TSTP Solution File: GRP124-2.004 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP124-2.004 : 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/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 : n024.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 10:39:55 EDT 2023

% Result   : Unsatisfiable 7.43s 2.69s
% Output   : CNFRefutation 7.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   33
% Syntax   : Number of formulae    :  151 (  74 unt;   9 typ;   0 def)
%            Number of atoms       :  319 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  304 ( 127   ~; 177   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 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   :  101 (; 101   !;   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_72,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_58,axiom,
    ~ equalish(e_1,e_2),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ~ equalish(e_1,e_4),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_64,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(f_53,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_54,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

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

tff(f_94,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_43,axiom,
    greater(e_4,e_3),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [X,Y,X1] :
      ( ~ product(X,e_1,Y)
      | ~ next(X,X1)
      | ~ greater(Y,X1) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [X] : product(X,X,X),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_55,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ~ equalish(e_2,e_4),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ~ equalish(e_4,e_2),
    file(unknown,unknown) ).

tff(f_56,axiom,
    group_element(e_4),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ~ equalish(e_3,e_4),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ~ equalish(e_4,e_3),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_148,axiom,
    ! [Y1,X1,Z2,Y2,X2,Z1] :
      ( ~ product(X1,Y1,Z1)
      | ~ product(X2,Y2,Z1)
      | ~ product(Z2,X1,Y1)
      | ~ product(Z2,X2,Y2)
      | equalish(Y1,Y2) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(c_44,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_38,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_30,plain,
    ~ equalish(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_34,plain,
    ~ equalish(e_1,e_4),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_42,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_36,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_22,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_24,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_4,plain,
    next(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_141,plain,
    ! [X_80,Y_81] :
      ( product(X_80,Y_81,e_4)
      | product(X_80,Y_81,e_3)
      | product(X_80,Y_81,e_2)
      | product(X_80,Y_81,e_1)
      | ~ group_element(Y_81)
      | ~ group_element(X_80) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_18,plain,
    greater(e_4,e_3),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_68,plain,
    ! [Y_32,X1_33,X_34] :
      ( ~ greater(Y_32,X1_33)
      | ~ next(X_34,X1_33)
      | ~ product(X_34,e_1,Y_32) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_83,plain,
    ! [X_34] :
      ( ~ next(X_34,e_3)
      | ~ product(X_34,e_1,e_4) ),
    inference(resolution,[status(thm)],[c_18,c_68]) ).

tff(c_169,plain,
    ! [X_80] :
      ( ~ next(X_80,e_3)
      | product(X_80,e_1,e_3)
      | product(X_80,e_1,e_2)
      | product(X_80,e_1,e_1)
      | ~ group_element(e_1)
      | ~ group_element(X_80) ),
    inference(resolution,[status(thm)],[c_141,c_83]) ).

tff(c_195,plain,
    ! [X_80] :
      ( ~ next(X_80,e_3)
      | product(X_80,e_1,e_3)
      | product(X_80,e_1,e_2)
      | product(X_80,e_1,e_1)
      | ~ group_element(X_80) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_169]) ).

tff(c_62,plain,
    ! [X_18] : product(X_18,X_18,X_18),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_32,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_26,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

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_94]) ).

tff(c_40,plain,
    ~ equalish(e_2,e_4),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_50,plain,
    ~ equalish(e_4,e_2),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_28,plain,
    group_element(e_4),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_102,plain,
    ! [W_47,Z_48,X_49,Y_50] :
      ( equalish(W_47,Z_48)
      | ~ product(X_49,Z_48,Y_50)
      | ~ product(X_49,W_47,Y_50) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_105,plain,
    ! [W_47,X_18] :
      ( equalish(W_47,X_18)
      | ~ product(X_18,W_47,X_18) ),
    inference(resolution,[status(thm)],[c_62,c_102]) ).

tff(c_159,plain,
    ! [Y_81] :
      ( equalish(Y_81,e_4)
      | product(e_4,Y_81,e_3)
      | product(e_4,Y_81,e_2)
      | product(e_4,Y_81,e_1)
      | ~ group_element(Y_81)
      | ~ group_element(e_4) ),
    inference(resolution,[status(thm)],[c_141,c_105]) ).

tff(c_188,plain,
    ! [Y_81] :
      ( equalish(Y_81,e_4)
      | product(e_4,Y_81,e_3)
      | product(e_4,Y_81,e_2)
      | product(e_4,Y_81,e_1)
      | ~ group_element(Y_81) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_159]) ).

tff(c_46,plain,
    ~ equalish(e_3,e_4),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_52,plain,
    ~ equalish(e_4,e_3),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_1031,plain,
    ! [Y_121] :
      ( equalish(Y_121,e_4)
      | product(e_4,Y_121,e_3)
      | product(e_4,Y_121,e_2)
      | product(e_4,Y_121,e_1)
      | ~ group_element(Y_121) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_159]) ).

tff(c_89,plain,
    ! [W_37,Z_38,Y_39,X_40] :
      ( equalish(W_37,Z_38)
      | ~ product(Z_38,Y_39,X_40)
      | ~ product(W_37,Y_39,X_40) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_92,plain,
    ! [W_37,X_18] :
      ( equalish(W_37,X_18)
      | ~ product(W_37,X_18,X_18) ),
    inference(resolution,[status(thm)],[c_62,c_89]) ).

tff(c_1063,plain,
    ( equalish(e_4,e_3)
    | equalish(e_3,e_4)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_1031,c_92]) ).

tff(c_1099,plain,
    ( equalish(e_4,e_3)
    | equalish(e_3,e_4)
    | product(e_4,e_3,e_2)
    | product(e_4,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_1063]) ).

tff(c_1100,plain,
    ( product(e_4,e_3,e_2)
    | product(e_4,e_3,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_1099]) ).

tff(c_1106,plain,
    product(e_4,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_1100]) ).

tff(c_117,plain,
    ! [Y2_60,Z1_63,Z2_58,X1_59,Y1_62,X2_61] :
      ( equalish(Y1_62,Y2_60)
      | ~ product(Z2_58,X2_61,Y2_60)
      | ~ product(Z2_58,X1_59,Y1_62)
      | ~ product(X2_61,Y2_60,Z1_63)
      | ~ product(X1_59,Y1_62,Z1_63) ),
    inference(cnfTransformation,[status(thm)],[f_148]) ).

tff(c_120,plain,
    ! [Y1_62,X_18,X1_59,Z1_63] :
      ( equalish(Y1_62,X_18)
      | ~ product(X_18,X1_59,Y1_62)
      | ~ product(X_18,X_18,Z1_63)
      | ~ product(X1_59,Y1_62,Z1_63) ),
    inference(resolution,[status(thm)],[c_62,c_117]) ).

tff(c_1183,plain,
    ! [Z1_63] :
      ( equalish(e_1,e_4)
      | ~ product(e_4,e_4,Z1_63)
      | ~ product(e_3,e_1,Z1_63) ),
    inference(resolution,[status(thm)],[c_1106,c_120]) ).

tff(c_1296,plain,
    ! [Z1_130] :
      ( ~ product(e_4,e_4,Z1_130)
      | ~ product(e_3,e_1,Z1_130) ),
    inference(negUnitSimplification,[status(thm)],[c_34,c_1183]) ).

tff(c_1361,plain,
    ~ product(e_3,e_1,e_4),
    inference(resolution,[status(thm)],[c_62,c_1296]) ).

tff(c_1364,plain,
    ( 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_54,c_1361]) ).

tff(c_1367,plain,
    ( 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_1364]) ).

tff(c_2094,plain,
    product(e_3,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_1367]) ).

tff(c_165,plain,
    ! [X_80] :
      ( equalish(X_80,e_4)
      | product(X_80,e_4,e_3)
      | product(X_80,e_4,e_2)
      | product(X_80,e_4,e_1)
      | ~ group_element(e_4)
      | ~ group_element(X_80) ),
    inference(resolution,[status(thm)],[c_141,c_92]) ).

tff(c_1369,plain,
    ! [X_131] :
      ( equalish(X_131,e_4)
      | product(X_131,e_4,e_3)
      | product(X_131,e_4,e_2)
      | product(X_131,e_4,e_1)
      | ~ group_element(X_131) ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_165]) ).

tff(c_1397,plain,
    ( equalish(e_4,e_3)
    | equalish(e_3,e_4)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_1369,c_105]) ).

tff(c_1424,plain,
    ( equalish(e_4,e_3)
    | equalish(e_3,e_4)
    | product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_1397]) ).

tff(c_1425,plain,
    ( product(e_3,e_4,e_2)
    | product(e_3,e_4,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_46,c_52,c_1424]) ).

tff(c_1428,plain,
    product(e_3,e_4,e_1),
    inference(splitLeft,[status(thm)],[c_1425]) ).

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_110]) ).

tff(c_1483,plain,
    ! [W_11] :
      ( equalish(W_11,e_4)
      | ~ product(e_3,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_1428,c_58]) ).

tff(c_2097,plain,
    equalish(e_1,e_4),
    inference(resolution,[status(thm)],[c_2094,c_1483]) ).

tff(c_2135,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34,c_2097]) ).

tff(c_2136,plain,
    ( product(e_3,e_1,e_2)
    | product(e_3,e_1,e_3) ),
    inference(splitRight,[status(thm)],[c_1367]) ).

tff(c_2144,plain,
    product(e_3,e_1,e_3),
    inference(splitLeft,[status(thm)],[c_2136]) ).

tff(c_2166,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_2144,c_105]) ).

tff(c_2203,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_2166]) ).

tff(c_2204,plain,
    product(e_3,e_1,e_2),
    inference(splitRight,[status(thm)],[c_2136]) ).

tff(c_1446,plain,
    ! [Z1_63] :
      ( equalish(e_1,e_3)
      | ~ product(e_3,e_3,Z1_63)
      | ~ product(e_4,e_1,Z1_63) ),
    inference(resolution,[status(thm)],[c_1428,c_120]) ).

tff(c_1559,plain,
    ! [Z1_135] :
      ( ~ product(e_3,e_3,Z1_135)
      | ~ product(e_4,e_1,Z1_135) ),
    inference(negUnitSimplification,[status(thm)],[c_32,c_1446]) ).

tff(c_1563,plain,
    ( ~ product(e_3,e_3,e_3)
    | equalish(e_1,e_4)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_188,c_1559]) ).

tff(c_1582,plain,
    ( equalish(e_1,e_4)
    | product(e_4,e_1,e_2)
    | product(e_4,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_62,c_1563]) ).

tff(c_1583,plain,
    ( product(e_4,e_1,e_2)
    | product(e_4,e_1,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_34,c_1582]) ).

tff(c_1596,plain,
    product(e_4,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_1583]) ).

tff(c_1220,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(e_4,W_11,e_1) ),
    inference(resolution,[status(thm)],[c_1106,c_58]) ).

tff(c_1669,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_1596,c_1220]) ).

tff(c_1708,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_1669]) ).

tff(c_1709,plain,
    product(e_4,e_1,e_2),
    inference(splitRight,[status(thm)],[c_1583]) ).

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_118]) ).

tff(c_1773,plain,
    ! [W_14] :
      ( equalish(W_14,e_4)
      | ~ product(W_14,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_1709,c_60]) ).

tff(c_2303,plain,
    equalish(e_3,e_4),
    inference(resolution,[status(thm)],[c_2204,c_1773]) ).

tff(c_2333,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_46,c_2303]) ).

tff(c_2334,plain,
    product(e_3,e_4,e_2),
    inference(splitRight,[status(thm)],[c_1425]) ).

tff(c_2347,plain,
    ! [Z1_63] :
      ( equalish(e_2,e_3)
      | ~ product(e_3,e_3,Z1_63)
      | ~ product(e_4,e_2,Z1_63) ),
    inference(resolution,[status(thm)],[c_2334,c_120]) ).

tff(c_2452,plain,
    ! [Z1_146] :
      ( ~ product(e_3,e_3,Z1_146)
      | ~ product(e_4,e_2,Z1_146) ),
    inference(negUnitSimplification,[status(thm)],[c_38,c_2347]) ).

tff(c_2456,plain,
    ( ~ product(e_3,e_3,e_3)
    | equalish(e_2,e_4)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_188,c_2452]) ).

tff(c_2463,plain,
    ( equalish(e_2,e_4)
    | product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_62,c_2456]) ).

tff(c_2464,plain,
    ( product(e_4,e_2,e_2)
    | product(e_4,e_2,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_2463]) ).

tff(c_2535,plain,
    product(e_4,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_2464]) ).

tff(c_2541,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_2535,c_1220]) ).

tff(c_2572,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38,c_2541]) ).

tff(c_2573,plain,
    product(e_4,e_2,e_2),
    inference(splitRight,[status(thm)],[c_2464]) ).

tff(c_2598,plain,
    equalish(e_4,e_2),
    inference(resolution,[status(thm)],[c_2573,c_92]) ).

tff(c_2626,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_50,c_2598]) ).

tff(c_2627,plain,
    product(e_4,e_3,e_2),
    inference(splitRight,[status(thm)],[c_1100]) ).

tff(c_2639,plain,
    ! [Z1_63] :
      ( equalish(e_2,e_4)
      | ~ product(e_4,e_4,Z1_63)
      | ~ product(e_3,e_2,Z1_63) ),
    inference(resolution,[status(thm)],[c_2627,c_120]) ).

tff(c_2805,plain,
    ! [Z1_156] :
      ( ~ product(e_4,e_4,Z1_156)
      | ~ product(e_3,e_2,Z1_156) ),
    inference(negUnitSimplification,[status(thm)],[c_40,c_2639]) ).

tff(c_2870,plain,
    ~ product(e_3,e_2,e_4),
    inference(resolution,[status(thm)],[c_62,c_2805]) ).

tff(c_2873,plain,
    ( 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_54,c_2870]) ).

tff(c_2876,plain,
    ( 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_2873]) ).

tff(c_2975,plain,
    product(e_3,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_2876]) ).

tff(c_2993,plain,
    ! [Z1_63] :
      ( equalish(e_1,e_3)
      | ~ product(e_3,e_3,Z1_63)
      | ~ product(e_2,e_1,Z1_63) ),
    inference(resolution,[status(thm)],[c_2975,c_120]) ).

tff(c_3098,plain,
    ! [Z1_161] :
      ( ~ product(e_3,e_3,Z1_161)
      | ~ product(e_2,e_1,Z1_161) ),
    inference(negUnitSimplification,[status(thm)],[c_32,c_2993]) ).

tff(c_3158,plain,
    ~ product(e_2,e_1,e_3),
    inference(resolution,[status(thm)],[c_62,c_3098]) ).

tff(c_3161,plain,
    ( ~ 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_195,c_3158]) ).

tff(c_3164,plain,
    ( 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_3161]) ).

tff(c_3165,plain,
    product(e_2,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_3164]) ).

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_102]) ).

tff(c_608,plain,
    ! [W_105,X_106,Y_107] :
      ( equalish(W_105,e_4)
      | ~ product(X_106,Y_107,W_105)
      | product(X_106,Y_107,e_3)
      | product(X_106,Y_107,e_2)
      | product(X_106,Y_107,e_1)
      | ~ group_element(Y_107)
      | ~ group_element(X_106) ),
    inference(resolution,[status(thm)],[c_141,c_56]) ).

tff(c_634,plain,
    ! [X_108] :
      ( equalish(X_108,e_4)
      | product(X_108,X_108,e_3)
      | product(X_108,X_108,e_2)
      | product(X_108,X_108,e_1)
      | ~ group_element(X_108) ),
    inference(resolution,[status(thm)],[c_62,c_608]) ).

tff(c_113,plain,
    ! [W_54,Z_55,X_56,Y_57] :
      ( equalish(W_54,Z_55)
      | ~ product(X_56,Y_57,Z_55)
      | ~ product(X_56,Y_57,W_54) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_116,plain,
    ! [W_54,X_18] :
      ( equalish(W_54,X_18)
      | ~ product(X_18,X_18,W_54) ),
    inference(resolution,[status(thm)],[c_62,c_113]) ).

tff(c_705,plain,
    ! [X_109] :
      ( equalish(e_3,X_109)
      | equalish(X_109,e_4)
      | product(X_109,X_109,e_2)
      | product(X_109,X_109,e_1)
      | ~ group_element(X_109) ),
    inference(resolution,[status(thm)],[c_634,c_116]) ).

tff(c_768,plain,
    ! [X_110] :
      ( equalish(e_2,X_110)
      | equalish(e_3,X_110)
      | equalish(X_110,e_4)
      | product(X_110,X_110,e_1)
      | ~ group_element(X_110) ),
    inference(resolution,[status(thm)],[c_705,c_116]) ).

tff(c_833,plain,
    ! [W_14,X_110] :
      ( equalish(W_14,X_110)
      | ~ product(W_14,X_110,e_1)
      | equalish(e_2,X_110)
      | equalish(e_3,X_110)
      | equalish(X_110,e_4)
      | ~ group_element(X_110) ),
    inference(resolution,[status(thm)],[c_768,c_60]) ).

tff(c_3241,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_1)
    | equalish(e_1,e_4)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_3165,c_833]) ).

tff(c_3277,plain,
    ( equalish(e_2,e_1)
    | equalish(e_3,e_1)
    | equalish(e_1,e_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_3241]) ).

tff(c_3279,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_34,c_42,c_36,c_3277]) ).

tff(c_3280,plain,
    product(e_2,e_1,e_2),
    inference(splitRight,[status(thm)],[c_3164]) ).

tff(c_3309,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_3280,c_105]) ).

tff(c_3343,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30,c_3309]) ).

tff(c_3344,plain,
    ( product(e_3,e_2,e_2)
    | product(e_3,e_2,e_3) ),
    inference(splitRight,[status(thm)],[c_2876]) ).

tff(c_3431,plain,
    product(e_3,e_2,e_3),
    inference(splitLeft,[status(thm)],[c_3344]) ).

tff(c_3450,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_3431,c_105]) ).

tff(c_3477,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_38,c_3450]) ).

tff(c_3478,plain,
    product(e_3,e_2,e_2),
    inference(splitRight,[status(thm)],[c_3344]) ).

tff(c_3500,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_3478,c_92]) ).

tff(c_3527,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_44,c_3500]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GRP124-2.004 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.14  % 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
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 22:19:00 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.43/2.69  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.43/2.71  
% 7.43/2.71  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.43/2.76  
% 7.43/2.76  Inference rules
% 7.43/2.76  ----------------------
% 7.43/2.76  #Ref     : 0
% 7.43/2.76  #Sup     : 687
% 7.43/2.76  #Fact    : 0
% 7.43/2.76  #Define  : 0
% 7.43/2.76  #Split   : 17
% 7.43/2.76  #Chain   : 0
% 7.43/2.76  #Close   : 0
% 7.43/2.76  
% 7.43/2.76  Ordering : KBO
% 7.43/2.76  
% 7.43/2.76  Simplification rules
% 7.43/2.76  ----------------------
% 7.43/2.76  #Subsume      : 87
% 7.43/2.76  #Demod        : 494
% 7.43/2.76  #Tautology    : 188
% 7.43/2.76  #SimpNegUnit  : 269
% 7.43/2.76  #BackRed      : 0
% 7.43/2.76  
% 7.43/2.76  #Partial instantiations: 0
% 7.43/2.76  #Strategies tried      : 1
% 7.43/2.76  
% 7.43/2.76  Timing (in seconds)
% 7.43/2.76  ----------------------
% 7.43/2.76  Preprocessing        : 0.47
% 7.43/2.76  Parsing              : 0.26
% 7.43/2.76  CNF conversion       : 0.03
% 7.43/2.76  Main loop            : 1.19
% 7.43/2.76  Inferencing          : 0.40
% 7.43/2.76  Reduction            : 0.33
% 7.43/2.76  Demodulation         : 0.21
% 7.43/2.76  BG Simplification    : 0.04
% 7.43/2.76  Subsumption          : 0.34
% 7.43/2.76  Abstraction          : 0.05
% 7.43/2.76  MUC search           : 0.00
% 7.43/2.76  Cooper               : 0.00
% 7.43/2.76  Total                : 1.74
% 7.72/2.76  Index Insertion      : 0.00
% 7.72/2.76  Index Deletion       : 0.00
% 7.72/2.76  Index Matching       : 0.00
% 7.72/2.76  BG Taut test         : 0.00
%------------------------------------------------------------------------------