TSTP Solution File: GRP128-1.003 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP128-1.003 : 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/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 : n017.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 10:40:06 EDT 2023

% Result   : Unsatisfiable 6.14s 2.51s
% Output   : CNFRefutation 6.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  125 (  48 unt;   6 typ;   0 def)
%            Number of atoms       :  296 (   0 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  285 ( 108   ~; 177   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 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   :   89 (;  89   !;   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_42,axiom,
    ~ equalish(e_2,e_3),
    file(unknown,unknown) ).

tff(f_33,axiom,
    group_element(e_2),
    file(unknown,unknown) ).

tff(f_34,axiom,
    group_element(e_3),
    file(unknown,unknown) ).

tff(f_58,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_40,axiom,
    ~ equalish(e_2,e_1),
    file(unknown,unknown) ).

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

tff(f_44,axiom,
    ~ equalish(e_3,e_1),
    file(unknown,unknown) ).

tff(f_32,axiom,
    group_element(e_1),
    file(unknown,unknown) ).

tff(f_46,axiom,
    ~ equalish(e_3,e_2),
    file(unknown,unknown) ).

tff(f_90,axiom,
    ! [X,Y,Z1,Z2] :
      ( ~ product(X,Y,Z1)
      | ~ product(Z1,Y,Z2)
      | product(X,Z1,Z2) ),
    file(unknown,unknown) ).

tff(f_82,axiom,
    ! [W,Y,X,Z] :
      ( ~ product(W,Y,X)
      | ~ product(Z,Y,X)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ! [X,W,Y,Z] :
      ( ~ product(X,W,Y)
      | ~ product(X,Z,Y)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(f_38,axiom,
    ~ equalish(e_1,e_3),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y,W,Z] :
      ( ~ product(X,Y,W)
      | ~ product(X,Y,Z)
      | equalish(W,Z) ),
    file(unknown,unknown) ).

tff(c_14,plain,
    ~ equalish(e_2,e_3),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_4,plain,
    group_element(e_2),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_6,plain,
    group_element(e_3),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

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_58]) ).

tff(c_12,plain,
    ~ equalish(e_2,e_1),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_8,plain,
    ~ equalish(e_1,e_2),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_16,plain,
    ~ equalish(e_3,e_1),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_2,plain,
    group_element(e_1),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_18,plain,
    ~ equalish(e_3,e_2),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

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_58]) ).

tff(c_28,plain,
    ! [X_15,Z1_17,Z2_18,Y_16] :
      ( product(X_15,Z1_17,Z2_18)
      | ~ product(Z1_17,Y_16,Z2_18)
      | ~ product(X_15,Y_16,Z1_17) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_59,plain,
    ! [X_46,X_47,Y_48] :
      ( product(X_46,X_47,e_3)
      | ~ product(X_46,Y_48,X_47)
      | 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_61,plain,
    ! [X_1,Y_2] :
      ( product(X_1,e_3,e_3)
      | product(e_3,Y_2,e_2)
      | product(e_3,Y_2,e_1)
      | ~ group_element(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(resolution,[status(thm)],[c_20,c_59]) ).

tff(c_64,plain,
    ! [X_1,Y_2] :
      ( product(X_1,e_3,e_3)
      | product(e_3,Y_2,e_2)
      | product(e_3,Y_2,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(demodulation,[status(thm),theory(equality)],[c_6,c_61]) ).

tff(c_76,plain,
    ! [Y_2] :
      ( product(e_3,e_3,e_3)
      | product(e_3,Y_2,e_1)
      | ~ group_element(Y_2)
      | ~ group_element(e_3)
      | product(e_3,Y_2,e_2) ),
    inference(factorization,[status(thm),theory(equality)],[c_64]) ).

tff(c_79,plain,
    ! [Y_2] :
      ( product(e_3,e_3,e_3)
      | product(e_3,Y_2,e_1)
      | ~ group_element(Y_2)
      | product(e_3,Y_2,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_76]) ).

tff(c_158,plain,
    product(e_3,e_3,e_3),
    inference(splitLeft,[status(thm)],[c_79]) ).

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_82]) ).

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_166,plain,
    ! [X_35] :
      ( equalish(e_3,X_35)
      | product(X_35,e_3,e_2)
      | product(X_35,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_158,c_43]) ).

tff(c_186,plain,
    ! [X_35] :
      ( equalish(e_3,X_35)
      | product(X_35,e_3,e_2)
      | product(X_35,e_3,e_1)
      | ~ group_element(X_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_166]) ).

tff(c_337,plain,
    ! [X_57] :
      ( equalish(e_3,X_57)
      | product(X_57,e_3,e_2)
      | product(X_57,e_3,e_1)
      | ~ group_element(X_57) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_166]) ).

tff(c_1493,plain,
    ! [X_100,X_101] :
      ( product(X_100,X_101,e_2)
      | ~ product(X_100,e_3,X_101)
      | equalish(e_3,X_101)
      | product(X_101,e_3,e_1)
      | ~ group_element(X_101) ),
    inference(resolution,[status(thm)],[c_337,c_28]) ).

tff(c_1515,plain,
    ! [X_35] :
      ( product(X_35,e_2,e_2)
      | equalish(e_3,e_2)
      | product(e_2,e_3,e_1)
      | ~ group_element(e_2)
      | equalish(e_3,X_35)
      | product(X_35,e_3,e_1)
      | ~ group_element(X_35) ),
    inference(resolution,[status(thm)],[c_186,c_1493]) ).

tff(c_1563,plain,
    ! [X_35] :
      ( product(X_35,e_2,e_2)
      | equalish(e_3,e_2)
      | product(e_2,e_3,e_1)
      | equalish(e_3,X_35)
      | product(X_35,e_3,e_1)
      | ~ group_element(X_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_1515]) ).

tff(c_1564,plain,
    ! [X_35] :
      ( product(X_35,e_2,e_2)
      | product(e_2,e_3,e_1)
      | equalish(e_3,X_35)
      | product(X_35,e_3,e_1)
      | ~ group_element(X_35) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_1563]) ).

tff(c_1693,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_1564]) ).

tff(c_365,plain,
    ! [X_15,X_57] :
      ( product(X_15,X_57,e_2)
      | ~ product(X_15,e_3,X_57)
      | equalish(e_3,X_57)
      | product(X_57,e_3,e_1)
      | ~ group_element(X_57) ),
    inference(resolution,[status(thm)],[c_337,c_28]) ).

tff(c_1697,plain,
    ( product(e_2,e_1,e_2)
    | equalish(e_3,e_1)
    | product(e_1,e_3,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_1693,c_365]) ).

tff(c_1720,plain,
    ( product(e_2,e_1,e_2)
    | equalish(e_3,e_1)
    | product(e_1,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1697]) ).

tff(c_1721,plain,
    ( product(e_2,e_1,e_2)
    | product(e_1,e_3,e_1) ),
    inference(negUnitSimplification,[status(thm)],[c_16,c_1720]) ).

tff(c_1921,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_1721]) ).

tff(c_1738,plain,
    ! [W_11] :
      ( equalish(W_11,e_2)
      | ~ product(W_11,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_1693,c_26]) ).

tff(c_1924,plain,
    equalish(e_1,e_2),
    inference(resolution,[status(thm)],[c_1921,c_1738]) ).

tff(c_1948,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_1924]) ).

tff(c_1949,plain,
    product(e_2,e_1,e_2),
    inference(splitRight,[status(thm)],[c_1721]) ).

tff(c_2442,plain,
    ! [X_122] :
      ( product(X_122,e_2,e_2)
      | ~ product(X_122,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_1949,c_28]) ).

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_74]) ).

tff(c_2003,plain,
    ! [W_8] :
      ( equalish(W_8,e_1)
      | ~ product(e_2,W_8,e_2) ),
    inference(resolution,[status(thm)],[c_1949,c_24]) ).

tff(c_2446,plain,
    ( equalish(e_2,e_1)
    | ~ product(e_2,e_1,e_2) ),
    inference(resolution,[status(thm)],[c_2442,c_2003]) ).

tff(c_2486,plain,
    equalish(e_2,e_1),
    inference(demodulation,[status(thm),theory(equality)],[c_1949,c_2446]) ).

tff(c_2488,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12,c_2486]) ).

tff(c_2490,plain,
    ~ product(e_2,e_3,e_1),
    inference(splitRight,[status(thm)],[c_1564]) ).

tff(c_2504,plain,
    ! [X_126] :
      ( product(X_126,e_2,e_2)
      | equalish(e_3,X_126)
      | product(X_126,e_3,e_1)
      | ~ group_element(X_126) ),
    inference(splitRight,[status(thm)],[c_1564]) ).

tff(c_2507,plain,
    ( product(e_2,e_2,e_2)
    | equalish(e_3,e_2)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_2504,c_2490]) ).

tff(c_2543,plain,
    ( product(e_2,e_2,e_2)
    | equalish(e_3,e_2) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2507]) ).

tff(c_2544,plain,
    product(e_2,e_2,e_2),
    inference(negUnitSimplification,[status(thm)],[c_18,c_2543]) ).

tff(c_191,plain,
    ! [W_51] :
      ( equalish(W_51,e_3)
      | ~ product(W_51,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_158,c_26]) ).

tff(c_201,plain,
    ! [X_1] :
      ( equalish(X_1,e_3)
      | product(X_1,e_3,e_2)
      | product(X_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_1) ),
    inference(resolution,[status(thm)],[c_20,c_191]) ).

tff(c_430,plain,
    ! [X_61] :
      ( equalish(X_61,e_3)
      | product(X_61,e_3,e_2)
      | product(X_61,e_3,e_1)
      | ~ group_element(X_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_201]) ).

tff(c_464,plain,
    ! [W_8,X_61] :
      ( equalish(W_8,e_3)
      | ~ product(X_61,W_8,e_2)
      | equalish(X_61,e_3)
      | product(X_61,e_3,e_1)
      | ~ group_element(X_61) ),
    inference(resolution,[status(thm)],[c_430,c_24]) ).

tff(c_2589,plain,
    ( equalish(e_2,e_3)
    | product(e_2,e_3,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_2544,c_464]) ).

tff(c_2616,plain,
    ( equalish(e_2,e_3)
    | product(e_2,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_2589]) ).

tff(c_2618,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2490,c_14,c_2616]) ).

tff(c_2620,plain,
    ~ product(e_3,e_3,e_3),
    inference(splitRight,[status(thm)],[c_79]) ).

tff(c_2626,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1)
    | ~ group_element(e_3) ),
    inference(resolution,[status(thm)],[c_20,c_2620]) ).

tff(c_2632,plain,
    ( product(e_3,e_3,e_2)
    | product(e_3,e_3,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2626]) ).

tff(c_2696,plain,
    product(e_3,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_2632]) ).

tff(c_2858,plain,
    ! [X_136] :
      ( product(X_136,e_3,e_1)
      | ~ product(X_136,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_2696,c_28]) ).

tff(c_2865,plain,
    ! [X_1] :
      ( product(X_1,e_3,e_2)
      | product(X_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_1) ),
    inference(resolution,[status(thm)],[c_20,c_2858]) ).

tff(c_2869,plain,
    ! [X_1] :
      ( product(X_1,e_3,e_2)
      | product(X_1,e_3,e_1)
      | ~ group_element(X_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2865]) ).

tff(c_10,plain,
    ~ equalish(e_1,e_3),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_2619,plain,
    ! [Y_2] :
      ( product(e_3,Y_2,e_1)
      | ~ group_element(Y_2)
      | product(e_3,Y_2,e_2) ),
    inference(splitRight,[status(thm)],[c_79]) ).

tff(c_42,plain,
    ! [X_15,X_35,Y_36] :
      ( product(X_15,X_35,e_3)
      | ~ product(X_15,Y_36,X_35)
      | 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_2698,plain,
    ( product(e_3,e_1,e_3)
    | 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_2696,c_42]) ).

tff(c_2711,plain,
    ( product(e_3,e_1,e_3)
    | 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_2698]) ).

tff(c_2934,plain,
    product(e_1,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_2711]) ).

tff(c_2717,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(W_11,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_2696,c_26]) ).

tff(c_2937,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_2934,c_2717]) ).

tff(c_2953,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_2937]) ).

tff(c_2954,plain,
    ( product(e_1,e_3,e_2)
    | product(e_3,e_1,e_3) ),
    inference(splitRight,[status(thm)],[c_2711]) ).

tff(c_2957,plain,
    product(e_3,e_1,e_3),
    inference(splitLeft,[status(thm)],[c_2954]) ).

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_66]) ).

tff(c_3004,plain,
    ! [W_140] :
      ( equalish(W_140,e_3)
      | ~ product(e_3,e_1,W_140) ),
    inference(resolution,[status(thm)],[c_2957,c_22]) ).

tff(c_3011,plain,
    ( equalish(e_2,e_3)
    | product(e_3,e_1,e_1)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_2619,c_3004]) ).

tff(c_3036,plain,
    ( equalish(e_2,e_3)
    | product(e_3,e_1,e_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3011]) ).

tff(c_3037,plain,
    product(e_3,e_1,e_1),
    inference(negUnitSimplification,[status(thm)],[c_14,c_3036]) ).

tff(c_2989,plain,
    ! [W_5] :
      ( equalish(W_5,e_3)
      | ~ product(e_3,e_1,W_5) ),
    inference(resolution,[status(thm)],[c_2957,c_22]) ).

tff(c_3059,plain,
    equalish(e_1,e_3),
    inference(resolution,[status(thm)],[c_3037,c_2989]) ).

tff(c_3078,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_3059]) ).

tff(c_3079,plain,
    product(e_1,e_3,e_2),
    inference(splitRight,[status(thm)],[c_2954]) ).

tff(c_3110,plain,
    ! [W_141] :
      ( equalish(W_141,e_1)
      | ~ product(W_141,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_3079,c_26]) ).

tff(c_3550,plain,
    ! [X_152] :
      ( equalish(X_152,e_1)
      | product(X_152,e_3,e_1)
      | ~ group_element(X_152) ),
    inference(resolution,[status(thm)],[c_2869,c_3110]) ).

tff(c_3689,plain,
    ! [X_155] :
      ( equalish(X_155,e_3)
      | equalish(X_155,e_1)
      | ~ group_element(X_155) ),
    inference(resolution,[status(thm)],[c_3550,c_2717]) ).

tff(c_3695,plain,
    ( equalish(e_2,e_1)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_3689,c_14]) ).

tff(c_3701,plain,
    equalish(e_2,e_1),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_3695]) ).

tff(c_3703,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_12,c_3701]) ).

tff(c_3704,plain,
    product(e_3,e_3,e_2),
    inference(splitRight,[status(thm)],[c_2632]) ).

tff(c_3939,plain,
    ! [X_162] :
      ( product(X_162,e_3,e_2)
      | ~ product(X_162,e_3,e_3) ),
    inference(resolution,[status(thm)],[c_3704,c_28]) ).

tff(c_3946,plain,
    ! [X_1] :
      ( product(X_1,e_3,e_2)
      | product(X_1,e_3,e_1)
      | ~ group_element(e_3)
      | ~ group_element(X_1) ),
    inference(resolution,[status(thm)],[c_20,c_3939]) ).

tff(c_4033,plain,
    ! [X_165] :
      ( product(X_165,e_3,e_2)
      | product(X_165,e_3,e_1)
      | ~ group_element(X_165) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_3946]) ).

tff(c_3726,plain,
    ! [W_11] :
      ( equalish(W_11,e_3)
      | ~ product(W_11,e_3,e_2) ),
    inference(resolution,[status(thm)],[c_3704,c_26]) ).

tff(c_4065,plain,
    ! [X_165] :
      ( equalish(X_165,e_3)
      | product(X_165,e_3,e_1)
      | ~ group_element(X_165) ),
    inference(resolution,[status(thm)],[c_4033,c_3726]) ).

tff(c_3707,plain,
    ( product(e_3,e_2,e_3)
    | 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_3704,c_42]) ).

tff(c_3720,plain,
    ( product(e_3,e_2,e_3)
    | 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_3707]) ).

tff(c_4116,plain,
    product(e_2,e_3,e_1),
    inference(splitLeft,[status(thm)],[c_3720]) ).

tff(c_4140,plain,
    ! [W_167] :
      ( equalish(W_167,e_2)
      | ~ product(W_167,e_3,e_1) ),
    inference(resolution,[status(thm)],[c_4116,c_26]) ).

tff(c_4464,plain,
    ! [X_176] :
      ( equalish(X_176,e_2)
      | equalish(X_176,e_3)
      | ~ group_element(X_176) ),
    inference(resolution,[status(thm)],[c_4065,c_4140]) ).

tff(c_4467,plain,
    ( equalish(e_1,e_2)
    | ~ group_element(e_1) ),
    inference(resolution,[status(thm)],[c_4464,c_10]) ).

tff(c_4473,plain,
    equalish(e_1,e_2),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4467]) ).

tff(c_4475,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8,c_4473]) ).

tff(c_4477,plain,
    ~ product(e_2,e_3,e_1),
    inference(splitRight,[status(thm)],[c_3720]) ).

tff(c_4480,plain,
    ( equalish(e_2,e_3)
    | ~ group_element(e_2) ),
    inference(resolution,[status(thm)],[c_4065,c_4477]) ).

tff(c_4483,plain,
    equalish(e_2,e_3),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4480]) ).

tff(c_4485,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_4483]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP128-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14  % 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
% 0.13/0.36  % Computer : n017.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 21:48:36 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 6.14/2.51  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.14/2.52  
% 6.14/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.26/2.56  
% 6.26/2.56  Inference rules
% 6.26/2.56  ----------------------
% 6.26/2.56  #Ref     : 0
% 6.26/2.56  #Sup     : 821
% 6.26/2.56  #Fact    : 12
% 6.26/2.56  #Define  : 0
% 6.26/2.56  #Split   : 9
% 6.26/2.56  #Chain   : 0
% 6.26/2.56  #Close   : 0
% 6.26/2.56  
% 6.26/2.56  Ordering : KBO
% 6.26/2.56  
% 6.26/2.56  Simplification rules
% 6.26/2.56  ----------------------
% 6.26/2.56  #Subsume      : 87
% 6.26/2.56  #Demod        : 852
% 6.26/2.56  #Tautology    : 280
% 6.26/2.56  #SimpNegUnit  : 229
% 6.26/2.57  #BackRed      : 0
% 6.26/2.57  
% 6.26/2.57  #Partial instantiations: 0
% 6.26/2.57  #Strategies tried      : 1
% 6.26/2.57  
% 6.26/2.57  Timing (in seconds)
% 6.26/2.57  ----------------------
% 6.26/2.57  Preprocessing        : 0.42
% 6.26/2.57  Parsing              : 0.24
% 6.26/2.57  CNF conversion       : 0.02
% 6.26/2.57  Main loop            : 0.93
% 6.26/2.57  Inferencing          : 0.33
% 6.26/2.57  Reduction            : 0.25
% 6.26/2.57  Demodulation         : 0.16
% 6.26/2.57  BG Simplification    : 0.04
% 6.26/2.57  Subsumption          : 0.25
% 6.26/2.57  Abstraction          : 0.04
% 6.26/2.57  MUC search           : 0.00
% 6.26/2.57  Cooper               : 0.00
% 6.26/2.57  Total                : 1.42
% 6.26/2.57  Index Insertion      : 0.00
% 6.26/2.57  Index Deletion       : 0.00
% 6.26/2.57  Index Matching       : 0.00
% 6.26/2.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------