TSTP Solution File: GRP134-1.003 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP134-1.003 : 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 : n027.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 10:40:15 EDT 2023

% Result   : Unsatisfiable 10.42s 3.47s
% Output   : CNFRefutation 10.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  175 (  82 unt;   6 typ;   0 def)
%            Number of atoms       :  368 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  313 ( 114   ~; 199   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   96 (;  96   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(f_40,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_28,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_30,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_34,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_29,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [X,Y] :
      ( ~ group_element(X)
      | ~ group_element(Y)
      | product(X,Y,e_1)
      | product(X,Y,e_2)
      | product(X,Y,e_3) ),
    file(unknown,unknown) ).

tff(f_86,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product(X,Y,Z1)
      | ~ product(Y,X,Z2)
      | product(Z1,Z2,Y) ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ~ equalish(e_1,e_2),
    file(unknown,unknown) ).

tff(c_16,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_18,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_2,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_6,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_14,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_10,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_4,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_20,plain,
    ! [X_1,Y_2] :
      ( product(X_1,Y_2,e_3)
      | product(X_1,Y_2,e_2)
      | product(X_1,Y_2,e_1)
      | ~ group_element(Y_2)
      | ~ group_element(X_1) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_33,plain,
    ! [X_35,Y_36] :
      ( product(X_35,Y_36,e_3)
      | product(X_35,Y_36,e_2)
      | product(X_35,Y_36,e_1)
      | ~ group_element(Y_36)
      | ~ group_element(X_35) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_28,plain,
    ! [Z1_17,Z2_18,Y_16,X_15] :
      ( product(Z1_17,Z2_18,Y_16)
      | ~ product(Y_16,X_15,Z2_18)
      | ~ product(X_15,Y_16,Z1_17) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_59,plain,
    ! [Z1_46,X_47,Y_48] :
      ( product(Z1_46,e_3,X_47)
      | ~ product(Y_48,X_47,Z1_46)
      | 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_33,c_28]) ).

tff(c_62,plain,
    ! [Y_2,X_1] :
      ( product(e_3,e_3,Y_2)
      | product(Y_2,X_1,e_2)
      | product(Y_2,X_1,e_1)
      | product(X_1,Y_2,e_2)
      | product(X_1,Y_2,e_1)
      | ~ group_element(Y_2)
      | ~ group_element(X_1) ),
    inference(resolution,[status(thm)],[c_20,c_59]) ).

tff(c_150,plain,
    ! [Y_51] :
      ( product(e_3,e_3,Y_51)
      | product(Y_51,Y_51,e_1)
      | ~ group_element(Y_51)
      | product(Y_51,Y_51,e_2) ),
    inference(factorization,[status(thm),theory(equality)],[c_62]) ).

tff(c_24,plain,
    ! [W_8,Z_10,X_7,Y_9] :
      ( equalish(W_8,Z_10)
      | ~ product(X_7,Z_10,Y_9)
      | ~ product(X_7,W_8,Y_9) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_45,plain,
    ! [W_8,Y_36,X_35] :
      ( equalish(W_8,Y_36)
      | ~ product(X_35,W_8,e_3)
      | product(X_35,Y_36,e_2)
      | product(X_35,Y_36,e_1)
      | ~ group_element(Y_36)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_33,c_24]) ).

tff(c_157,plain,
    ! [Y_36] :
      ( equalish(e_3,Y_36)
      | product(e_3,Y_36,e_2)
      | product(e_3,Y_36,e_1)
      | ~ group_element(Y_36)
      | product(e_3,e_3,e_1)
      | ~ group_element(e_3)
      | product(e_3,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_150,c_45]) ).

tff(c_189,plain,
    ! [Y_36] :
      ( equalish(e_3,Y_36)
      | product(e_3,Y_36,e_2)
      | product(e_3,Y_36,e_1)
      | ~ group_element(Y_36)
      | product(e_3,e_3,e_1)
      | product(e_3,e_3,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_157]) ).

tff(c_3104,plain,
    product(e_3,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_189]) ).

tff(c_3625,plain,
    ! [Z1_148] :
      ( product(Z1_148,e_2,e_3)
      | ~ product(e_3,e_3,Z1_148) ),
    inference(resolution,[status(thm)],[c_3104,c_28]) ).

tff(c_3663,plain,
    product(e_2,e_2,e_3),
    inference(resolution,[status(thm)],[c_3104,c_3625]) ).

tff(c_26,plain,
    ! [W_11,Z_14,Y_12,X_13] :
      ( equalish(W_11,Z_14)
      | ~ product(Z_14,Y_12,X_13)
      | ~ product(W_11,Y_12,X_13) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_43,plain,
    ! [W_11,X_35,Y_36] :
      ( equalish(W_11,X_35)
      | ~ product(W_11,Y_36,e_3)
      | product(X_35,Y_36,e_2)
      | product(X_35,Y_36,e_1)
      | ~ group_element(Y_36)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_33,c_26]) ).

tff(c_3772,plain,
    ! [X_35] :
      ( equalish(e_2,X_35)
      | product(X_35,e_2,e_2)
      | product(X_35,e_2,e_1)
      | ~ group_element(e_2)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_3663,c_43]) ).

tff(c_5466,plain,
    ! [X_167] :
      ( equalish(e_2,X_167)
      | product(X_167,e_2,e_2)
      | product(X_167,e_2,e_1)
      | ~ group_element(X_167) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_3772]) ).

tff(c_3328,plain,
    ! [W_8] :
      ( equalish(W_8,e_3)
      | ~ product(e_3,W_8,e_2) ),
    inference(resolution,[status(thm)],[c_3104,c_24]) ).

tff(c_5481,plain,
    ( equalish(e_2,e_3)
    | product(e_3,e_2,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_5466,c_3328]) ).

tff(c_5544,plain,
    ( equalish(e_2,e_3)
    | product(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_5481]) ).

tff(c_5545,plain,
    product(e_3,e_2,e_1),
    inference(negUnitSimplification,[status(thm)],[c_14,c_5544]) ).

tff(c_42,plain,
    ! [Z1_17,X_35,Y_36] :
      ( product(Z1_17,e_3,X_35)
      | ~ product(Y_36,X_35,Z1_17)
      | product(X_35,Y_36,e_2)
      | product(X_35,Y_36,e_1)
      | ~ group_element(Y_36)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_33,c_28]) ).

tff(c_5621,plain,
    ( product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_3)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_5545,c_42]) ).

tff(c_5670,plain,
    ( product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_5621]) ).

tff(c_6508,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_5670]) ).

tff(c_5675,plain,
    ! [Z1_17] :
      ( product(Z1_17,e_1,e_3)
      | ~ product(e_2,e_3,Z1_17) ),
    inference(resolution,[status(thm)],[c_5545,c_28]) ).

tff(c_6542,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_6508,c_5675]) ).

tff(c_12,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_75,plain,
    ! [Y_2] :
      ( product(e_3,e_3,Y_2)
      | product(Y_2,Y_2,e_1)
      | ~ group_element(Y_2)
      | product(Y_2,Y_2,e_2) ),
    inference(factorization,[status(thm),theory(equality)],[c_62]) ).

tff(c_1666,plain,
    ! [Z1_100,Y_101] :
      ( product(Z1_100,e_2,Y_101)
      | ~ product(Y_101,Y_101,Z1_100)
      | product(e_3,e_3,Y_101)
      | product(Y_101,Y_101,e_1)
      | ~ group_element(Y_101) ),
    inference(resolution,[status(thm)],[c_150,c_28]) ).

tff(c_1722,plain,
    ! [Y_102] :
      ( product(e_2,e_2,Y_102)
      | product(e_3,e_3,Y_102)
      | product(Y_102,Y_102,e_1)
      | ~ group_element(Y_102) ),
    inference(resolution,[status(thm)],[c_75,c_1666]) ).

tff(c_22,plain,
    ! [W_5,Z_6,X_3,Y_4] :
      ( equalish(W_5,Z_6)
      | ~ product(X_3,Y_4,Z_6)
      | ~ product(X_3,Y_4,W_5) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_1811,plain,
    ! [W_5,Y_102] :
      ( equalish(W_5,Y_102)
      | ~ product(e_3,e_3,W_5)
      | product(e_2,e_2,Y_102)
      | product(Y_102,Y_102,e_1)
      | ~ group_element(Y_102) ),
    inference(resolution,[status(thm)],[c_1722,c_22]) ).

tff(c_3294,plain,
    ! [Y_102] :
      ( equalish(e_2,Y_102)
      | product(e_2,e_2,Y_102)
      | product(Y_102,Y_102,e_1)
      | ~ group_element(Y_102) ),
    inference(resolution,[status(thm)],[c_3104,c_1811]) ).

tff(c_5679,plain,
    ! [W_168] :
      ( equalish(W_168,e_3)
      | ~ product(W_168,e_2,e_1) ),
    inference(resolution,[status(thm)],[c_5545,c_26]) ).

tff(c_5690,plain,
    ( equalish(e_2,e_3)
    | equalish(e_2,e_1)
    | product(e_1,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_3294,c_5679]) ).

tff(c_5721,plain,
    ( equalish(e_2,e_3)
    | equalish(e_2,e_1)
    | product(e_1,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_5690]) ).

tff(c_5722,plain,
    product(e_1,e_1,e_1),
    inference(negUnitSimplification,[status(thm)],[c_12,c_14,c_5721]) ).

tff(c_5953,plain,
    ! [W_5] :
      ( equalish(W_5,e_1)
      | ~ product(e_1,e_1,W_5) ),
    inference(resolution,[status(thm)],[c_5722,c_22]) ).

tff(c_6594,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_6542,c_5953]) ).

tff(c_6627,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16,c_6594]) ).

tff(c_6628,plain,
    ( product(e_2,e_3,e_2)
    | product(e_1,e_3,e_2) ),
    inference(splitRight,[status(thm)],[c_5670]) ).

tff(c_6783,plain,
    product(e_1,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_6628]) ).

tff(c_3326,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(W_11,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_3104,c_26]) ).

tff(c_6796,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_6783,c_3326]) ).

tff(c_6846,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_6796]) ).

tff(c_6847,plain,
    product(e_2,e_3,e_2),
    inference(splitRight,[status(thm)],[c_6628]) ).

tff(c_6972,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_6847,c_3326]) ).

tff(c_7025,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_6972]) ).

tff(c_7026,plain,
    ! [Y_36] :
      ( product(e_3,e_3,e_1)
      | equalish(e_3,Y_36)
      | product(e_3,Y_36,e_2)
      | product(e_3,Y_36,e_1)
      | ~ group_element(Y_36) ),
    inference(splitRight,[status(thm)],[c_189]) ).

tff(c_14085,plain,
    product(e_3,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_7026]) ).

tff(c_14537,plain,
    ! [Z1_287] :
      ( product(Z1_287,e_1,e_3)
      | ~ product(e_3,e_3,Z1_287) ),
    inference(resolution,[status(thm)],[c_14085,c_28]) ).

tff(c_14575,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_14085,c_14537]) ).

tff(c_8,plain,
    ~ equalish(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_7496,plain,
    product(e_3,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_7026]) ).

tff(c_7934,plain,
    ! [Z1_202] :
      ( product(Z1_202,e_1,e_3)
      | ~ product(e_3,e_3,Z1_202) ),
    inference(resolution,[status(thm)],[c_7496,c_28]) ).

tff(c_7972,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_7496,c_7934]) ).

tff(c_8012,plain,
    ! [X_35] :
      ( equalish(e_1,X_35)
      | product(X_35,e_1,e_2)
      | product(X_35,e_1,e_1)
      | ~ group_element(e_1)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_7972,c_43]) ).

tff(c_9835,plain,
    ! [X_216] :
      ( equalish(e_1,X_216)
      | product(X_216,e_1,e_2)
      | product(X_216,e_1,e_1)
      | ~ group_element(X_216) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_8012]) ).

tff(c_7027,plain,
    ~ product(e_3,e_3,e_2),
    inference(splitRight,[status(thm)],[c_189]) ).

tff(c_7056,plain,
    ( product(e_2,e_2,e_1)
    | ~ group_element(e_2)
    | product(e_2,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_75,c_7027]) ).

tff(c_7089,plain,
    ( product(e_2,e_2,e_1)
    | product(e_2,e_2,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_7056]) ).

tff(c_7093,plain,
    product(e_2,e_2,e_2),
    inference(splitLeft,[status(thm)],[c_7089]) ).

tff(c_7175,plain,
    ! [W_8] :
      ( equalish(W_8,e_2)
      | ~ product(e_2,W_8,e_2) ),
    inference(resolution,[status(thm)],[c_7093,c_24]) ).

tff(c_9848,plain,
    ( equalish(e_1,e_2)
    | product(e_2,e_1,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_9835,c_7175]) ).

tff(c_9910,plain,
    ( equalish(e_1,e_2)
    | product(e_2,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_9848]) ).

tff(c_9911,plain,
    product(e_2,e_1,e_1),
    inference(negUnitSimplification,[status(thm)],[c_8,c_9910]) ).

tff(c_9975,plain,
    ( product(e_1,e_3,e_1)
    | 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_9911,c_42]) ).

tff(c_10004,plain,
    ( product(e_1,e_3,e_1)
    | product(e_1,e_2,e_2)
    | product(e_1,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4,c_9975]) ).

tff(c_10467,plain,
    product(e_1,e_2,e_1),
    inference(splitLeft,[status(thm)],[c_10004]) ).

tff(c_10009,plain,
    ! [Z1_17] :
      ( product(Z1_17,e_1,e_2)
      | ~ product(e_1,e_2,Z1_17) ),
    inference(resolution,[status(thm)],[c_9911,c_28]) ).

tff(c_10490,plain,
    product(e_1,e_1,e_2),
    inference(resolution,[status(thm)],[c_10467,c_10009]) ).

tff(c_8053,plain,
    ! [W_5] :
      ( equalish(W_5,e_3)
      | ~ product(e_1,e_1,W_5) ),
    inference(resolution,[status(thm)],[c_7972,c_22]) ).

tff(c_10526,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_10490,c_8053]) ).

tff(c_10569,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_10526]) ).

tff(c_10570,plain,
    ( product(e_1,e_2,e_2)
    | product(e_1,e_3,e_1) ),
    inference(splitRight,[status(thm)],[c_10004]) ).

tff(c_10574,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_10570]) ).

tff(c_7612,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(W_11,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_7496,c_26]) ).

tff(c_10683,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_10574,c_7612]) ).

tff(c_10719,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_10683]) ).

tff(c_10720,plain,
    product(e_1,e_2,e_2),
    inference(splitRight,[status(thm)],[c_10570]) ).

tff(c_7173,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(W_11,e_2,e_2) ),
    inference(resolution,[status(thm)],[c_7093,c_26]) ).

tff(c_10732,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_10720,c_7173]) ).

tff(c_10768,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_10732]) ).

tff(c_10769,plain,
    ! [Y_36] :
      ( equalish(e_3,Y_36)
      | product(e_3,Y_36,e_2)
      | product(e_3,Y_36,e_1)
      | ~ group_element(Y_36) ),
    inference(splitRight,[status(thm)],[c_7026]) ).

tff(c_11336,plain,
    ! [Y_239] :
      ( equalish(e_3,Y_239)
      | product(e_3,Y_239,e_2)
      | product(e_3,Y_239,e_1)
      | ~ group_element(Y_239) ),
    inference(splitRight,[status(thm)],[c_7026]) ).

tff(c_11347,plain,
    ( equalish(e_3,e_2)
    | product(e_3,e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_11336,c_7173]) ).

tff(c_11436,plain,
    ( equalish(e_3,e_2)
    | product(e_3,e_2,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_11347]) ).

tff(c_11437,plain,
    product(e_3,e_2,e_1),
    inference(negUnitSimplification,[status(thm)],[c_18,c_11436]) ).

tff(c_11548,plain,
    ( product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_3)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_11437,c_42]) ).

tff(c_11589,plain,
    ( product(e_1,e_3,e_2)
    | product(e_2,e_3,e_2)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_11548]) ).

tff(c_12456,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_11589]) ).

tff(c_11594,plain,
    ! [Z1_17] :
      ( product(Z1_17,e_1,e_3)
      | ~ product(e_2,e_3,Z1_17) ),
    inference(resolution,[status(thm)],[c_11437,c_28]) ).

tff(c_12493,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_12456,c_11594]) ).

tff(c_10770,plain,
    ~ product(e_3,e_3,e_1),
    inference(splitRight,[status(thm)],[c_7026]) ).

tff(c_10886,plain,
    ( product(e_1,e_1,e_1)
    | ~ group_element(e_1)
    | product(e_1,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_75,c_10770]) ).

tff(c_10904,plain,
    ( product(e_1,e_1,e_1)
    | product(e_1,e_1,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10886]) ).

tff(c_10908,plain,
    product(e_1,e_1,e_2),
    inference(splitLeft,[status(thm)],[c_10904]) ).

tff(c_1821,plain,
    ! [W_5,Y_102] :
      ( equalish(W_5,e_1)
      | ~ product(Y_102,Y_102,W_5)
      | product(e_2,e_2,Y_102)
      | product(e_3,e_3,Y_102)
      | ~ group_element(Y_102) ),
    inference(resolution,[status(thm)],[c_1722,c_22]) ).

tff(c_10918,plain,
    ( equalish(e_2,e_1)
    | product(e_2,e_2,e_1)
    | product(e_3,e_3,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_10908,c_1821]) ).

tff(c_10958,plain,
    ( equalish(e_2,e_1)
    | product(e_2,e_2,e_1)
    | product(e_3,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_10918]) ).

tff(c_10959,plain,
    product(e_2,e_2,e_1),
    inference(negUnitSimplification,[status(thm)],[c_10770,c_12,c_10958]) ).

tff(c_7174,plain,
    ! [W_5] :
      ( equalish(W_5,e_2)
      | ~ product(e_2,e_2,W_5) ),
    inference(resolution,[status(thm)],[c_7093,c_22]) ).

tff(c_10995,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_10959,c_7174]) ).

tff(c_11026,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_10995]) ).

tff(c_11027,plain,
    product(e_1,e_1,e_1),
    inference(splitRight,[status(thm)],[c_10904]) ).

tff(c_11092,plain,
    ! [W_5] :
      ( equalish(W_5,e_1)
      | ~ product(e_1,e_1,W_5) ),
    inference(resolution,[status(thm)],[c_11027,c_22]) ).

tff(c_12617,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_12493,c_11092]) ).

tff(c_12656,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16,c_12617]) ).

tff(c_12657,plain,
    ( product(e_2,e_3,e_2)
    | product(e_1,e_3,e_2) ),
    inference(splitRight,[status(thm)],[c_11589]) ).

tff(c_12662,plain,
    product(e_1,e_3,e_2),
    inference(splitLeft,[status(thm)],[c_12657]) ).

tff(c_13070,plain,
    ! [Z1_263] :
      ( product(Z1_263,e_2,e_1)
      | ~ product(e_3,e_1,Z1_263) ),
    inference(resolution,[status(thm)],[c_12662,c_28]) ).

tff(c_13073,plain,
    ( product(e_2,e_2,e_1)
    | equalish(e_3,e_1)
    | product(e_3,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_10769,c_13070]) ).

tff(c_13097,plain,
    ( product(e_2,e_2,e_1)
    | equalish(e_3,e_1)
    | product(e_3,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_13073]) ).

tff(c_13098,plain,
    ( product(e_2,e_2,e_1)
    | product(e_3,e_1,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_16,c_13097]) ).

tff(c_13114,plain,
    product(e_3,e_1,e_1),
    inference(splitLeft,[status(thm)],[c_13098]) ).

tff(c_11597,plain,
    ! [W_8] :
      ( equalish(W_8,e_2)
      | ~ product(e_3,W_8,e_1) ),
    inference(resolution,[status(thm)],[c_11437,c_24]) ).

tff(c_13121,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_13114,c_11597]) ).

tff(c_13162,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_13121]) ).

tff(c_13163,plain,
    product(e_2,e_2,e_1),
    inference(splitRight,[status(thm)],[c_13098]) ).

tff(c_11595,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(W_11,e_2,e_1) ),
    inference(resolution,[status(thm)],[c_11437,c_26]) ).

tff(c_13171,plain,
    equalish(e_2,e_3),
    inference(resolution,[status(thm)],[c_13163,c_11595]) ).

tff(c_13212,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_13171]) ).

tff(c_13213,plain,
    product(e_2,e_3,e_2),
    inference(splitRight,[status(thm)],[c_12657]) ).

tff(c_13227,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_13213,c_7175]) ).

tff(c_13277,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_13227]) ).

tff(c_13278,plain,
    product(e_2,e_2,e_1),
    inference(splitRight,[status(thm)],[c_7089]) ).

tff(c_13574,plain,
    ! [Z1_270] :
      ( product(Z1_270,e_1,e_2)
      | ~ product(e_2,e_2,Z1_270) ),
    inference(resolution,[status(thm)],[c_13278,c_28]) ).

tff(c_13600,plain,
    product(e_1,e_1,e_2),
    inference(resolution,[status(thm)],[c_13278,c_13574]) ).

tff(c_13689,plain,
    ! [W_5] :
      ( equalish(W_5,e_2)
      | ~ product(e_1,e_1,W_5) ),
    inference(resolution,[status(thm)],[c_13600,c_22]) ).

tff(c_14604,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_14575,c_13689]) ).

tff(c_14639,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_14604]) ).

tff(c_14787,plain,
    ! [Y_291] :
      ( equalish(e_3,Y_291)
      | product(e_3,Y_291,e_2)
      | product(e_3,Y_291,e_1)
      | ~ group_element(Y_291) ),
    inference(splitRight,[status(thm)],[c_7026]) ).

tff(c_13688,plain,
    ! [W_11] :
      ( equalish(W_11,e_1)
      | ~ product(W_11,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_13600,c_26]) ).

tff(c_14798,plain,
    ( equalish(e_3,e_1)
    | product(e_3,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_14787,c_13688]) ).

tff(c_14889,plain,
    ( equalish(e_3,e_1)
    | product(e_3,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_14798]) ).

tff(c_14890,plain,
    product(e_3,e_1,e_1),
    inference(negUnitSimplification,[status(thm)],[c_16,c_14889]) ).

tff(c_15008,plain,
    ( 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_14890,c_42]) ).

tff(c_15053,plain,
    ( product(e_1,e_3,e_2)
    | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_15008]) ).

tff(c_15374,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_15053]) ).

tff(c_15058,plain,
    ! [Z1_17] :
      ( product(Z1_17,e_1,e_3)
      | ~ product(e_1,e_3,Z1_17) ),
    inference(resolution,[status(thm)],[c_14890,c_28]) ).

tff(c_15408,plain,
    product(e_1,e_1,e_3),
    inference(resolution,[status(thm)],[c_15374,c_15058]) ).

tff(c_15605,plain,
    equalish(e_3,e_2),
    inference(resolution,[status(thm)],[c_15408,c_13689]) ).

tff(c_15644,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_15605]) ).

tff(c_15645,plain,
    product(e_1,e_3,e_2),
    inference(splitRight,[status(thm)],[c_15053]) ).

tff(c_13690,plain,
    ! [W_8] :
      ( equalish(W_8,e_1)
      | ~ product(e_1,W_8,e_2) ),
    inference(resolution,[status(thm)],[c_13600,c_24]) ).

tff(c_15657,plain,
    equalish(e_3,e_1),
    inference(resolution,[status(thm)],[c_15645,c_13690]) ).

tff(c_15704,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16,c_15657]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GRP134-1.003 : 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
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 22:19:09 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 10.42/3.47  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.51/3.49  
% 10.51/3.49  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.65/3.55  
% 10.65/3.55  Inference rules
% 10.65/3.55  ----------------------
% 10.65/3.55  #Ref     : 0
% 10.65/3.55  #Sup     : 2921
% 10.65/3.55  #Fact    : 12
% 10.65/3.55  #Define  : 0
% 10.65/3.55  #Split   : 18
% 10.65/3.55  #Chain   : 0
% 10.65/3.55  #Close   : 0
% 10.65/3.55  
% 10.65/3.55  Ordering : KBO
% 10.65/3.55  
% 10.65/3.55  Simplification rules
% 10.65/3.55  ----------------------
% 10.65/3.55  #Subsume      : 303
% 10.65/3.55  #Demod        : 3491
% 10.65/3.55  #Tautology    : 1194
% 10.65/3.55  #SimpNegUnit  : 896
% 10.65/3.55  #BackRed      : 0
% 10.65/3.55  
% 10.65/3.55  #Partial instantiations: 0
% 10.65/3.55  #Strategies tried      : 1
% 10.65/3.55  
% 10.65/3.55  Timing (in seconds)
% 10.65/3.55  ----------------------
% 10.65/3.55  Preprocessing        : 0.41
% 10.65/3.55  Parsing              : 0.23
% 10.65/3.55  CNF conversion       : 0.02
% 10.65/3.55  Main loop            : 2.03
% 10.65/3.55  Inferencing          : 0.59
% 10.65/3.55  Reduction            : 0.55
% 10.65/3.55  Demodulation         : 0.35
% 10.65/3.55  BG Simplification    : 0.06
% 10.65/3.55  Subsumption          : 0.70
% 10.65/3.55  Abstraction          : 0.06
% 10.65/3.55  MUC search           : 0.00
% 10.65/3.55  Cooper               : 0.00
% 10.65/3.55  Total                : 2.53
% 10.65/3.55  Index Insertion      : 0.00
% 10.65/3.55  Index Deletion       : 0.00
% 10.65/3.55  Index Matching       : 0.00
% 10.65/3.55  BG Taut test         : 0.00
%------------------------------------------------------------------------------