TSTP Solution File: GRP579-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP579-1 : 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/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 : n015.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 10:41:33 EDT 2023

% Result   : Unsatisfiable 23.93s 14.68s
% Output   : CNFRefutation 23.93s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   31
%            Number of leaves      :   12
% Syntax   : Number of formulae    :  119 ( 112 unt;   7 typ;   0 def)
%            Number of atoms       :  112 ( 111 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    9 (   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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :  206 (; 206   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > identity > c3 > b3 > a3

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a3,type,
    a3: $i ).

tff(c3,type,
    c3: $i ).

tff(inverse,type,
    inverse: $i > $i ).

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

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

tff(b3,type,
    b3: $i ).

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

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

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

tff(f_31,axiom,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    file(unknown,unknown) ).

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_6,plain,
    ! [A_6] : ( double_divide(A_6,identity) = inverse(A_6) ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_37,plain,
    ! [B_10,A_11] : ( inverse(double_divide(B_10,A_11)) = multiply(A_11,B_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).

tff(c_65,plain,
    ! [B_13,A_14] : ( inverse(double_divide(B_13,A_14)) = multiply(A_14,B_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_6]) ).

tff(c_83,plain,
    ! [A_6] : ( inverse(inverse(A_6)) = multiply(identity,A_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_65]) ).

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(double_divide(A_1,double_divide(double_divide(double_divide(B_2,A_1),C_3),double_divide(B_2,identity))),double_divide(identity,identity)) = C_3 ),
    inference(cnfTransformation,[status(thm)],[f_23]) ).

tff(c_236,plain,
    ! [A_21,B_22,C_23] : ( double_divide(double_divide(A_21,double_divide(double_divide(double_divide(B_22,A_21),C_23),inverse(B_22))),inverse(identity)) = C_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_2]) ).

tff(c_531,plain,
    ! [A_31,C_32] : ( double_divide(double_divide(inverse(A_31),double_divide(double_divide(identity,C_32),inverse(A_31))),inverse(identity)) = C_32 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_236]) ).

tff(c_590,plain,
    ! [C_32] : ( double_divide(double_divide(inverse(double_divide(identity,C_32)),identity),inverse(identity)) = C_32 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_531]) ).

tff(c_603,plain,
    ! [C_33] : ( double_divide(inverse(multiply(C_33,identity)),inverse(identity)) = C_33 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_590]) ).

tff(c_631,plain,
    double_divide(inverse(inverse(identity)),inverse(identity)) = inverse(identity),
    inference(superposition,[status(thm),theory(equality)],[c_57,c_603]) ).

tff(c_636,plain,
    double_divide(multiply(identity,identity),inverse(identity)) = inverse(identity),
    inference(demodulation,[status(thm),theory(equality)],[c_83,c_631]) ).

tff(c_655,plain,
    multiply(inverse(identity),multiply(identity,identity)) = inverse(inverse(identity)),
    inference(superposition,[status(thm),theory(equality)],[c_636,c_37]) ).

tff(c_663,plain,
    multiply(inverse(identity),multiply(identity,identity)) = multiply(identity,identity),
    inference(demodulation,[status(thm),theory(equality)],[c_83,c_655]) ).

tff(c_302,plain,
    ! [A_21,B_22] : ( double_divide(double_divide(A_21,double_divide(inverse(double_divide(B_22,A_21)),inverse(B_22))),inverse(identity)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_236]) ).

tff(c_319,plain,
    ! [A_21,B_22] : ( double_divide(double_divide(A_21,double_divide(multiply(A_21,B_22),inverse(B_22))),inverse(identity)) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_302]) ).

tff(c_696,plain,
    double_divide(double_divide(inverse(identity),double_divide(multiply(identity,identity),inverse(multiply(identity,identity)))),inverse(identity)) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_663,c_319]) ).

tff(c_705,plain,
    inverse(identity) = identity,
    inference(demodulation,[status(thm),theory(equality)],[c_636,c_83,c_6,c_8,c_696]) ).

tff(c_602,plain,
    ! [C_32] : ( double_divide(inverse(multiply(C_32,identity)),inverse(identity)) = C_32 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_590]) ).

tff(c_856,plain,
    ! [C_38] : ( double_divide(inverse(multiply(C_38,identity)),identity) = C_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_705,c_602]) ).

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_868,plain,
    ! [C_38] : ( multiply(identity,multiply(C_38,identity)) = C_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_856,c_46]) ).

tff(c_115,plain,
    ! [A_16] : ( double_divide(inverse(A_16),identity) = multiply(identity,A_16) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_28]) ).

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_124,plain,
    ! [A_16] : ( multiply(identity,inverse(A_16)) = double_divide(multiply(identity,A_16),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_115,c_4]) ).

tff(c_141,plain,
    ! [A_16] : ( multiply(identity,inverse(A_16)) = inverse(multiply(identity,A_16)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_124]) ).

tff(c_298,plain,
    ! [A_6,C_23] : ( double_divide(double_divide(identity,double_divide(double_divide(inverse(A_6),C_23),inverse(A_6))),inverse(identity)) = C_23 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_236]) ).

tff(c_927,plain,
    ! [A_40,C_41] : ( multiply(double_divide(double_divide(inverse(A_40),C_41),inverse(A_40)),identity) = C_41 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_705,c_298]) ).

tff(c_948,plain,
    ! [C_41] : ( multiply(double_divide(double_divide(identity,C_41),inverse(identity)),identity) = C_41 ),
    inference(superposition,[status(thm),theory(equality)],[c_705,c_927]) ).

tff(c_1117,plain,
    ! [C_44] : ( multiply(multiply(C_44,identity),identity) = C_44 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_705,c_948]) ).

tff(c_877,plain,
    ! [C_38] : ( inverse(inverse(multiply(C_38,identity))) = C_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_856,c_6]) ).

tff(c_1162,plain,
    ! [C_45] : ( inverse(inverse(C_45)) = multiply(C_45,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1117,c_877]) ).

tff(c_1183,plain,
    ! [C_45] : ( inverse(multiply(identity,inverse(C_45))) = multiply(identity,multiply(C_45,identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1162,c_141]) ).

tff(c_1227,plain,
    ! [C_45] : ( multiply(identity,multiply(identity,C_45)) = C_45 ),
    inference(demodulation,[status(thm),theory(equality)],[c_868,c_83,c_141,c_1183]) ).

tff(c_1132,plain,
    ! [C_44] : ( multiply(identity,C_44) = multiply(C_44,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1117,c_868]) ).

tff(c_1198,plain,
    ! [C_45] : ( double_divide(inverse(C_45),multiply(C_45,identity)) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_1162,c_8]) ).

tff(c_926,plain,
    ! [A_6,C_23] : ( multiply(double_divide(double_divide(inverse(A_6),C_23),inverse(A_6)),identity) = C_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_705,c_298]) ).

tff(c_80,plain,
    ! [B_5,A_4] : ( multiply(identity,double_divide(B_5,A_4)) = inverse(multiply(A_4,B_5)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_65]) ).

tff(c_292,plain,
    ! [A_4,B_5,C_23] : ( double_divide(double_divide(identity,double_divide(double_divide(multiply(A_4,B_5),C_23),inverse(double_divide(B_5,A_4)))),inverse(identity)) = C_23 ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_236]) ).

tff(c_318,plain,
    ! [A_4,B_5,C_23] : ( double_divide(double_divide(identity,double_divide(double_divide(multiply(A_4,B_5),C_23),multiply(A_4,B_5))),inverse(identity)) = C_23 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_292]) ).

tff(c_1801,plain,
    ! [A_55,B_56,C_57] : ( inverse(multiply(multiply(A_55,B_56),double_divide(multiply(A_55,B_56),C_57))) = C_57 ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_1132,c_37,c_6,c_705,c_318]) ).

tff(c_1882,plain,
    ! [C_23,A_6,C_57] : ( inverse(multiply(C_23,double_divide(multiply(double_divide(double_divide(inverse(A_6),C_23),inverse(A_6)),identity),C_57))) = C_57 ),
    inference(superposition,[status(thm),theory(equality)],[c_926,c_1801]) ).

tff(c_3184,plain,
    ! [C_74,C_75] : ( inverse(multiply(C_74,double_divide(C_74,C_75))) = C_75 ),
    inference(demodulation,[status(thm),theory(equality)],[c_926,c_1882]) ).

tff(c_3271,plain,
    ! [C_45] : ( inverse(multiply(inverse(C_45),identity)) = multiply(C_45,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1198,c_3184]) ).

tff(c_3314,plain,
    ! [C_45] : ( multiply(C_45,identity) = C_45 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1227,c_83,c_141,c_1132,c_3271]) ).

tff(c_3331,plain,
    ! [C_38] : ( multiply(identity,C_38) = C_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3314,c_868]) ).

tff(c_3506,plain,
    ! [A_4,B_5] : ( inverse(multiply(A_4,B_5)) = double_divide(B_5,A_4) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3331,c_80]) ).

tff(c_1233,plain,
    ! [C_46] : ( multiply(identity,C_46) = multiply(C_46,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_1117,c_868]) ).

tff(c_1251,plain,
    ! [C_46] : ( inverse(inverse(multiply(identity,C_46))) = C_46 ),
    inference(superposition,[status(thm),theory(equality)],[c_1233,c_877]) ).

tff(c_3223,plain,
    ! [C_75] : ( double_divide(identity,C_75) = inverse(C_75) ),
    inference(superposition,[status(thm),theory(equality)],[c_3184,c_1251]) ).

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

tff(c_546,plain,
    ! [C_32,A_31] : ( double_divide(double_divide(double_divide(double_divide(identity,C_32),inverse(A_31)),double_divide(C_32,inverse(inverse(A_31)))),inverse(identity)) = inverse(identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_531,c_11]) ).

tff(c_593,plain,
    ! [C_32,A_31] : ( double_divide(double_divide(double_divide(double_divide(identity,C_32),inverse(A_31)),double_divide(C_32,multiply(identity,A_31))),inverse(identity)) = inverse(identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_83,c_546]) ).

tff(c_11631,plain,
    ! [C_32,A_31] : ( multiply(double_divide(C_32,A_31),double_divide(inverse(C_32),inverse(A_31))) = identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_3223,c_3331,c_705,c_37,c_6,c_705,c_593]) ).

tff(c_3330,plain,
    ! [C_38] : ( inverse(inverse(C_38)) = C_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3314,c_877]) ).

tff(c_268,plain,
    ! [B_2,A_21,C_3] : ( double_divide(double_divide(double_divide(B_2,double_divide(identity,A_21)),C_3),inverse(B_2)) = double_divide(double_divide(A_21,C_3),inverse(identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_11,c_236]) ).

tff(c_2322,plain,
    ! [B_62,A_63,C_64] : ( double_divide(double_divide(double_divide(B_62,double_divide(identity,A_63)),C_64),inverse(B_62)) = multiply(C_64,A_63) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_6,c_705,c_268]) ).

tff(c_2400,plain,
    ! [A_63,B_5] : ( double_divide(multiply(double_divide(identity,A_63),B_5),inverse(B_5)) = multiply(identity,A_63) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_2322]) ).

tff(c_5414,plain,
    ! [A_109,B_110] : ( double_divide(multiply(inverse(A_109),B_110),inverse(B_110)) = A_109 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3223,c_3331,c_2400]) ).

tff(c_13213,plain,
    ! [C_190,B_191] : ( double_divide(multiply(C_190,B_191),inverse(B_191)) = inverse(C_190) ),
    inference(superposition,[status(thm),theory(equality)],[c_3330,c_5414]) ).

tff(c_13316,plain,
    ! [C_32,A_31] : ( double_divide(identity,inverse(double_divide(inverse(C_32),inverse(A_31)))) = inverse(double_divide(C_32,A_31)) ),
    inference(superposition,[status(thm),theory(equality)],[c_11631,c_13213]) ).

tff(c_13443,plain,
    ! [C_32,A_31] : ( double_divide(inverse(C_32),inverse(A_31)) = multiply(A_31,C_32) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3506,c_3223,c_37,c_37,c_13316]) ).

tff(c_309,plain,
    ! [A_21,B_22] : ( double_divide(double_divide(A_21,double_divide(identity,inverse(B_22))),inverse(identity)) = inverse(double_divide(B_22,A_21)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_236]) ).

tff(c_709,plain,
    ! [A_35,B_36] : ( double_divide(double_divide(A_35,double_divide(identity,inverse(B_36))),inverse(identity)) = multiply(A_35,B_36) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_309]) ).

tff(c_741,plain,
    ! [A_35,B_36] : ( multiply(inverse(identity),double_divide(A_35,double_divide(identity,inverse(B_36)))) = double_divide(multiply(A_35,B_36),identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_709,c_4]) ).

tff(c_757,plain,
    ! [A_35,B_36] : ( multiply(inverse(identity),double_divide(A_35,double_divide(identity,inverse(B_36)))) = inverse(multiply(A_35,B_36)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_741]) ).

tff(c_5822,plain,
    ! [B_36,A_35] : ( double_divide(B_36,A_35) = double_divide(A_35,B_36) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3506,c_3330,c_3223,c_3331,c_705,c_757]) ).

tff(c_2393,plain,
    ! [A_6,A_63,C_64] : ( double_divide(double_divide(double_divide(inverse(A_6),double_divide(identity,A_63)),C_64),multiply(identity,A_6)) = multiply(C_64,A_63) ),
    inference(superposition,[status(thm),theory(equality)],[c_83,c_2322]) ).

tff(c_43329,plain,
    ! [A_366,A_367,C_368] : ( double_divide(A_366,double_divide(multiply(A_367,A_366),C_368)) = multiply(C_368,A_367) ),
    inference(demodulation,[status(thm),theory(equality)],[c_13443,c_5822,c_3223,c_3331,c_2393]) ).

tff(c_239,plain,
    ! [C_23,C_3,A_21,B_22] : ( double_divide(double_divide(inverse(identity),double_divide(double_divide(C_23,C_3),inverse(double_divide(A_21,double_divide(double_divide(double_divide(B_22,A_21),C_23),inverse(B_22)))))),inverse(identity)) = C_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_236,c_11]) ).

tff(c_310,plain,
    ! [C_23,C_3,B_22,A_21] : ( double_divide(double_divide(inverse(identity),double_divide(double_divide(C_23,C_3),multiply(double_divide(double_divide(double_divide(B_22,A_21),C_23),inverse(B_22)),A_21))),inverse(identity)) = C_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_239]) ).

tff(c_3635,plain,
    ! [C_80,C_81,B_82,A_83] : ( double_divide(double_divide(C_80,C_81),multiply(double_divide(double_divide(double_divide(B_82,A_83),C_80),inverse(B_82)),A_83)) = C_81 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3314,c_37,c_6,c_705,c_705,c_310]) ).

tff(c_3762,plain,
    ! [C_80,C_81,A_6] : ( double_divide(double_divide(C_80,C_81),multiply(double_divide(double_divide(inverse(A_6),C_80),inverse(A_6)),identity)) = C_81 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_3635]) ).

tff(c_3794,plain,
    ! [C_80,C_81] : ( double_divide(double_divide(C_80,C_81),C_80) = C_81 ),
    inference(demodulation,[status(thm),theory(equality)],[c_926,c_3762]) ).

tff(c_5829,plain,
    ! [B_115,A_116] : ( double_divide(B_115,A_116) = double_divide(A_116,B_115) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3506,c_3330,c_3223,c_3331,c_705,c_757]) ).

tff(c_6359,plain,
    ! [B_121,A_122] : ( double_divide(double_divide(B_121,A_122),identity) = multiply(B_121,A_122) ),
    inference(superposition,[status(thm),theory(equality)],[c_5829,c_4]) ).

tff(c_6470,plain,
    ! [C_80,C_81] : ( multiply(double_divide(C_80,C_81),C_80) = double_divide(C_81,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_3794,c_6359]) ).

tff(c_6530,plain,
    ! [C_80,C_81] : ( multiply(double_divide(C_80,C_81),C_80) = inverse(C_81) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6470]) ).

tff(c_43550,plain,
    ! [A_367,A_366,C_368] : ( inverse(double_divide(multiply(A_367,A_366),C_368)) = multiply(multiply(C_368,A_367),A_366) ),
    inference(superposition,[status(thm),theory(equality)],[c_43329,c_6530]) ).

tff(c_43922,plain,
    ! [C_368,A_367,A_366] : ( multiply(multiply(C_368,A_367),A_366) = multiply(C_368,multiply(A_367,A_366)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_43550]) ).

tff(c_725,plain,
    ! [A_35,B_36,C_3] : ( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(A_35,B_36),C_3),inverse(double_divide(A_35,double_divide(identity,inverse(B_36)))))),inverse(identity)) = C_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_709,c_11]) ).

tff(c_756,plain,
    ! [A_35,B_36,C_3] : ( double_divide(double_divide(inverse(identity),double_divide(double_divide(multiply(A_35,B_36),C_3),multiply(double_divide(identity,inverse(B_36)),A_35))),inverse(identity)) = C_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_37,c_725]) ).

tff(c_13667,plain,
    ! [B_194,A_195,C_196] : ( double_divide(multiply(B_194,A_195),double_divide(multiply(A_195,B_194),C_196)) = C_196 ),
    inference(demodulation,[status(thm),theory(equality)],[c_5822,c_3330,c_3223,c_3314,c_37,c_6,c_705,c_705,c_756]) ).

tff(c_29031,plain,
    ! [A_296,B_297,C_298] : ( double_divide(multiply(A_296,B_297),C_298) = double_divide(C_298,multiply(B_297,A_296)) ),
    inference(superposition,[status(thm),theory(equality)],[c_13667,c_3794]) ).

tff(c_29407,plain,
    ! [C_298,B_297,A_296] : ( double_divide(double_divide(C_298,multiply(B_297,A_296)),multiply(A_296,B_297)) = C_298 ),
    inference(superposition,[status(thm),theory(equality)],[c_29031,c_3794]) ).

tff(c_4185,plain,
    ! [C_90,C_91] : ( double_divide(double_divide(C_90,C_91),C_90) = C_91 ),
    inference(demodulation,[status(thm),theory(equality)],[c_926,c_3762]) ).

tff(c_4188,plain,
    ! [C_91,C_90] : ( double_divide(C_91,double_divide(C_90,C_91)) = C_90 ),
    inference(superposition,[status(thm),theory(equality)],[c_4185,c_3794]) ).

tff(c_6418,plain,
    ! [B_121,A_122] : ( multiply(B_121,A_122) = multiply(A_122,B_121) ),
    inference(superposition,[status(thm),theory(equality)],[c_6359,c_4]) ).

tff(c_289,plain,
    ! [A_21,B_10,A_11,C_23] : ( double_divide(double_divide(A_21,double_divide(double_divide(double_divide(double_divide(B_10,A_11),A_21),C_23),multiply(A_11,B_10))),inverse(identity)) = C_23 ),
    inference(superposition,[status(thm),theory(equality)],[c_37,c_236]) ).

tff(c_12726,plain,
    ! [A_186,A_187,B_188,C_189] : ( multiply(A_186,double_divide(multiply(A_187,B_188),double_divide(double_divide(double_divide(B_188,A_187),A_186),C_189))) = C_189 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6418,c_5822,c_37,c_6,c_705,c_289]) ).

tff(c_77301,plain,
    ! [A_502,B_503,A_504] : ( multiply(A_502,double_divide(double_divide(B_503,A_504),A_502)) = multiply(A_504,B_503) ),
    inference(superposition,[status(thm),theory(equality)],[c_4188,c_12726]) ).

tff(c_77671,plain,
    ! [B_297,A_296,C_298] : ( multiply(multiply(B_297,A_296),C_298) = multiply(multiply(A_296,B_297),C_298) ),
    inference(superposition,[status(thm),theory(equality)],[c_29407,c_77301]) ).

tff(c_77981,plain,
    ! [B_297,A_296,C_298] : ( multiply(B_297,multiply(A_296,C_298)) = multiply(A_296,multiply(B_297,C_298)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_43922,c_43922,c_77671]) ).

tff(c_61521,plain,
    ! [C_436,B_437,A_438] : ( double_divide(double_divide(C_436,multiply(B_437,A_438)),identity) = multiply(C_436,multiply(A_438,B_437)) ),
    inference(superposition,[status(thm),theory(equality)],[c_29031,c_4]) ).

tff(c_1938,plain,
    ! [C_23,C_57] : ( inverse(multiply(C_23,double_divide(C_23,C_57))) = C_57 ),
    inference(demodulation,[status(thm),theory(equality)],[c_926,c_1882]) ).

tff(c_3413,plain,
    ! [C_77] : ( inverse(inverse(C_77)) = C_77 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3314,c_877]) ).

tff(c_3470,plain,
    ! [C_23,C_57] : ( multiply(C_23,double_divide(C_23,C_57)) = inverse(C_57) ),
    inference(superposition,[status(thm),theory(equality)],[c_1938,c_3413]) ).

tff(c_5859,plain,
    ! [B_115,A_116] : ( multiply(B_115,double_divide(A_116,B_115)) = inverse(A_116) ),
    inference(superposition,[status(thm),theory(equality)],[c_5829,c_3470]) ).

tff(c_61631,plain,
    ! [C_436,A_438,B_437] : ( multiply(identity,multiply(C_436,multiply(A_438,B_437))) = inverse(double_divide(C_436,multiply(B_437,A_438))) ),
    inference(superposition,[status(thm),theory(equality)],[c_61521,c_5859]) ).

tff(c_62020,plain,
    ! [C_436,A_438,B_437] : ( multiply(C_436,multiply(A_438,B_437)) = multiply(B_437,multiply(A_438,C_436)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_43922,c_3331,c_37,c_61631]) ).

tff(c_10,plain,
    multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_6543,plain,
    multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_6418,c_10]) ).

tff(c_84534,plain,
    multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_62020,c_6543]) ).

tff(c_100435,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_77981,c_84534]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : GRP579-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 22:40:59 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 23.93/14.68  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.93/14.71  
% 23.93/14.71  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.93/14.75  
% 23.93/14.75  Inference rules
% 23.93/14.75  ----------------------
% 23.93/14.75  #Ref     : 0
% 23.93/14.75  #Sup     : 25464
% 23.93/14.75  #Fact    : 0
% 23.93/14.75  #Define  : 0
% 23.93/14.75  #Split   : 0
% 23.93/14.75  #Chain   : 0
% 23.93/14.75  #Close   : 0
% 23.93/14.75  
% 23.93/14.75  Ordering : KBO
% 23.93/14.75  
% 23.93/14.75  Simplification rules
% 23.93/14.75  ----------------------
% 23.93/14.75  #Subsume      : 1699
% 23.93/14.75  #Demod        : 43060
% 23.93/14.75  #Tautology    : 10469
% 23.93/14.75  #SimpNegUnit  : 0
% 23.93/14.75  #BackRed      : 95
% 23.93/14.75  
% 23.93/14.75  #Partial instantiations: 0
% 23.93/14.75  #Strategies tried      : 1
% 23.93/14.75  
% 23.93/14.75  Timing (in seconds)
% 23.93/14.75  ----------------------
% 23.93/14.75  Preprocessing        : 0.42
% 23.93/14.75  Parsing              : 0.22
% 23.93/14.75  CNF conversion       : 0.02
% 23.93/14.75  Main loop            : 13.24
% 23.93/14.75  Inferencing          : 1.62
% 23.93/14.75  Reduction            : 9.13
% 23.93/14.76  Demodulation         : 8.64
% 23.93/14.76  BG Simplification    : 0.21
% 23.93/14.76  Subsumption          : 1.71
% 23.93/14.76  Abstraction          : 0.39
% 23.93/14.76  MUC search           : 0.00
% 23.93/14.76  Cooper               : 0.00
% 23.93/14.76  Total                : 13.74
% 23.93/14.76  Index Insertion      : 0.00
% 23.93/14.76  Index Deletion       : 0.00
% 23.93/14.76  Index Matching       : 0.00
% 23.93/14.76  BG Taut test         : 0.00
%------------------------------------------------------------------------------