TSTP Solution File: GRP488-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP488-1 : TPTP v8.1.2. Released v2.6.0.
% 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 10:41:21 EDT 2023

% Result   : Unsatisfiable 5.46s 2.45s
% Output   : CNFRefutation 5.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   97 (  92 unt;   5 typ;   0 def)
%            Number of atoms       :   92 (  91 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  136 (; 136   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > a2

%Foreground sorts:

%Background operators:

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

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

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

tff(a2,type,
    a2: $i ).

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

tff(f_27,axiom,
    ! [A] : ( inverse(A) = double_divide(A,identity) ),
    file(unknown,unknown) ).

tff(f_25,axiom,
    ! [A,B] : ( multiply(A,B) = double_divide(double_divide(B,A),identity) ),
    file(unknown,unknown) ).

tff(f_29,axiom,
    ! [A] : ( identity = double_divide(A,inverse(A)) ),
    file(unknown,unknown) ).

tff(f_23,axiom,
    ! [A,B,C] : ( double_divide(A,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,C))),B),identity)) = C ),
    file(unknown,unknown) ).

tff(f_31,axiom,
    multiply(identity,a2) != a2,
    file(unknown,unknown) ).

tff(c_6,plain,
    ! [A_6] : ( double_divide(A_6,identity) = inverse(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_28,plain,
    ! [B_10,A_11] : ( double_divide(double_divide(B_10,A_11),identity) = multiply(A_11,B_10) ),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_49,plain,
    ! [B_10,A_11] : ( inverse(double_divide(B_10,A_11)) = multiply(A_11,B_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_8,plain,
    ! [A_7] : ( double_divide(A_7,inverse(A_7)) = identity ),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_52,plain,
    ! [A_7] : ( multiply(inverse(A_7),A_7) = double_divide(identity,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_28]) ).

tff(c_57,plain,
    ! [A_7] : ( multiply(inverse(A_7),A_7) = inverse(identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_52]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( double_divide(A_1,double_divide(double_divide(double_divide(identity,double_divide(double_divide(A_1,identity),double_divide(B_2,C_3))),B_2),identity)) = C_3 ),
    inference(cnfTransformation,[status(thm)],[f_23]) ).

tff(c_65,plain,
    ! [A_13,B_14,C_15] : ( double_divide(A_13,inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),double_divide(B_14,C_15))),B_14))) = C_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).

tff(c_90,plain,
    ! [A_13,A_6] : ( double_divide(A_13,inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),inverse(A_6))),A_6))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).

tff(c_872,plain,
    ! [A_39,A_40] : ( double_divide(A_39,multiply(A_40,double_divide(identity,double_divide(inverse(A_39),inverse(A_40))))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_90]) ).

tff(c_945,plain,
    ! [A_39] : ( double_divide(A_39,multiply(inverse(A_39),double_divide(identity,identity))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_872]) ).

tff(c_955,plain,
    ! [A_41] : ( double_divide(A_41,multiply(inverse(A_41),inverse(identity))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_945]) ).

tff(c_997,plain,
    double_divide(inverse(identity),inverse(identity)) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_57,c_955]) ).

tff(c_103,plain,
    ! [B_16,A_17] : ( inverse(double_divide(B_16,A_17)) = multiply(A_17,B_16) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_109,plain,
    ! [A_17,B_16] : ( multiply(multiply(A_17,B_16),double_divide(B_16,A_17)) = inverse(identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_103,c_57]) ).

tff(c_121,plain,
    ! [A_6] : ( inverse(inverse(A_6)) = multiply(identity,A_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_103]) ).

tff(c_97,plain,
    ! [A_13,A_7] : ( double_divide(A_13,inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),identity)),A_7))) = inverse(A_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_65]) ).

tff(c_101,plain,
    ! [A_13,A_7] : ( double_divide(A_13,inverse(double_divide(double_divide(identity,inverse(inverse(A_13))),A_7))) = inverse(A_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_97]) ).

tff(c_405,plain,
    ! [A_29,A_30] : ( double_divide(A_29,multiply(A_30,double_divide(identity,multiply(identity,A_29)))) = inverse(A_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_49,c_101]) ).

tff(c_438,plain,
    ! [A_29] : ( inverse(multiply(multiply(identity,A_29),identity)) = double_divide(A_29,inverse(identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_405]) ).

tff(c_4,plain,
    ! [B_5,A_4] : ( double_divide(double_divide(B_5,A_4),identity) = multiply(A_4,B_5) ),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_31,plain,
    ! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = double_divide(multiply(A_11,B_10),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_4]) ).

tff(c_53,plain,
    ! [B_10,A_11] : ( multiply(identity,double_divide(B_10,A_11)) = inverse(multiply(A_11,B_10)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_31]) ).

tff(c_445,plain,
    ! [A_29] : ( double_divide(A_29,inverse(multiply(multiply(identity,A_29),identity))) = inverse(identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_53,c_405]) ).

tff(c_497,plain,
    ! [A_29] : ( double_divide(A_29,double_divide(A_29,inverse(identity))) = inverse(identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_438,c_445]) ).

tff(c_1019,plain,
    double_divide(inverse(identity),identity) = inverse(identity),
    inference(superposition,[status(thm),theory(equality)],[c_997,c_497]) ).

tff(c_46,plain,
    ! [A_6] : ( double_divide(inverse(A_6),identity) = multiply(identity,A_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_1127,plain,
    multiply(identity,identity) = inverse(identity),
    inference(superposition,[status(thm),theory(equality)],[c_1019,c_46]) ).

tff(c_498,plain,
    ! [A_32] : ( inverse(multiply(multiply(identity,A_32),identity)) = double_divide(A_32,inverse(identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_405]) ).

tff(c_736,plain,
    ! [A_38] : ( double_divide(multiply(multiply(identity,A_38),identity),double_divide(A_38,inverse(identity))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_498,c_8]) ).

tff(c_765,plain,
    double_divide(multiply(multiply(identity,identity),identity),identity) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_8,c_736]) ).

tff(c_1155,plain,
    double_divide(multiply(inverse(identity),identity),identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1127,c_765]) ).

tff(c_1160,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1127,c_121,c_6,c_57,c_1155]) ).

tff(c_1192,plain,
    multiply(identity,identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_1160,c_1127]) ).

tff(c_404,plain,
    ! [A_13,A_7] : ( double_divide(A_13,multiply(A_7,double_divide(identity,multiply(identity,A_13)))) = inverse(A_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_49,c_101]) ).

tff(c_954,plain,
    ! [A_39] : ( double_divide(A_39,multiply(inverse(A_39),inverse(identity))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_945]) ).

tff(c_1636,plain,
    ! [A_52] : ( double_divide(A_52,multiply(inverse(A_52),identity)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_1160,c_954]) ).

tff(c_11,plain,
    ! [A_1,B_2,C_3] : ( double_divide(A_1,inverse(double_divide(double_divide(identity,double_divide(inverse(A_1),double_divide(B_2,C_3))),B_2))) = C_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).

tff(c_102,plain,
    ! [A_1,B_2,C_3] : ( double_divide(A_1,multiply(B_2,double_divide(identity,double_divide(inverse(A_1),double_divide(B_2,C_3))))) = C_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_11]) ).

tff(c_1651,plain,
    ! [A_1,A_52] : ( double_divide(A_1,multiply(A_52,double_divide(identity,double_divide(inverse(A_1),identity)))) = multiply(inverse(A_52),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1636,c_102]) ).

tff(c_1687,plain,
    ! [A_52] : ( multiply(inverse(A_52),identity) = inverse(A_52) ),
    inference(demodulation,[status(thm),theory(equality)],[c_404,c_121,c_6,c_1651]) ).

tff(c_153,plain,
    ! [A_19] : ( double_divide(inverse(A_19),identity) = multiply(identity,A_19) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_159,plain,
    ! [A_19] : ( multiply(identity,inverse(A_19)) = inverse(multiply(identity,A_19)) ),
    inference(superposition,[status(thm),theory(equality)],[c_153,c_49]) ).

tff(c_83,plain,
    ! [A_13,A_4,B_5] : ( double_divide(A_13,inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),multiply(A_4,B_5))),double_divide(B_5,A_4)))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_65]) ).

tff(c_1492,plain,
    ! [A_49,B_50,A_51] : ( double_divide(A_49,multiply(double_divide(B_50,A_51),double_divide(identity,double_divide(inverse(A_49),multiply(A_51,B_50))))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_83]) ).

tff(c_2063,plain,
    ! [A_59,A_60] : ( double_divide(A_59,multiply(inverse(A_60),double_divide(identity,double_divide(inverse(A_59),multiply(identity,A_60))))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1492]) ).

tff(c_2141,plain,
    ! [A_59] : ( double_divide(A_59,multiply(inverse(double_divide(identity,multiply(identity,inverse(A_59)))),double_divide(identity,inverse(identity)))) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_404,c_2063]) ).

tff(c_2260,plain,
    ! [A_62] : ( double_divide(A_62,inverse(multiply(identity,A_62))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_1687,c_1687,c_159,c_49,c_8,c_2141]) ).

tff(c_2278,plain,
    ! [A_1,A_62] : ( double_divide(A_1,multiply(A_62,double_divide(identity,double_divide(inverse(A_1),identity)))) = inverse(multiply(identity,A_62)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2260,c_102]) ).

tff(c_2315,plain,
    ! [A_62] : ( inverse(multiply(identity,A_62)) = inverse(A_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_404,c_121,c_6,c_2278]) ).

tff(c_2326,plain,
    ! [A_19] : ( multiply(identity,inverse(A_19)) = inverse(A_19) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2315,c_159]) ).

tff(c_1328,plain,
    ! [A_7] : ( double_divide(identity,multiply(A_7,double_divide(identity,identity))) = inverse(A_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_1192,c_404]) ).

tff(c_2192,plain,
    ! [A_61] : ( double_divide(identity,multiply(A_61,identity)) = inverse(A_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1160,c_6,c_1328]) ).

tff(c_2232,plain,
    ! [A_52] : ( double_divide(identity,inverse(A_52)) = inverse(inverse(A_52)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1687,c_2192]) ).

tff(c_2632,plain,
    ! [A_68] : ( double_divide(identity,inverse(A_68)) = multiply(identity,A_68) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_2232]) ).

tff(c_2689,plain,
    ! [A_6] : ( multiply(identity,inverse(A_6)) = double_divide(identity,multiply(identity,A_6)) ),
    inference(superposition,[status(thm),theory(equality)],[c_121,c_2632]) ).

tff(c_2712,plain,
    ! [A_6] : ( double_divide(identity,multiply(identity,A_6)) = inverse(A_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2326,c_2689]) ).

tff(c_2253,plain,
    ! [A_52] : ( double_divide(identity,inverse(A_52)) = multiply(identity,A_52) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_2232]) ).

tff(c_68,plain,
    ! [A_13,B_14,C_15,A_1] : ( inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),double_divide(B_14,C_15))),B_14)) = double_divide(A_1,inverse(double_divide(double_divide(identity,double_divide(inverse(A_1),C_15)),A_13))) ),
    inference(superposition,[status(thm),theory(equality)],[c_65,c_11]) ).

tff(c_1778,plain,
    ! [A_55,B_56,C_57,A_58] : ( inverse(double_divide(double_divide(identity,double_divide(inverse(A_55),double_divide(B_56,C_57))),B_56)) = double_divide(A_58,multiply(A_55,double_divide(identity,double_divide(inverse(A_58),C_57)))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_68]) ).

tff(c_2001,plain,
    ! [A_55,A_6,A_58] : ( inverse(double_divide(double_divide(identity,double_divide(inverse(A_55),inverse(A_6))),A_6)) = double_divide(A_58,multiply(A_55,double_divide(identity,double_divide(inverse(A_58),identity)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1778]) ).

tff(c_3424,plain,
    ! [A_80,A_81] : ( inverse(double_divide(double_divide(identity,double_divide(inverse(A_80),inverse(A_81))),A_81)) = inverse(A_80) ),
    inference(demodulation,[status(thm),theory(equality)],[c_404,c_121,c_6,c_2001]) ).

tff(c_3523,plain,
    ! [A_81] : ( inverse(double_divide(double_divide(identity,double_divide(identity,inverse(A_81))),A_81)) = inverse(identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1160,c_3424]) ).

tff(c_3587,plain,
    ! [A_82] : ( multiply(A_82,inverse(A_82)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_2712,c_49,c_2253,c_1160,c_3523]) ).

tff(c_1200,plain,
    ! [A_17,B_16] : ( multiply(multiply(A_17,B_16),double_divide(B_16,A_17)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_1160,c_109]) ).

tff(c_3684,plain,
    ! [A_83] : ( multiply(identity,double_divide(inverse(A_83),A_83)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_3587,c_1200]) ).

tff(c_2009,plain,
    ! [A_55,B_56,A_58] : ( inverse(double_divide(double_divide(identity,double_divide(inverse(A_55),double_divide(B_56,identity))),B_56)) = double_divide(A_58,multiply(A_55,double_divide(identity,inverse(inverse(A_58))))) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1778]) ).

tff(c_2528,plain,
    ! [B_66,A_67] : ( multiply(B_66,double_divide(identity,double_divide(inverse(A_67),inverse(B_66)))) = inverse(A_67) ),
    inference(demodulation,[status(thm),theory(equality)],[c_404,c_121,c_49,c_6,c_2009]) ).

tff(c_2597,plain,
    ! [A_67] : ( inverse(multiply(double_divide(inverse(A_67),inverse(identity)),identity)) = inverse(A_67) ),
    inference(superposition,[status(thm),theory(equality)],[c_53,c_2528]) ).

tff(c_2628,plain,
    ! [A_67] : ( inverse(multiply(multiply(identity,A_67),identity)) = inverse(A_67) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_6,c_1160,c_2597]) ).

tff(c_3698,plain,
    ! [A_83] : ( inverse(double_divide(inverse(A_83),A_83)) = inverse(multiply(identity,identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_3684,c_2628]) ).

tff(c_3783,plain,
    ! [A_84] : ( inverse(double_divide(inverse(A_84),A_84)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_1160,c_1192,c_3698]) ).

tff(c_3578,plain,
    ! [A_81] : ( multiply(A_81,inverse(A_81)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_2712,c_49,c_2253,c_1160,c_3523]) ).

tff(c_4021,plain,
    ! [A_86] : ( multiply(double_divide(inverse(A_86),A_86),identity) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_3783,c_3578]) ).

tff(c_87,plain,
    ! [A_13,C_15] : ( double_divide(A_13,inverse(multiply(double_divide(inverse(A_13),double_divide(identity,C_15)),identity))) = C_15 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_65]) ).

tff(c_4039,plain,
    ! [C_15] : ( double_divide(double_divide(identity,C_15),inverse(identity)) = C_15 ),
    inference(superposition,[status(thm),theory(equality)],[c_4021,c_87]) ).

tff(c_4078,plain,
    ! [C_15] : ( multiply(C_15,identity) = C_15 ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_6,c_1160,c_4039]) ).

tff(c_74,plain,
    ! [A_13,B_14,C_15] : ( multiply(inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),double_divide(B_14,C_15))),B_14)),A_13) = double_divide(C_15,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_65,c_4]) ).

tff(c_99,plain,
    ! [A_13,B_14,C_15] : ( multiply(inverse(double_divide(double_divide(identity,double_divide(inverse(A_13),double_divide(B_14,C_15))),B_14)),A_13) = inverse(C_15) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_74]) ).

tff(c_1384,plain,
    ! [B_45,A_46,C_47] : ( multiply(multiply(B_45,double_divide(identity,double_divide(inverse(A_46),double_divide(B_45,C_47)))),A_46) = inverse(C_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_99]) ).

tff(c_1443,plain,
    ! [A_7,A_46] : ( multiply(multiply(A_7,double_divide(identity,double_divide(inverse(A_46),identity))),A_46) = inverse(inverse(A_7)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1384]) ).

tff(c_1456,plain,
    ! [A_7,A_46] : ( multiply(multiply(A_7,double_divide(identity,multiply(identity,A_46))),A_46) = multiply(identity,A_7) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_121,c_6,c_1443]) ).

tff(c_4180,plain,
    ! [A_88,A_89] : ( multiply(multiply(A_88,inverse(A_89)),A_89) = multiply(identity,A_88) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2712,c_1456]) ).

tff(c_4243,plain,
    ! [A_88] : ( multiply(multiply(A_88,identity),identity) = multiply(identity,A_88) ),
    inference(superposition,[status(thm),theory(equality)],[c_1160,c_4180]) ).

tff(c_4263,plain,
    ! [A_88] : ( multiply(identity,A_88) = A_88 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4078,c_4078,c_4243]) ).

tff(c_10,plain,
    multiply(identity,a2) != a2,
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_4283,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4263,c_10]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GRP488-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n009.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 21:53:08 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 5.46/2.45  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.75/2.46  
% 5.75/2.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.78/2.50  
% 5.78/2.50  Inference rules
% 5.78/2.50  ----------------------
% 5.78/2.50  #Ref     : 0
% 5.78/2.50  #Sup     : 1086
% 5.78/2.50  #Fact    : 0
% 5.78/2.50  #Define  : 0
% 5.78/2.50  #Split   : 0
% 5.78/2.50  #Chain   : 0
% 5.78/2.50  #Close   : 0
% 5.78/2.50  
% 5.78/2.50  Ordering : KBO
% 5.78/2.50  
% 5.78/2.50  Simplification rules
% 5.78/2.50  ----------------------
% 5.78/2.50  #Subsume      : 1
% 5.78/2.50  #Demod        : 1614
% 5.78/2.50  #Tautology    : 521
% 5.78/2.50  #SimpNegUnit  : 0
% 5.78/2.50  #BackRed      : 43
% 5.78/2.50  
% 5.78/2.50  #Partial instantiations: 0
% 5.78/2.50  #Strategies tried      : 1
% 5.78/2.50  
% 5.78/2.50  Timing (in seconds)
% 5.78/2.50  ----------------------
% 5.95/2.50  Preprocessing        : 0.41
% 5.95/2.50  Parsing              : 0.22
% 5.95/2.50  CNF conversion       : 0.02
% 5.95/2.50  Main loop            : 0.98
% 5.95/2.50  Inferencing          : 0.32
% 5.95/2.50  Reduction            : 0.41
% 5.95/2.50  Demodulation         : 0.34
% 5.95/2.50  BG Simplification    : 0.04
% 5.95/2.51  Subsumption          : 0.14
% 5.95/2.51  Abstraction          : 0.05
% 5.95/2.51  MUC search           : 0.00
% 5.95/2.51  Cooper               : 0.00
% 5.95/2.51  Total                : 1.45
% 5.95/2.51  Index Insertion      : 0.00
% 5.95/2.51  Index Deletion       : 0.00
% 5.95/2.51  Index Matching       : 0.00
% 5.95/2.51  BG Taut test         : 0.00
%------------------------------------------------------------------------------