).

tff(c_15910,plain,
    ( product(e_2,e_4,e_2)
    | product(e_2,e_4,e_3)
    | product(e_4,e_4,e_4) ),
    inference(splitRight,[status(thm)],[c_15274]) ).

tff(c_15912,plain,
    product(e_4,e_4,e_4),
    inference(splitLeft,[status(thm)],[c_15910]) ).

tff(c_15285,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(e_4,W_11,e_4) ),
    inference(resolution,[status(thm)],[c_15228,c_58]) ).

tff(c_15915,plain,
    equalish(e_4,e_2),
    inference(resolution,[status(thm)],[c_15912,c_15285]) ).

tff(c_15947,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_15915]) ).

tff(c_15948,plain,
    ( product(e_2,e_4,e_3)
    | product(e_2,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_15910]) ).

tff(c_15981,plain,
    product(e_2,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_15948]) ).

tff(c_11527,plain,
    ! [W_11] :
      ( equalish(W_11,e_1)
      | ~ product(e_2,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_11451,c_58]) ).

tff(c_15988,plain,
    equalish(e_4,e_1),
    inference(resolution,[status(thm)],[c_15981,c_11527]) ).

tff(c_16019,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_48,c_15988]) ).

tff(c_16020,plain,
    product(e_2,e_4,e_3),
    inference(splitRight,[status(thm)],[c_15948]) ).

tff(c_16388,plain,
    ! [Y_366] :
      ( product(e_4,Y_366,e_3)
      | ~ product(Y_366,e_2,e_4) ),
    inference(resolution,[status(thm)],[c_16020,c_62]) ).

tff(c_16397,plain,
    product(e_4,e_4,e_3),
    inference(resolution,[status(thm)],[c_15228,c_16388]) ).

tff(c_16196,plain,
    ! [W_14] :
      ( equalish(W_14,e_2)
      | ~ product(W_14,e_4,e_3) ),
    inference(resolution,[status(thm)],[c_16020,c_60]) ).

tff(c_16445,plain,
    equalish(e_4,e_2),
    inference(resolution,[status(thm)],[c_16397,c_16196]) ).

tff(c_16492,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_16445]) ).

tff(c_16493,plain,
    ( product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_15195]) ).

tff(c_16507,plain,
    product(e_3,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_16493]) ).

tff(c_11361,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(e_3,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_11312,c_58]) ).

tff(c_16597,plain,
    equalish(e_4,e_2),
    inference(resolution,[status(thm)],[c_16507,c_11361]) ).

tff(c_16627,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_16597]) ).

tff(c_16628,plain,
    product(e_3,e_4,e_3),
    inference(splitRight,[status(thm)],[c_16493]) ).

tff(c_17098,plain,
    ! [Y_378] :
      ( product(e_4,Y_378,e_3)
      | ~ product(Y_378,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_16628,c_62]) ).

tff(c_17107,plain,
    product(e_4,e_2,e_3),
    inference(resolution,[status(thm)],[c_14353,c_17098]) ).

tff(c_14489,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_4)
      | ~ product(Y_18,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_14353,c_62]) ).

tff(c_17161,plain,
    product(e_3,e_4,e_4),
    inference(resolution,[status(thm)],[c_17107,c_14489]) ).

tff(c_56,plain,
    ! [W_8,Z_9,X_6,Y_7] :
      ( equalish(W_8,Z_9)
      | ~ product(X_6,Y_7,Z_9)
      | ~ product(X_6,Y_7,W_8) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_16720,plain,
    ! [W_8] :
      ( equalish(W_8,e_3)
      | ~ product(e_3,e_4,W_8) ),
    inference(resolution,[status(thm)],[c_16628,c_56]) ).

tff(c_17281,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_17161,c_16720]) ).

tff(c_17313,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_17281]) ).

tff(c_17314,plain,
    ( product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2) ),
    inference(splitRight,[status(thm)],[c_14351]) ).

tff(c_17322,plain,
    product(e_2,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_17314]) ).

tff(c_17325,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_17322,c_11527]) ).

tff(c_17354,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_17325]) ).

tff(c_17355,plain,
    product(e_2,e_2,e_3),
    inference(splitRight,[status(thm)],[c_17314]) ).

tff(c_17654,plain,
    ! [Y_386] :
      ( product(e_2,Y_386,e_3)
      | ~ product(Y_386,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_17355,c_62]) ).

tff(c_17657,plain,
    product(e_2,e_3,e_3),
    inference(resolution,[status(thm)],[c_11312,c_17654]) ).

tff(c_17430,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(e_2,W_11,e_3) ),
    inference(resolution,[status(thm)],[c_17355,c_58]) ).

tff(c_17660,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_17657,c_17430]) ).

tff(c_17698,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_44,c_17660]) ).

tff(c_17700,plain,
    ~ product(e_3,e_2,e_2),
    inference(splitRight,[status(thm)],[c_11303]) ).

tff(c_17699,plain,
    product(e_3,e_2,e_3),
    inference(splitRight,[status(thm)],[c_11303]) ).

tff(c_17957,plain,
    ! [Y_390] :
      ( product(e_2,Y_390,e_3)
      | ~ product(Y_390,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_17699,c_62]) ).

tff(c_17960,plain,
    product(e_2,e_1,e_3),
    inference(resolution,[status(thm)],[c_10630,c_17957]) ).

tff(c_10684,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_2)
      | ~ product(Y_18,e_1,e_3) ),
    inference(resolution,[status(thm)],[c_10630,c_62]) ).

tff(c_17962,plain,
    product(e_3,e_2,e_2),
    inference(resolution,[status(thm)],[c_17960,c_10684]) ).

tff(c_18012,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_17700,c_17962]) ).

tff(c_18014,plain,
    ~ product(e_1,e_3,e_2),
    inference(splitRight,[status(thm)],[c_10585]) ).

tff(c_54,plain,
    ! [X_4,Y_5] :
      ( product(X_4,Y_5,e_4)
      | product(X_4,Y_5,e_3)
      | product(X_4,Y_5,e_2)
      | product(X_4,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(X_4) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_258,plain,
    ! [W_63,Y_64,X_65] :
      ( equalish(W_63,Y_64)
      | ~ product(X_65,W_63,e_4)
      | product(X_65,Y_64,e_3)
      | product(X_65,Y_64,e_2)
      | product(X_65,Y_64,e_1)
      | ~ group_element(Y_64)
      | ~ group_element(X_65) ),
    inference(resolution,[status(thm)],[c_92,c_58]) ).

tff(c_261,plain,
    ! [Y_5,Y_64,X_4] :
      ( equalish(Y_5,Y_64)
      | product(X_4,Y_64,e_3)
      | product(X_4,Y_64,e_2)
      | product(X_4,Y_64,e_1)
      | ~ group_element(Y_64)
      | product(X_4,Y_5,e_3)
      | product(X_4,Y_5,e_2)
      | product(X_4,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(X_4) ),
    inference(resolution,[status(thm)],[c_54,c_258]) ).

tff(c_10586,plain,
    ~ product(e_1,e_3,e_3),
    inference(splitRight,[status(thm)],[c_3432]) ).

tff(c_10601,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_261,c_10586]) ).

tff(c_10624,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10601]) ).

tff(c_10625,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5) ),
    inference(negUnitSimplification,[status(thm)],[c_3433,c_10624]) ).

tff(c_18842,plain,
    ! [Y_413] :
      ( equalish(Y_413,e_3)
      | product(e_1,Y_413,e_3)
      | product(e_1,Y_413,e_2)
      | product(e_1,Y_413,e_1)
      | ~ group_element(Y_413) ),
    inference(negUnitSimplification,[status(thm)],[c_18014,c_10625]) ).

tff(c_20505,plain,
    ! [Y_446,Y_447] :
      ( product(Y_446,Y_447,e_3)
      | ~ product(Y_447,e_1,Y_446)
      | equalish(Y_446,e_3)
      | product(e_1,Y_446,e_2)
      | product(e_1,Y_446,e_1)
      | ~ group_element(Y_446) ),
    inference(resolution,[status(thm)],[c_18842,c_62]) ).

tff(c_20575,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | equalish(e_2,e_3)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ group_element(e_2)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(resolution,[status(thm)],[c_255,c_20505]) ).

tff(c_20683,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | equalish(e_2,e_3)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_20575]) ).

tff(c_20684,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(negUnitSimplification,[status(thm)],[c_38,c_20683]) ).

tff(c_20881,plain,
    product(e_1,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_20684]) ).

tff(c_20906,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_20881,c_1185]) ).

tff(c_20966,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_20906]) ).

tff(c_20968,plain,
    ~ product(e_1,e_2,e_1),
    inference(splitRight,[status(thm)],[c_20684]) ).

tff(c_30,plain,
    ~ equalish(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_10604,plain,
    ! [Y_64] :
      ( equalish(e_3,Y_64)
      | product(e_1,Y_64,e_3)
      | product(e_1,Y_64,e_2)
      | product(e_1,Y_64,e_1)
      | ~ group_element(Y_64)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_261,c_10586]) ).

tff(c_10628,plain,
    ! [Y_64] :
      ( equalish(e_3,Y_64)
      | product(e_1,Y_64,e_3)
      | product(e_1,Y_64,e_2)
      | product(e_1,Y_64,e_1)
      | ~ group_element(Y_64)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10604]) ).

tff(c_10629,plain,
    ! [Y_64] :
      ( equalish(e_3,Y_64)
      | product(e_1,Y_64,e_3)
      | product(e_1,Y_64,e_2)
      | product(e_1,Y_64,e_1)
      | ~ group_element(Y_64)
      | product(e_1,e_3,e_2) ),
    inference(negUnitSimplification,[status(thm)],[c_3433,c_10628]) ).

tff(c_19500,plain,
    ! [Y_425] :
      ( equalish(e_3,Y_425)
      | product(e_1,Y_425,e_3)
      | product(e_1,Y_425,e_2)
      | product(e_1,Y_425,e_1)
      | ~ group_element(Y_425) ),
    inference(negUnitSimplification,[status(thm)],[c_18014,c_10629]) ).

tff(c_20693,plain,
    ! [Y_448,Y_449] :
      ( product(Y_448,Y_449,e_3)
      | ~ product(Y_449,e_1,Y_448)
      | equalish(e_3,Y_448)
      | product(e_1,Y_448,e_2)
      | product(e_1,Y_448,e_1)
      | ~ group_element(Y_448) ),
    inference(resolution,[status(thm)],[c_19500,c_62]) ).

tff(c_20763,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | equalish(e_3,e_2)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ group_element(e_2)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(resolution,[status(thm)],[c_255,c_20693]) ).

tff(c_20871,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | equalish(e_3,e_2)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_20763]) ).

tff(c_20872,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | product(e_1,e_2,e_2)
      | product(e_1,e_2,e_1)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(negUnitSimplification,[status(thm)],[c_44,c_20871]) ).

tff(c_21060,plain,
    ! [X_62] :
      ( product(e_2,X_62,e_3)
      | product(e_1,e_2,e_2)
      | ~ next(X_62,e_2)
      | product(X_62,e_1,e_1)
      | ~ group_element(X_62) ),
    inference(negUnitSimplification,[status(thm)],[c_20968,c_20872]) ).

tff(c_21061,plain,
    product(e_1,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_21060]) ).

tff(c_21079,plain,
    ( product(e_2,e_1,e_4)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_21061,c_113]) ).

tff(c_21124,plain,
    ( product(e_2,e_1,e_4)
    | product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2)
    | product(e_2,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_21079]) ).

tff(c_22244,plain,
    product(e_2,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_21124]) ).

tff(c_22735,plain,
    ! [Y_475] :
      ( product(e_2,Y_475,e_1)
      | ~ product(Y_475,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_22244,c_62]) ).

tff(c_22758,plain,
    product(e_2,e_1,e_1),
    inference(resolution,[status(thm)],[c_21061,c_22735]) ).

tff(c_22534,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(e_2,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_22244,c_58]) ).

tff(c_22761,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_22758,c_22534]) ).

tff(c_22825,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30,c_22761]) ).

tff(c_22826,plain,
    ( product(e_2,e_2,e_2)
    | product(e_2,e_2,e_3)
    | product(e_2,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_21124]) ).

tff(c_22828,plain,
    product(e_2,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_22826]) ).

tff(c_22875,plain,
    ~ next(e_2,e_3),
    inference(resolution,[status(thm)],[c_22828,c_79]) ).

tff(c_22949,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_22875]) ).

tff(c_22950,plain,
    ( product(e_2,e_2,e_3)
    | product(e_2,e_2,e_2) ),
    inference(splitRight,[status(thm)],[c_22826]) ).

tff(c_23153,plain,
    product(e_2,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_22950]) ).

tff(c_21135,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_21061,c_60]) ).

tff(c_23166,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_23153,c_21135]) ).

tff(c_23207,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_23166]) ).

tff(c_23209,plain,
    ~ product(e_2,e_2,e_2),
    inference(splitRight,[status(thm)],[c_22950]) ).

tff(c_23208,plain,
    product(e_2,e_2,e_3),
    inference(splitRight,[status(thm)],[c_22950]) ).

tff(c_199,plain,
    ! [X_60] :
      ( ~ next(X_60,e_3)
      | product(X_60,e_1,e_3)
      | product(X_60,e_1,e_2)
      | product(X_60,e_1,e_1)
      | ~ group_element(X_60) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_106]) ).

tff(c_215,plain,
    ! [W_11,X_60] :
      ( equalish(W_11,e_1)
      | ~ product(X_60,W_11,e_3)
      | ~ next(X_60,e_3)
      | product(X_60,e_1,e_2)
      | product(X_60,e_1,e_1)
      | ~ group_element(X_60) ),
    inference(resolution,[status(thm)],[c_199,c_58]) ).

tff(c_23435,plain,
    ( equalish(e_2,e_1)
    | ~ next(e_2,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_23208,c_215]) ).

tff(c_23511,plain,
    ( equalish(e_2,e_1)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_23435]) ).

tff(c_23512,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_36,c_23511]) ).

tff(c_23833,plain,
    product(e_2,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_23512]) ).

tff(c_1184,plain,
    ! [Y_18] :
      ( product(e_1,Y_18,e_1)
      | ~ product(Y_18,e_1,e_1) ),
    inference(resolution,[status(thm)],[c_1124,c_62]) ).

tff(c_23864,plain,
    product(e_1,e_2,e_1),
    inference(resolution,[status(thm)],[c_23833,c_1184]) ).

tff(c_23951,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20968,c_23864]) ).

tff(c_23952,plain,
    product(e_2,e_1,e_2),
    inference(splitRight,[status(thm)],[c_23512]) ).

tff(c_21133,plain,
    ! [Y_18] :
      ( product(e_2,Y_18,e_2)
      | ~ product(Y_18,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_21061,c_62]) ).

tff(c_24023,plain,
    product(e_2,e_2,e_2),
    inference(resolution,[status(thm)],[c_23952,c_21133]) ).

tff(c_24087,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_23209,c_24023]) ).

tff(c_24089,plain,
    ~ product(e_1,e_2,e_2),
    inference(splitRight,[status(thm)],[c_21060]) ).

tff(c_19499,plain,
    ! [Y_64] :
      ( equalish(e_3,Y_64)
      | product(e_1,Y_64,e_3)
      | product(e_1,Y_64,e_2)
      | product(e_1,Y_64,e_1)
      | ~ group_element(Y_64) ),
    inference(negUnitSimplification,[status(thm)],[c_18014,c_10629]) ).

tff(c_24090,plain,
    ! [X_488] :
      ( product(e_2,X_488,e_3)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(splitRight,[status(thm)],[c_21060]) ).

tff(c_195,plain,
    ! [W_57,X_58,Y_59] :
      ( equalish(W_57,X_58)
      | ~ product(W_57,Y_59,e_4)
      | product(X_58,Y_59,e_3)
      | product(X_58,Y_59,e_2)
      | product(X_58,Y_59,e_1)
      | ~ group_element(Y_59)
      | ~ group_element(X_58) ),
    inference(resolution,[status(thm)],[c_92,c_60]) ).

tff(c_198,plain,
    ! [X_4,X_58,Y_5] :
      ( equalish(X_4,X_58)
      | product(X_58,Y_5,e_3)
      | product(X_58,Y_5,e_2)
      | product(X_58,Y_5,e_1)
      | ~ group_element(X_58)
      | product(X_4,Y_5,e_3)
      | product(X_4,Y_5,e_2)
      | product(X_4,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(X_4) ),
    inference(resolution,[status(thm)],[c_54,c_195]) ).

tff(c_10595,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_198,c_10586]) ).

tff(c_10616,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_10595]) ).

tff(c_10617,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2) ),
    inference(negUnitSimplification,[status(thm)],[c_3433,c_10616]) ).

tff(c_18502,plain,
    ! [X_404] :
      ( equalish(e_1,X_404)
      | product(X_404,e_3,e_3)
      | product(X_404,e_3,e_2)
      | product(X_404,e_3,e_1)
      | ~ group_element(X_404) ),
    inference(negUnitSimplification,[status(thm)],[c_18014,c_10617]) ).

tff(c_18585,plain,
    ! [W_11,X_404] :
      ( equalish(W_11,e_3)
      | ~ product(X_404,W_11,e_3)
      | equalish(e_1,X_404)
      | product(X_404,e_3,e_2)
      | product(X_404,e_3,e_1)
      | ~ group_element(X_404) ),
    inference(resolution,[status(thm)],[c_18502,c_58]) ).

tff(c_24116,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | equalish(e_1,e_2)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ group_element(e_2)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(resolution,[status(thm)],[c_24090,c_18585]) ).

tff(c_24265,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | equalish(e_1,e_2)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_24116]) ).

tff(c_24266,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(negUnitSimplification,[status(thm)],[c_30,c_24265]) ).

tff(c_29252,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_24266]) ).

tff(c_29647,plain,
    ! [Y_581] :
      ( product(e_3,Y_581,e_1)
      | ~ product(Y_581,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_29252,c_62]) ).

tff(c_29656,plain,
    ( product(e_3,e_1,e_1)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_19499,c_29647]) ).

tff(c_29691,plain,
    ( product(e_3,e_1,e_1)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_29656]) ).

tff(c_29692,plain,
    product(e_3,e_1,e_1),
    inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_29691]) ).

tff(c_29755,plain,
    product(e_1,e_3,e_1),
    inference(resolution,[status(thm)],[c_29692,c_1184]) ).

tff(c_29856,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3433,c_29755]) ).

tff(c_29858,plain,
    ~ product(e_2,e_3,e_1),
    inference(splitRight,[status(thm)],[c_24266]) ).

tff(c_25447,plain,
    ! [W_504,X_505] :
      ( equalish(W_504,X_505)
      | ~ product(W_504,e_1,e_1)
      | product(e_2,X_505,e_3)
      | ~ next(X_505,e_2)
      | ~ group_element(X_505) ),
    inference(resolution,[status(thm)],[c_24090,c_60]) ).

tff(c_25511,plain,
    ! [X_506] :
      ( equalish(e_1,X_506)
      | product(e_2,X_506,e_3)
      | ~ next(X_506,e_2)
      | ~ group_element(X_506) ),
    inference(resolution,[status(thm)],[c_1124,c_25447]) ).

tff(c_25935,plain,
    ! [W_510,X_511] :
      ( equalish(W_510,X_511)
      | ~ product(e_2,W_510,e_3)
      | equalish(e_1,X_511)
      | ~ next(X_511,e_2)
      | ~ group_element(X_511) ),
    inference(resolution,[status(thm)],[c_25511,c_58]) ).

tff(c_25974,plain,
    ! [X_511] :
      ( equalish(e_1,X_511)
      | ~ next(X_511,e_2)
      | ~ group_element(X_511)
      | ~ next(e_2,e_3)
      | product(e_2,e_1,e_2)
      | product(e_2,e_1,e_1)
      | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_121,c_25935]) ).

tff(c_26010,plain,
    ! [X_511] :
      ( equalish(e_1,X_511)
      | ~ next(X_511,e_2)
      | ~ group_element(X_511)
      | product(e_2,e_1,e_2)
      | product(e_2,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_25974]) ).

tff(c_26746,plain,
    product(e_2,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_26010]) ).

tff(c_26786,plain,
    product(e_1,e_2,e_1),
    inference(resolution,[status(thm)],[c_26746,c_1184]) ).

tff(c_26885,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20968,c_26786]) ).

tff(c_26887,plain,
    ~ product(e_2,e_1,e_1),
    inference(splitRight,[status(thm)],[c_26010]) ).

tff(c_26886,plain,
    ! [X_511] :
      ( product(e_2,e_1,e_2)
      | equalish(e_1,X_511)
      | ~ next(X_511,e_2)
      | ~ group_element(X_511) ),
    inference(splitRight,[status(thm)],[c_26010]) ).

tff(c_26983,plain,
    product(e_2,e_1,e_2),
    inference(splitLeft,[status(thm)],[c_26886]) ).

tff(c_19668,plain,
    ! [Y_425,Y_18] :
      ( product(Y_425,Y_18,e_3)
      | ~ product(Y_18,e_1,Y_425)
      | equalish(e_3,Y_425)
      | product(e_1,Y_425,e_2)
      | product(e_1,Y_425,e_1)
      | ~ group_element(Y_425) ),
    inference(resolution,[status(thm)],[c_19500,c_62]) ).

tff(c_26997,plain,
    ( product(e_2,e_2,e_3)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_26983,c_19668]) ).

tff(c_27063,plain,
    ( product(e_2,e_2,e_3)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_26997]) ).

tff(c_27064,plain,
    product(e_2,e_2,e_3),
    inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_27063]) ).

tff(c_19670,plain,
    ! [W_14,Y_425] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,Y_425,e_3)
      | equalish(e_3,Y_425)
      | product(e_1,Y_425,e_2)
      | product(e_1,Y_425,e_1)
      | ~ group_element(Y_425) ),
    inference(resolution,[status(thm)],[c_19500,c_60]) ).

tff(c_27164,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_27064,c_19670]) ).

tff(c_27253,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_2)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_27164]) ).

tff(c_27255,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20968,c_24089,c_44,c_36,c_27253]) ).

tff(c_27257,plain,
    ~ product(e_2,e_1,e_2),
    inference(splitRight,[status(thm)],[c_26886]) ).

tff(c_18529,plain,
    ! [X_404] :
      ( equalish(e_3,e_1)
      | ~ next(X_404,e_3)
      | product(X_404,e_1,e_2)
      | product(X_404,e_1,e_1)
      | equalish(e_1,X_404)
      | product(X_404,e_3,e_2)
      | product(X_404,e_3,e_1)
      | ~ group_element(X_404) ),
    inference(resolution,[status(thm)],[c_18502,c_215]) ).

tff(c_37516,plain,
    ! [X_718] :
      ( ~ next(X_718,e_3)
      | product(X_718,e_1,e_2)
      | product(X_718,e_1,e_1)
      | equalish(e_1,X_718)
      | product(X_718,e_3,e_2)
      | product(X_718,e_3,e_1)
      | ~ group_element(X_718) ),
    inference(negUnitSimplification,[status(thm)],[c_42,c_18529]) ).

tff(c_10592,plain,
    ! [X_4] :
      ( equalish(X_4,e_1)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_1)
      | product(X_4,e_3,e_3)
      | product(X_4,e_3,e_2)
      | product(X_4,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_4) ),
    inference(resolution,[status(thm)],[c_198,c_10586]) ).

tff(c_10612,plain,
    ! [X_4] :
      ( equalish(X_4,e_1)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | product(X_4,e_3,e_3)
      | product(X_4,e_3,e_2)
      | product(X_4,e_3,e_1)
      | ~ group_element(X_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_10592]) ).

tff(c_10613,plain,
    ! [X_4] :
      ( equalish(X_4,e_1)
      | product(e_1,e_3,e_2)
      | product(X_4,e_3,e_3)
      | product(X_4,e_3,e_2)
      | product(X_4,e_3,e_1)
      | ~ group_element(X_4) ),
    inference(negUnitSimplification,[status(thm)],[c_3433,c_10612]) ).

tff(c_19942,plain,
    ! [X_432] :
      ( equalish(X_432,e_1)
      | product(X_432,e_3,e_3)
      | product(X_432,e_3,e_2)
      | product(X_432,e_3,e_1)
      | ~ group_element(X_432) ),
    inference(negUnitSimplification,[status(thm)],[c_18014,c_10613]) ).

tff(c_20088,plain,
    ! [W_11,X_432] :
      ( equalish(W_11,e_3)
      | ~ product(X_432,W_11,e_3)
      | equalish(X_432,e_1)
      | product(X_432,e_3,e_2)
      | product(X_432,e_3,e_1)
      | ~ group_element(X_432) ),
    inference(resolution,[status(thm)],[c_19942,c_58]) ).

tff(c_24107,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | equalish(e_2,e_1)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ group_element(e_2)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(resolution,[status(thm)],[c_24090,c_20088]) ).

tff(c_24255,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | equalish(e_2,e_1)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_24107]) ).

tff(c_24256,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | product(e_2,e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(negUnitSimplification,[status(thm)],[c_36,c_24255]) ).

tff(c_29859,plain,
    ! [X_488] :
      ( equalish(X_488,e_3)
      | product(e_2,e_3,e_2)
      | ~ next(X_488,e_2)
      | product(X_488,e_1,e_1)
      | ~ group_element(X_488) ),
    inference(negUnitSimplification,[status(thm)],[c_29858,c_24256]) ).

tff(c_29860,plain,
    product(e_2,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_29859]) ).

tff(c_18015,plain,
    ! [X_391] :
      ( product(e_3,X_391,e_4)
      | ~ next(X_391,e_3)
      | product(X_391,e_1,e_2)
      | product(X_391,e_1,e_1)
      | ~ group_element(X_391) ),
    inference(splitRight,[status(thm)],[c_10585]) ).

tff(c_18141,plain,
    ! [X_391,Y_18] :
      ( product(X_391,Y_18,e_4)
      | ~ product(Y_18,e_3,X_391)
      | ~ next(X_391,e_3)
      | product(X_391,e_1,e_2)
      | product(X_391,e_1,e_1)
      | ~ group_element(X_391) ),
    inference(resolution,[status(thm)],[c_18015,c_62]) ).

tff(c_29877,plain,
    ( product(e_2,e_2,e_4)
    | ~ next(e_2,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_29860,c_18141]) ).

tff(c_29934,plain,
    ( product(e_2,e_2,e_4)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_29877]) ).

tff(c_29935,plain,
    product(e_2,e_2,e_4),
    inference(negUnitSimplification,[status(thm)],[c_26887,c_27257,c_29934]) ).

tff(c_18143,plain,
    ! [W_14,X_391] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,X_391,e_4)
      | ~ next(X_391,e_3)
      | product(X_391,e_1,e_2)
      | product(X_391,e_1,e_1)
      | ~ group_element(X_391) ),
    inference(resolution,[status(thm)],[c_18015,c_60]) ).

tff(c_29989,plain,
    ( equalish(e_2,e_3)
    | ~ next(e_2,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_29935,c_18143]) ).

tff(c_30042,plain,
    ( equalish(e_2,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_29989]) ).

tff(c_30044,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26887,c_27257,c_38,c_30042]) ).

tff(c_30046,plain,
    ~ product(e_2,e_3,e_2),
    inference(splitRight,[status(thm)],[c_29859]) ).

tff(c_37535,plain,
    ( ~ next(e_2,e_3)
    | product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1)
    | equalish(e_1,e_2)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_37516,c_30046]) ).

tff(c_37617,plain,
    ( product(e_2,e_1,e_2)
    | product(e_2,e_1,e_1)
    | equalish(e_1,e_2)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_37535]) ).

tff(c_37619,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_29858,c_30,c_26887,c_27257,c_37617]) ).

tff(c_37621,plain,
    ~ product(e_1,e_1,e_1),
    inference(splitRight,[status(thm)],[c_856]) ).

tff(c_38628,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_350]) ).

tff(c_38638,plain,
    ( product(e_1,e_1,e_4)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_1)
    | ~ group_element(e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_38628,c_113]) ).

tff(c_38668,plain,
    ( product(e_1,e_1,e_4)
    | product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2)
    | product(e_3,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_22,c_38638]) ).

tff(c_38837,plain,
    product(e_3,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_38668]) ).

tff(c_38855,plain,
    ( product(e_1,e_3,e_2)
    | ~ next(e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_38837,c_274]) ).

tff(c_38895,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_38855]) ).

tff(c_38896,plain,
    product(e_1,e_3,e_2),
    inference(negUnitSimplification,[status(thm)],[c_37621,c_38895]) ).

tff(c_38679,plain,
    ! [W_8] :
      ( equalish(W_8,e_1)
      | ~ product(e_1,e_3,W_8) ),
    inference(resolution,[status(thm)],[c_38628,c_56]) ).

tff(c_38938,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_38896,c_38679]) ).

tff(c_38962,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_38938]) ).

tff(c_38964,plain,
    ~ product(e_3,e_1,e_1),
    inference(splitRight,[status(thm)],[c_38668]) ).

tff(c_38963,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3)
    | product(e_1,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_38668]) ).

tff(c_38983,plain,
    product(e_1,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_38963]) ).

tff(c_277,plain,
    ! [W_8,X_66] :
      ( equalish(W_8,e_2)
      | ~ product(X_66,e_1,W_8)
      | ~ next(X_66,e_2)
      | product(X_66,e_1,e_1)
      | ~ group_element(X_66) ),
    inference(resolution,[status(thm)],[c_262,c_56]) ).

tff(c_38997,plain,
    ( equalish(e_4,e_2)
    | ~ next(e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_38983,c_277]) ).

tff(c_39043,plain,
    ( equalish(e_4,e_2)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_38997]) ).

tff(c_39045,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_37621,c_50,c_39043]) ).

tff(c_39047,plain,
    ~ product(e_1,e_1,e_4),
    inference(splitRight,[status(thm)],[c_38963]) ).

tff(c_39050,plain,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_54,c_39047]) ).

tff(c_39053,plain,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_39050]) ).

tff(c_39054,plain,
    ( product(e_1,e_1,e_3)
    | product(e_1,e_1,e_2) ),
    inference(negUnitSimplification,[status(thm)],[c_37621,c_39053]) ).

tff(c_39265,plain,
    product(e_1,e_1,e_2),
    inference(splitLeft,[status(thm)],[c_39054]) ).

tff(c_39046,plain,
    ( product(e_3,e_1,e_3)
    | product(e_3,e_1,e_2) ),
    inference(splitRight,[status(thm)],[c_38963]) ).

tff(c_39063,plain,
    product(e_3,e_1,e_2),
    inference(splitLeft,[status(thm)],[c_39046]) ).

tff(c_39126,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_39063,c_60]) ).

tff(c_39268,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_39265,c_39126]) ).

tff(c_39305,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_39268]) ).

tff(c_39306,plain,
    product(e_1,e_1,e_3),
    inference(splitRight,[status(thm)],[c_39054]) ).

tff(c_38676,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_1)
      | ~ product(Y_18,e_1,e_3) ),
    inference(resolution,[status(thm)],[c_38628,c_62]) ).

tff(c_39309,plain,
    product(e_3,e_1,e_1),
    inference(resolution,[status(thm)],[c_39306,c_38676]) ).

tff(c_39347,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38964,c_39309]) ).

tff(c_39348,plain,
    product(e_3,e_1,e_3),
    inference(splitRight,[status(thm)],[c_39046]) ).

tff(c_39417,plain,
    product(e_3,e_3,e_1),
    inference(resolution,[status(thm)],[c_39348,c_38676]) ).

tff(c_38678,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_38628,c_60]) ).

tff(c_39528,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_39417,c_38678]) ).

tff(c_39552,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_39528]) ).

tff(c_39553,plain,
    ! [X_47] :
      ( product(e_1,e_3,e_2)
      | product(e_1,e_3,e_3)
      | product(e_3,X_47,e_4)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(splitRight,[status(thm)],[c_350]) ).

tff(c_39555,plain,
    product(e_1,e_3,e_3),
    inference(splitLeft,[status(thm)],[c_39553]) ).

tff(c_39563,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_39555,c_113]) ).

tff(c_39587,plain,
    ( product(e_3,e_1,e_4)
    | product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_39563]) ).

tff(c_39835,plain,
    product(e_3,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_39587]) ).

tff(c_39982,plain,
    ! [Y_777] :
      ( product(e_3,Y_777,e_1)
      | ~ product(Y_777,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_39835,c_62]) ).

tff(c_40006,plain,
    product(e_3,e_1,e_1),
    inference(resolution,[status(thm)],[c_39555,c_39982]) ).

tff(c_39878,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_3,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_39835,c_58]) ).

tff(c_40030,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_40006,c_39878]) ).

tff(c_40064,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_40030]) ).

tff(c_40065,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_3)
    | product(e_3,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_39587]) ).

tff(c_40067,plain,
    product(e_3,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_40065]) ).

tff(c_40073,plain,
    ( product(e_4,e_3,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_40067,c_113]) ).

tff(c_40110,plain,
    ( product(e_4,e_3,e_4)
    | product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2)
    | product(e_1,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_28,c_40073]) ).

tff(c_40365,plain,
    product(e_1,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_40110]) ).

tff(c_40533,plain,
    ! [Y_788] :
      ( product(e_4,Y_788,e_1)
      | ~ product(Y_788,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_40365,c_62]) ).

tff(c_40542,plain,
    product(e_4,e_3,e_1),
    inference(resolution,[status(thm)],[c_40067,c_40533]) ).

tff(c_40128,plain,
    ! [Y_18] :
      ( product(e_1,Y_18,e_4)
      | ~ product(Y_18,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_40067,c_62]) ).

tff(c_40577,plain,
    product(e_1,e_4,e_4),
    inference(resolution,[status(thm)],[c_40542,c_40128]) ).

tff(c_40422,plain,
    ! [W_8] :
      ( equalish(W_8,e_1)
      | ~ product(e_1,e_4,W_8) ),
    inference(resolution,[status(thm)],[c_40365,c_56]) ).

tff(c_40604,plain,
    equalish(e_4,e_1),
    inference(resolution,[status(thm)],[c_40577,c_40422]) ).

tff(c_40628,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_48,c_40604]) ).

tff(c_40629,plain,
    ( product(e_1,e_4,e_2)
    | product(e_1,e_4,e_3)
    | product(e_4,e_3,e_4) ),
    inference(splitRight,[status(thm)],[c_40110]) ).

tff(c_40699,plain,
    product(e_4,e_3,e_4),
    inference(splitLeft,[status(thm)],[c_40629]) ).

tff(c_40703,plain,
    ( product(e_4,e_4,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1)
    | ~ group_element(e_4)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_40699,c_113]) ).

tff(c_40724,plain,
    ( product(e_4,e_4,e_4)
    | product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_28,c_40703]) ).

tff(c_41304,plain,
    product(e_3,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_40724]) ).

tff(c_41494,plain,
    ! [Y_808] :
      ( product(e_4,Y_808,e_1)
      | ~ product(Y_808,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_41304,c_62]) ).

tff(c_41503,plain,
    product(e_4,e_4,e_1),
    inference(resolution,[status(thm)],[c_40699,c_41494]) ).

tff(c_41382,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_4,e_1) ),
    inference(resolution,[status(thm)],[c_41304,c_60]) ).

tff(c_41549,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_41503,c_41382]) ).

tff(c_41577,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_41549]) ).

tff(c_41578,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_3)
    | product(e_4,e_4,e_4) ),
    inference(splitRight,[status(thm)],[c_40724]) ).

tff(c_41580,plain,
    product(e_4,e_4,e_4),
    inference(splitLeft,[status(thm)],[c_41578]) ).

tff(c_40735,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_4,W_11,e_4) ),
    inference(resolution,[status(thm)],[c_40699,c_58]) ).

tff(c_41605,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_41580,c_40735]) ).

tff(c_41629,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_41605]) ).

tff(c_41630,plain,
    ( product(e_3,e_4,e_3)
    | product(e_3,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_41578]) ).

tff(c_41644,plain,
    product(e_3,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_41630]) ).

tff(c_41843,plain,
    ! [Y_820] :
      ( product(e_4,Y_820,e_2)
      | ~ product(Y_820,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_41644,c_62]) ).

tff(c_41852,plain,
    product(e_4,e_4,e_2),
    inference(resolution,[status(thm)],[c_40699,c_41843]) ).

tff(c_41690,plain,
    ! [W_14] :
      ( equalish(W_14,e_3)
      | ~ product(W_14,e_4,e_2) ),
    inference(resolution,[status(thm)],[c_41644,c_60]) ).

tff(c_41986,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_41852,c_41690]) ).

tff(c_42010,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_41986]) ).

tff(c_42011,plain,
    product(e_3,e_4,e_3),
    inference(splitRight,[status(thm)],[c_41630]) ).

tff(c_40734,plain,
    ! [Y_18] :
      ( product(e_3,Y_18,e_4)
      | ~ product(Y_18,e_4,e_3) ),
    inference(resolution,[status(thm)],[c_40699,c_62]) ).

tff(c_42040,plain,
    product(e_3,e_3,e_4),
    inference(resolution,[status(thm)],[c_42011,c_40734]) ).

tff(c_40736,plain,
    ! [W_14] :
      ( equalish(W_14,e_4)
      | ~ product(W_14,e_3,e_4) ),
    inference(resolution,[status(thm)],[c_40699,c_60]) ).

tff(c_42069,plain,
    equalish(e_3,e_4),
    inference(resolution,[status(thm)],[c_42040,c_40736]) ).

tff(c_42094,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_42069]) ).

tff(c_42095,plain,
    ( product(e_1,e_4,e_3)
    | product(e_1,e_4,e_2) ),
    inference(splitRight,[status(thm)],[c_40629]) ).

tff(c_42146,plain,
    product(e_1,e_4,e_2),
    inference(splitLeft,[status(thm)],[c_42095]) ).

tff(c_275,plain,
    ! [W_11,X_66] :
      ( equalish(W_11,e_1)
      | ~ product(X_66,W_11,e_2)
      | ~ next(X_66,e_2)
      | product(X_66,e_1,e_1)
      | ~ group_element(X_66) ),
    inference(resolution,[status(thm)],[c_262,c_58]) ).

tff(c_42162,plain,
    ( equalish(e_4,e_1)
    | ~ next(e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_42146,c_275]) ).

tff(c_42195,plain,
    ( equalish(e_4,e_1)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_42162]) ).

tff(c_42197,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_37621,c_48,c_42195]) ).

tff(c_42198,plain,
    product(e_1,e_4,e_3),
    inference(splitRight,[status(thm)],[c_42095]) ).

tff(c_39593,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_1,W_11,e_3) ),
    inference(resolution,[status(thm)],[c_39555,c_58]) ).

tff(c_42253,plain,
    equalish(e_4,e_3),
    inference(resolution,[status(thm)],[c_42198,c_39593]) ).

tff(c_42290,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_52,c_42253]) ).

tff(c_42291,plain,
    ( product(e_3,e_3,e_3)
    | product(e_3,e_3,e_2) ),
    inference(splitRight,[status(thm)],[c_40065]) ).

tff(c_42299,plain,
    product(e_3,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_42291]) ).

tff(c_42429,plain,
    ! [Y_832] :
      ( product(e_3,Y_832,e_2)
      | ~ product(Y_832,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_42299,c_62]) ).

tff(c_42453,plain,
    product(e_3,e_1,e_2),
    inference(resolution,[status(thm)],[c_39555,c_42429]) ).

tff(c_42332,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_3,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_42299,c_58]) ).

tff(c_42477,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_42453,c_42332]) ).

tff(c_42510,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_42477]) ).

tff(c_42511,plain,
    product(e_3,e_3,e_3),
    inference(splitRight,[status(thm)],[c_42291]) ).

tff(c_39594,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_39555,c_60]) ).

tff(c_42515,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_42511,c_39594]) ).

tff(c_42535,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_42515]) ).

tff(c_42536,plain,
    ! [X_47] :
      ( product(e_1,e_3,e_2)
      | product(e_3,X_47,e_4)
      | ~ next(X_47,e_3)
      | product(X_47,e_1,e_2)
      | product(X_47,e_1,e_1)
      | ~ group_element(X_47) ),
    inference(splitRight,[status(thm)],[c_39553]) ).

tff(c_42581,plain,
    product(e_1,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_42536]) ).

tff(c_42593,plain,
    ( equalish(e_3,e_1)
    | ~ next(e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_42581,c_275]) ).

tff(c_42618,plain,
    ( equalish(e_3,e_1)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_42593]) ).

tff(c_42620,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_37621,c_42,c_42618]) ).

tff(c_42622,plain,
    ~ product(e_1,e_3,e_2),
    inference(splitRight,[status(thm)],[c_42536]) ).

tff(c_39554,plain,
    ~ product(e_1,e_3,e_1),
    inference(splitRight,[status(thm)],[c_350]) ).

tff(c_42537,plain,
    ~ product(e_1,e_3,e_3),
    inference(splitRight,[status(thm)],[c_39553]) ).

tff(c_42552,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5)
      | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_261,c_42537]) ).

tff(c_42575,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_42552]) ).

tff(c_42576,plain,
    ! [Y_5] :
      ( equalish(Y_5,e_3)
      | product(e_1,e_3,e_2)
      | product(e_1,Y_5,e_3)
      | product(e_1,Y_5,e_2)
      | product(e_1,Y_5,e_1)
      | ~ group_element(Y_5) ),
    inference(negUnitSimplification,[status(thm)],[c_39554,c_42575]) ).

tff(c_43283,plain,
    ! [Y_856] :
      ( equalish(Y_856,e_3)
      | product(e_1,Y_856,e_3)
      | product(e_1,Y_856,e_2)
      | product(e_1,Y_856,e_1)
      | ~ group_element(Y_856) ),
    inference(negUnitSimplification,[status(thm)],[c_42622,c_42576]) ).

tff(c_43325,plain,
    ( equalish(e_3,e_2)
    | ~ next(e_1,e_2)
    | equalish(e_1,e_3)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_43283,c_277]) ).

tff(c_43398,plain,
    ( equalish(e_3,e_2)
    | equalish(e_1,e_3)
    | product(e_1,e_1,e_2)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2,c_43325]) ).

tff(c_43399,plain,
    product(e_1,e_1,e_2),
    inference(negUnitSimplification,[status(thm)],[c_37621,c_32,c_44,c_43398]) ).

tff(c_43429,plain,
    ( product(e_2,e_1,e_4)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1)
    | ~ group_element(e_2)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_43399,c_113]) ).

tff(c_43476,plain,
    ( product(e_2,e_1,e_4)
    | product(e_1,e_2,e_3)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_24,c_43429]) ).

tff(c_43894,plain,
    product(e_1,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_43476]) ).

tff(c_44074,plain,
    ! [Y_871] :
      ( product(e_2,Y_871,e_1)
      | ~ product(Y_871,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_43894,c_62]) ).

tff(c_44084,plain,
    product(e_2,e_1,e_1),
    inference(resolution,[status(thm)],[c_43399,c_44074]) ).

tff(c_43494,plain,
    ! [Y_18] :
      ( product(e_1,Y_18,e_2)
      | ~ product(Y_18,e_1,e_1) ),
    inference(resolution,[status(thm)],[c_43399,c_62]) ).

tff(c_44124,plain,
    product(e_1,e_2,e_2),
    inference(resolution,[status(thm)],[c_44084,c_43494]) ).

tff(c_43945,plain,
    ! [W_8] :
      ( equalish(W_8,e_1)
      | ~ product(e_1,e_2,W_8) ),
    inference(resolution,[status(thm)],[c_43894,c_56]) ).

tff(c_44172,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_44124,c_43945]) ).

tff(c_44201,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_44172]) ).

tff(c_44202,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_2,e_3)
    | product(e_2,e_1,e_4) ),
    inference(splitRight,[status(thm)],[c_43476]) ).

tff(c_44204,plain,
    product(e_2,e_1,e_4),
    inference(splitLeft,[status(thm)],[c_44202]) ).

tff(c_44236,plain,
    ~ next(e_2,e_3),
    inference(resolution,[status(thm)],[c_44204,c_79]) ).

tff(c_44284,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_44236]) ).

tff(c_44285,plain,
    ( product(e_1,e_2,e_3)
    | product(e_1,e_2,e_2) ),
    inference(splitRight,[status(thm)],[c_44202]) ).

tff(c_44303,plain,
    product(e_1,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_44285]) ).

tff(c_43495,plain,
    ! [W_11] :
      ( equalish(W_11,e_1)
      | ~ product(e_1,W_11,e_2) ),
    inference(resolution,[status(thm)],[c_43399,c_58]) ).

tff(c_44306,plain,
    equalish(e_2,e_1),
    inference(resolution,[status(thm)],[c_44303,c_43495]) ).

tff(c_44332,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_36,c_44306]) ).

tff(c_44333,plain,
    product(e_1,e_2,e_3),
    inference(splitRight,[status(thm)],[c_44285]) ).

tff(c_44750,plain,
    ! [Y_883] :
      ( product(e_2,Y_883,e_3)
      | ~ product(Y_883,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_44333,c_62]) ).

tff(c_44760,plain,
    product(e_2,e_1,e_3),
    inference(resolution,[status(thm)],[c_43399,c_44750]) ).

tff(c_42546,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_198,c_42537]) ).

tff(c_42567,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2)
      | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26,c_42546]) ).

tff(c_42568,plain,
    ! [X_58] :
      ( equalish(e_1,X_58)
      | product(X_58,e_3,e_3)
      | product(X_58,e_3,e_2)
      | product(X_58,e_3,e_1)
      | ~ group_element(X_58)
      | product(e_1,e_3,e_2) ),
    inference(negUnitSimplification,[status(thm)],[c_39554,c_42567]) ).

tff(c_43069,plain,
    ! [X_849] :
      ( equalish(e_1,X_849)
      | product(X_849,e_3,e_3)
      | product(X_849,e_3,e_2)
      | product(X_849,e_3,e_1)
      | ~ group_element(X_849) ),
    inference(negUnitSimplification,[status(thm)],[c_42622,c_42568]) ).

tff(c_43121,plain,
    ! [W_11,X_849] :
      ( equalish(W_11,e_3)
      | ~ product(X_849,W_11,e_3)
      | equalish(e_1,X_849)
      | product(X_849,e_3,e_2)
      | product(X_849,e_3,e_1)
      | ~ group_element(X_849) ),
    inference(resolution,[status(thm)],[c_43069,c_58]) ).

tff(c_44771,plain,
    ( equalish(e_1,e_3)
    | equalish(e_1,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_44760,c_43121]) ).

tff(c_44814,plain,
    ( equalish(e_1,e_3)
    | equalish(e_1,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_44771]) ).

tff(c_44815,plain,
    ( product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_30,c_32,c_44814]) ).

tff(c_45307,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_44815]) ).

tff(c_45563,plain,
    ! [Y_901] :
      ( product(e_3,Y_901,e_1)
      | ~ product(Y_901,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_45307,c_62]) ).

tff(c_45590,plain,
    product(e_3,e_1,e_1),
    inference(resolution,[status(thm)],[c_44333,c_45563]) ).

tff(c_45621,plain,
    product(e_1,e_3,e_2),
    inference(resolution,[status(thm)],[c_45590,c_43494]) ).

tff(c_45664,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42622,c_45621]) ).

tff(c_45665,plain,
    product(e_2,e_3,e_2),
    inference(splitRight,[status(thm)],[c_44815]) ).

tff(c_45899,plain,
    ! [Y_908] :
      ( product(e_3,Y_908,e_2)
      | ~ product(Y_908,e_2,e_3) ),
    inference(resolution,[status(thm)],[c_45665,c_62]) ).

tff(c_45926,plain,
    product(e_3,e_1,e_2),
    inference(resolution,[status(thm)],[c_44333,c_45899]) ).

tff(c_43496,plain,
    ! [W_14] :
      ( equalish(W_14,e_1)
      | ~ product(W_14,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_43399,c_60]) ).

tff(c_45958,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_45926,c_43496]) ).

tff(c_46004,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_45958]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP129-2.004 : TPTP v8.1.2. Released v1.2.0.
% 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
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 22:16:23 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 14.63/6.32  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.84/6.38  
% 14.84/6.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.30/6.46  
% 15.30/6.46  Inference rules
% 15.30/6.46  ----------------------
% 15.30/6.46  #Ref     : 0
% 15.30/6.46  #Sup     : 8555
% 15.30/6.46  #Fact    : 20
% 15.30/6.46  #Define  : 0
% 15.30/6.46  #Split   : 92
% 15.30/6.46  #Chain   : 0
% 15.30/6.46  #Close   : 0
% 15.30/6.46  
% 15.30/6.46  Ordering : KBO
% 15.30/6.46  
% 15.30/6.46  Simplification rules
% 15.30/6.46  ----------------------
% 15.30/6.46  #Subsume      : 2658
% 15.30/6.46  #Demod        : 11941
% 15.30/6.46  #Tautology    : 2816
% 15.30/6.46  #SimpNegUnit  : 3482
% 15.30/6.46  #BackRed      : 0
% 15.30/6.46  
% 15.30/6.46  #Partial instantiations: 0
% 15.30/6.46  #Strategies tried      : 1
% 15.30/6.46  
% 15.30/6.46  Timing (in seconds)
% 15.30/6.46  ----------------------
% 15.30/6.46  Preprocessing        : 0.48
% 15.30/6.46  Parsing              : 0.27
% 15.30/6.47  CNF conversion       : 0.02
% 15.30/6.47  Main loop            : 4.81
% 15.30/6.47  Inferencing          : 1.06
% 15.30/6.47  Reduction            : 1.54
% 15.30/6.47  Demodulation         : 0.99
% 15.30/6.47  BG Simplification    : 0.07
% 15.30/6.47  Subsumption          : 1.90
% 15.30/6.47  Abstraction          : 0.12
% 15.30/6.47  MUC search           : 0.00
% 15.30/6.47  Cooper               : 0.00
% 15.30/6.47  Total                : 5.44
% 15.30/6.47  Index Insertion      : 0.00
% 15.30/6.47  Index Deletion       : 0.00
% 15.30/6.47  Index Matching       : 0.00
% 15.30/6.47  BG Taut test         : 0.00
%------------------------------------------------------------------------------