TSTP Solution File: RNG009-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : RNG009-7 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 10:54:42 EDT 2023

% Result   : Unsatisfiable 168.45s 137.18s
% Output   : CNFRefutation 168.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  173 ( 166 unt;   7 typ;   0 def)
%            Number of atoms       :  166 ( 165 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    6 (   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   :  202 (; 202   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > add > #nlpp > additive_inverse > c > b > additive_identity > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff(f_77,axiom,
    multiply(b,a) != c,
    file(unknown,unknown) ).

tff(f_75,axiom,
    multiply(a,b) = c,
    file(unknown,unknown) ).

tff(f_65,axiom,
    ! [X,Y,Z] : ( multiply(X,multiply(Y,Z)) = multiply(multiply(X,Y),Z) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ! [X] : ( multiply(X,multiply(X,X)) = X ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [X] : ( add(additive_inverse(X),X) = additive_identity ),
    file(unknown,unknown) ).

tff(f_49,axiom,
    ! [X] : ( add(additive_identity,X) = X ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Y,Z] : ( add(X,add(Y,Z)) = add(add(X,Y),Z) ),
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [X] : ( add(X,additive_identity) = X ),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X,Y] : ( add(X,Y) = add(Y,X) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [X,Y,Z] : ( multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)) ),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [X] : ( add(X,additive_inverse(X)) = additive_identity ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X,Y,Z] : ( multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)) ),
    file(unknown,unknown) ).

tff(c_24,plain,
    multiply(b,a) != c,
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_22,plain,
    multiply(a,b) = c,
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_14,plain,
    ! [X_10,Y_11,Z_12] : ( multiply(multiply(X_10,Y_11),Z_12) = multiply(X_10,multiply(Y_11,Z_12)) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_20,plain,
    ! [X_19] : ( multiply(X_19,multiply(X_19,X_19)) = X_19 ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_198,plain,
    ! [X_27,Y_28,Z_29] : ( multiply(multiply(X_27,Y_28),Z_29) = multiply(X_27,multiply(Y_28,Z_29)) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_221,plain,
    ! [X_19,Z_29] : ( multiply(X_19,multiply(multiply(X_19,X_19),Z_29)) = multiply(X_19,Z_29) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_198]) ).

tff(c_2138,plain,
    ! [X_68,Z_69] : ( multiply(X_68,multiply(X_68,multiply(X_68,Z_69))) = multiply(X_68,Z_69) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_221]) ).

tff(c_2205,plain,
    multiply(a,multiply(a,c)) = multiply(a,b),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_2138]) ).

tff(c_2224,plain,
    multiply(a,multiply(a,c)) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_2205]) ).

tff(c_6,plain,
    ! [X_3] : ( add(additive_inverse(X_3),X_3) = additive_identity ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_2,plain,
    ! [X_1] : ( add(additive_identity,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_262,plain,
    ! [X_31,Y_32,Z_33] : ( add(add(X_31,Y_32),Z_33) = add(X_31,add(Y_32,Z_33)) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_305,plain,
    ! [X_3,Z_33] : ( add(additive_inverse(X_3),add(X_3,Z_33)) = add(additive_identity,Z_33) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_262]) ).

tff(c_333,plain,
    ! [X_34,Z_35] : ( add(additive_inverse(X_34),add(X_34,Z_35)) = Z_35 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_305]) ).

tff(c_380,plain,
    ! [X_36] : ( add(additive_inverse(additive_inverse(X_36)),additive_identity) = X_36 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_333]) ).

tff(c_4,plain,
    ! [X_2] : ( add(X_2,additive_identity) = X_2 ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_398,plain,
    ! [X_36] : ( additive_inverse(additive_inverse(X_36)) = X_36 ),
    inference(superposition,[status(thm),theory(equality)],[c_380,c_4]) ).

tff(c_12,plain,
    ! [Y_9,X_8] : ( add(Y_9,X_8) = add(X_8,Y_9) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_517,plain,
    ! [X_41,Y_42,Z_43] : ( add(multiply(X_41,Y_42),multiply(X_41,Z_43)) = multiply(X_41,add(Y_42,Z_43)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_573,plain,
    ! [X_19,Y_42] : ( multiply(X_19,add(Y_42,multiply(X_19,X_19))) = add(multiply(X_19,Y_42),X_19) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_517]) ).

tff(c_10113,plain,
    ! [X_131,Y_132] : ( multiply(X_131,add(Y_132,multiply(X_131,X_131))) = add(X_131,multiply(X_131,Y_132)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_573]) ).

tff(c_10272,plain,
    ! [X_131] : ( multiply(X_131,multiply(X_131,X_131)) = add(X_131,multiply(X_131,additive_identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_10113]) ).

tff(c_10298,plain,
    ! [X_133] : ( add(X_133,multiply(X_133,additive_identity)) = X_133 ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_10272]) ).

tff(c_328,plain,
    ! [X_3,Z_33] : ( add(additive_inverse(X_3),add(X_3,Z_33)) = Z_33 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_305]) ).

tff(c_10403,plain,
    ! [X_133] : ( add(additive_inverse(X_133),X_133) = multiply(X_133,additive_identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_10298,c_328]) ).

tff(c_10483,plain,
    ! [X_133] : ( multiply(X_133,additive_identity) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_10403]) ).

tff(c_8,plain,
    ! [X_4] : ( add(X_4,additive_inverse(X_4)) = additive_identity ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_48271,plain,
    ! [X_290,Y_291,Z_292] : ( add(additive_inverse(multiply(X_290,Y_291)),multiply(X_290,add(Y_291,Z_292))) = multiply(X_290,Z_292) ),
    inference(superposition,[status(thm),theory(equality)],[c_517,c_328]) ).

tff(c_48955,plain,
    ! [X_290,X_4] : ( add(additive_inverse(multiply(X_290,X_4)),multiply(X_290,additive_identity)) = multiply(X_290,additive_inverse(X_4)) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_48271]) ).

tff(c_49071,plain,
    ! [X_290,X_4] : ( multiply(X_290,additive_inverse(X_4)) = additive_inverse(multiply(X_290,X_4)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_10483,c_48955]) ).

tff(c_10500,plain,
    ! [X_134] : ( multiply(X_134,additive_identity) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_10403]) ).

tff(c_10560,plain,
    ! [X_134,Z_12] : ( multiply(X_134,multiply(additive_identity,Z_12)) = multiply(additive_identity,Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_10500,c_14]) ).

tff(c_452,plain,
    ! [X_38,Z_39,Y_40] : ( add(multiply(X_38,Z_39),multiply(Y_40,Z_39)) = multiply(add(X_38,Y_40),Z_39) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_11434,plain,
    ! [X_142,Y_143] : ( multiply(add(X_142,Y_143),multiply(X_142,X_142)) = add(X_142,multiply(Y_143,multiply(X_142,X_142))) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_452]) ).

tff(c_11586,plain,
    ! [X_2] : ( add(X_2,multiply(additive_identity,multiply(X_2,X_2))) = multiply(X_2,multiply(X_2,X_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_11434]) ).

tff(c_11607,plain,
    ! [X_144] : ( add(X_144,multiply(additive_identity,multiply(X_144,X_144))) = X_144 ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_11586]) ).

tff(c_11711,plain,
    ! [X_144] : ( multiply(additive_identity,multiply(X_144,X_144)) = add(additive_inverse(X_144),X_144) ),
    inference(superposition,[status(thm),theory(equality)],[c_11607,c_328]) ).

tff(c_11820,plain,
    ! [X_145] : ( multiply(additive_identity,multiply(X_145,X_145)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_11711]) ).

tff(c_12436,plain,
    ! [Z_149] : ( multiply(additive_identity,multiply(additive_identity,Z_149)) = additive_identity ),
    inference(superposition,[status(thm),theory(equality)],[c_10560,c_11820]) ).

tff(c_12449,plain,
    ! [Z_149] : ( multiply(additive_identity,Z_149) = additive_identity ),
    inference(superposition,[status(thm),theory(equality)],[c_12436,c_10560]) ).

tff(c_10,plain,
    ! [X_5,Y_6,Z_7] : ( add(add(X_5,Y_6),Z_7) = add(X_5,add(Y_6,Z_7)) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_15845,plain,
    ! [X_170,Z_171,Y_172,Z_173] : ( add(multiply(X_170,Z_171),add(multiply(Y_172,Z_171),Z_173)) = add(multiply(add(X_170,Y_172),Z_171),Z_173) ),
    inference(superposition,[status(thm),theory(equality)],[c_452,c_10]) ).

tff(c_16255,plain,
    ! [X_170,Y_172,Z_171] : ( add(multiply(add(X_170,Y_172),Z_171),additive_inverse(multiply(Y_172,Z_171))) = add(multiply(X_170,Z_171),additive_identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_15845]) ).

tff(c_44241,plain,
    ! [X_277,Y_278,Z_279] : ( add(multiply(add(X_277,Y_278),Z_279),additive_inverse(multiply(Y_278,Z_279))) = multiply(X_277,Z_279) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_16255]) ).

tff(c_44964,plain,
    ! [Z_279,X_3] : ( add(multiply(additive_identity,Z_279),additive_inverse(multiply(X_3,Z_279))) = multiply(additive_inverse(X_3),Z_279) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_44241]) ).

tff(c_45064,plain,
    ! [X_3,Z_279] : ( multiply(additive_inverse(X_3),Z_279) = additive_inverse(multiply(X_3,Z_279)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_12449,c_44964]) ).

tff(c_57,plain,
    ! [X_22] : ( add(X_22,additive_inverse(X_22)) = additive_identity ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_69,plain,
    additive_inverse(additive_identity) = additive_identity,
    inference(superposition,[status(thm),theory(equality)],[c_2,c_57]) ).

tff(c_506,plain,
    ! [X_38] : ( multiply(add(X_38,a),b) = add(multiply(X_38,b),c) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_452]) ).

tff(c_5865,plain,
    ! [X_99] : ( multiply(add(X_99,a),b) = add(c,multiply(X_99,b)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_506]) ).

tff(c_5945,plain,
    add(c,multiply(additive_identity,b)) = multiply(a,b),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_5865]) ).

tff(c_5953,plain,
    add(c,multiply(additive_identity,b)) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_5945]) ).

tff(c_6002,plain,
    add(additive_inverse(c),c) = multiply(additive_identity,b),
    inference(superposition,[status(thm),theory(equality)],[c_5953,c_328]) ).

tff(c_6016,plain,
    multiply(additive_identity,b) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6002]) ).

tff(c_5941,plain,
    add(c,multiply(additive_inverse(a),b)) = multiply(additive_identity,b),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_5865]) ).

tff(c_6253,plain,
    add(c,multiply(additive_inverse(a),b)) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6016,c_5941]) ).

tff(c_666,plain,
    ! [X_46,Y_47] : ( add(additive_inverse(X_46),add(Y_47,X_46)) = Y_47 ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_333]) ).

tff(c_714,plain,
    ! [X_3,Z_33] : ( add(additive_inverse(add(X_3,Z_33)),Z_33) = additive_inverse(X_3) ),
    inference(superposition,[status(thm),theory(equality)],[c_328,c_666]) ).

tff(c_6284,plain,
    add(additive_inverse(additive_identity),multiply(additive_inverse(a),b)) = additive_inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_6253,c_714]) ).

tff(c_6317,plain,
    multiply(additive_inverse(a),b) = additive_inverse(c),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_69,c_6284]) ).

tff(c_6344,plain,
    ! [Z_12] : ( multiply(additive_inverse(a),multiply(b,Z_12)) = multiply(additive_inverse(c),Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_6317,c_14]) ).

tff(c_45074,plain,
    ! [Z_12] : ( multiply(additive_inverse(a),multiply(b,Z_12)) = additive_inverse(multiply(c,Z_12)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_45064,c_6344]) ).

tff(c_862,plain,
    ! [X_50,Y_51] : ( add(X_50,add(Y_51,additive_inverse(add(X_50,Y_51)))) = additive_identity ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_262]) ).

tff(c_881,plain,
    ! [Y_51,X_50] : ( add(Y_51,additive_inverse(add(X_50,Y_51))) = add(additive_inverse(X_50),additive_identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_862,c_328]) ).

tff(c_969,plain,
    ! [Y_51,X_50] : ( add(Y_51,additive_inverse(add(X_50,Y_51))) = additive_inverse(X_50) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_881]) ).

tff(c_16333,plain,
    ! [X_174,Z_175,X_176,Y_177] : ( add(multiply(X_174,Z_175),multiply(X_176,multiply(Y_177,Z_175))) = multiply(add(X_174,multiply(X_176,Y_177)),Z_175) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_452]) ).

tff(c_16711,plain,
    ! [X_174,X_19] : ( multiply(add(X_174,multiply(X_19,X_19)),X_19) = add(multiply(X_174,X_19),X_19) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_16333]) ).

tff(c_37924,plain,
    ! [X_256,X_257] : ( multiply(add(X_256,multiply(X_257,X_257)),X_257) = add(X_257,multiply(X_256,X_257)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_16711]) ).

tff(c_38170,plain,
    ! [X_257] : ( add(X_257,multiply(additive_inverse(multiply(X_257,X_257)),X_257)) = multiply(additive_identity,X_257) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_37924]) ).

tff(c_38389,plain,
    ! [X_259] : ( add(X_259,multiply(additive_inverse(multiply(X_259,X_259)),X_259)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_12449,c_38170]) ).

tff(c_3226,plain,
    ! [X_81,Y_82,Z_83] : ( add(add(X_81,Y_82),Z_83) = add(Y_82,add(X_81,Z_83)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_262]) ).

tff(c_3324,plain,
    ! [X_81,Y_82,Z_83] : ( add(additive_inverse(add(X_81,Y_82)),add(Y_82,add(X_81,Z_83))) = Z_83 ),
    inference(superposition,[status(thm),theory(equality)],[c_3226,c_328]) ).

tff(c_38458,plain,
    ! [X_259,Y_82] : ( multiply(additive_inverse(multiply(X_259,X_259)),X_259) = add(additive_inverse(add(X_259,Y_82)),add(Y_82,additive_identity)) ),
    inference(superposition,[status(thm),theory(equality)],[c_38389,c_3324]) ).

tff(c_38714,plain,
    ! [X_259] : ( multiply(additive_inverse(multiply(X_259,X_259)),X_259) = additive_inverse(X_259) ),
    inference(demodulation,[status(thm),theory(equality)],[c_969,c_12,c_4,c_38458]) ).

tff(c_564,plain,
    ! [X_41,Z_43,Y_42] : ( add(multiply(X_41,Z_43),multiply(X_41,Y_42)) = multiply(X_41,add(Y_42,Z_43)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_517]) ).

tff(c_17726,plain,
    ! [X_181,Y_182,Z_183,Y_184] : ( add(multiply(X_181,multiply(Y_182,Z_183)),multiply(Y_184,Z_183)) = multiply(add(multiply(X_181,Y_182),Y_184),Z_183) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_452]) ).

tff(c_17978,plain,
    ! [X_41,Y_182,Y_42] : ( multiply(add(multiply(X_41,Y_182),X_41),Y_42) = multiply(X_41,add(Y_42,multiply(Y_182,Y_42))) ),
    inference(superposition,[status(thm),theory(equality)],[c_564,c_17726]) ).

tff(c_91198,plain,
    ! [X_396,Y_397,Y_398] : ( multiply(add(X_396,multiply(X_396,Y_397)),Y_398) = multiply(X_396,add(Y_398,multiply(Y_397,Y_398))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_17978]) ).

tff(c_91749,plain,
    ! [X_396,X_259] : ( multiply(add(X_396,multiply(X_396,additive_inverse(multiply(X_259,X_259)))),X_259) = multiply(X_396,add(X_259,additive_inverse(X_259))) ),
    inference(superposition,[status(thm),theory(equality)],[c_38714,c_91198]) ).

tff(c_298329,plain,
    ! [X_701,X_702] : ( multiply(add(X_701,additive_inverse(multiply(X_701,multiply(X_702,X_702)))),X_702) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_49071,c_10483,c_8,c_91749]) ).

tff(c_298881,plain,
    multiply(add(additive_inverse(a),additive_inverse(additive_inverse(multiply(c,b)))),b) = additive_identity,
    inference(superposition,[status(thm),theory(equality)],[c_45074,c_298329]) ).

tff(c_299179,plain,
    multiply(add(additive_inverse(a),multiply(c,b)),b) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_298881]) ).

tff(c_299416,plain,
    ! [Z_12] : ( multiply(add(additive_inverse(a),multiply(c,b)),multiply(b,Z_12)) = multiply(additive_identity,Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_299179,c_14]) ).

tff(c_330168,plain,
    ! [Z_736] : ( multiply(add(additive_inverse(a),multiply(c,b)),multiply(b,Z_736)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_12449,c_299416]) ).

tff(c_228,plain,
    ! [Z_29] : ( multiply(a,multiply(b,Z_29)) = multiply(c,Z_29) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_198]) ).

tff(c_225,plain,
    ! [X_27,Y_28] : ( multiply(X_27,multiply(Y_28,multiply(multiply(X_27,Y_28),multiply(X_27,Y_28)))) = multiply(X_27,Y_28) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_198]) ).

tff(c_14546,plain,
    ! [X_161,Y_162] : ( multiply(X_161,multiply(Y_162,multiply(X_161,multiply(Y_162,multiply(X_161,Y_162))))) = multiply(X_161,Y_162) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_225]) ).

tff(c_14601,plain,
    ! [Y_162] : ( multiply(c,multiply(Y_162,multiply(b,multiply(Y_162,multiply(b,Y_162))))) = multiply(a,multiply(b,Y_162)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14546,c_228]) ).

tff(c_14775,plain,
    ! [Y_162] : ( multiply(c,multiply(Y_162,multiply(b,multiply(Y_162,multiply(b,Y_162))))) = multiply(c,Y_162) ),
    inference(demodulation,[status(thm),theory(equality)],[c_228,c_14601]) ).

tff(c_330306,plain,
    multiply(c,multiply(add(additive_inverse(a),multiply(c,b)),multiply(b,additive_identity))) = multiply(c,add(additive_inverse(a),multiply(c,b))),
    inference(superposition,[status(thm),theory(equality)],[c_330168,c_14775]) ).

tff(c_330669,plain,
    multiply(c,add(additive_inverse(a),multiply(c,b))) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10483,c_10483,c_10483,c_330306]) ).

tff(c_527,plain,
    ! [X_41,Y_42,Z_43] : ( add(additive_inverse(multiply(X_41,Y_42)),multiply(X_41,add(Y_42,Z_43))) = multiply(X_41,Z_43) ),
    inference(superposition,[status(thm),theory(equality)],[c_517,c_328]) ).

tff(c_330885,plain,
    add(additive_inverse(multiply(c,additive_inverse(a))),additive_identity) = multiply(c,multiply(c,b)),
    inference(superposition,[status(thm),theory(equality)],[c_330669,c_527]) ).

tff(c_331010,plain,
    multiply(c,multiply(c,b)) = multiply(c,a),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_4,c_49071,c_330885]) ).

tff(c_234,plain,
    ! [X_19,Z_29] : ( multiply(X_19,multiply(X_19,multiply(X_19,Z_29))) = multiply(X_19,Z_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_221]) ).

tff(c_331260,plain,
    multiply(c,multiply(c,a)) = multiply(c,b),
    inference(superposition,[status(thm),theory(equality)],[c_331010,c_234]) ).

tff(c_1649,plain,
    ! [Y_62,X_63] : ( add(Y_62,additive_inverse(add(X_63,Y_62))) = additive_inverse(X_63) ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_881]) ).

tff(c_308,plain,
    ! [X_4,Z_33] : ( add(X_4,add(additive_inverse(X_4),Z_33)) = add(additive_identity,Z_33) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_262]) ).

tff(c_329,plain,
    ! [X_4,Z_33] : ( add(X_4,add(additive_inverse(X_4),Z_33)) = Z_33 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_308]) ).

tff(c_1686,plain,
    ! [X_63,X_4] : ( additive_inverse(add(X_63,additive_inverse(X_4))) = add(X_4,additive_inverse(X_63)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1649,c_329]) ).

tff(c_1689,plain,
    ! [Y_62,X_63] : ( add(additive_inverse(Y_62),additive_inverse(X_63)) = additive_inverse(add(X_63,Y_62)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1649,c_328]) ).

tff(c_5534,plain,
    ! [Z_97] : ( multiply(a,add(b,Z_97)) = add(c,multiply(a,Z_97)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_517]) ).

tff(c_5606,plain,
    add(c,multiply(a,additive_identity)) = multiply(a,b),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5534]) ).

tff(c_5612,plain,
    add(c,multiply(a,additive_identity)) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_5606]) ).

tff(c_5661,plain,
    add(additive_inverse(c),c) = multiply(a,additive_identity),
    inference(superposition,[status(thm),theory(equality)],[c_5612,c_328]) ).

tff(c_5675,plain,
    multiply(a,additive_identity) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_5661]) ).

tff(c_5602,plain,
    add(c,multiply(a,additive_inverse(b))) = multiply(a,additive_identity),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_5534]) ).

tff(c_5764,plain,
    add(c,multiply(a,additive_inverse(b))) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_5675,c_5602]) ).

tff(c_5795,plain,
    add(additive_inverse(additive_identity),multiply(a,additive_inverse(b))) = additive_inverse(c),
    inference(superposition,[status(thm),theory(equality)],[c_5764,c_714]) ).

tff(c_5828,plain,
    multiply(a,additive_inverse(b)) = additive_inverse(c),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_69,c_5795]) ).

tff(c_16,plain,
    ! [X_13,Y_14,Z_15] : ( add(multiply(X_13,Y_14),multiply(X_13,Z_15)) = multiply(X_13,add(Y_14,Z_15)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_8289,plain,
    ! [X_116,Z_117,Y_118] : ( add(multiply(X_116,Z_117),multiply(X_116,Y_118)) = multiply(X_116,add(Y_118,Z_117)) ),
    inference(superposition,[status(thm),theory(equality)],[c_12,c_517]) ).

tff(c_8536,plain,
    ! [X_19,Y_118,Z_29] : ( multiply(X_19,add(Y_118,multiply(X_19,multiply(X_19,Z_29)))) = add(multiply(X_19,Z_29),multiply(X_19,Y_118)) ),
    inference(superposition,[status(thm),theory(equality)],[c_234,c_8289]) ).

tff(c_94758,plain,
    ! [X_405,Y_406,Z_407] : ( multiply(X_405,add(Y_406,multiply(X_405,multiply(X_405,Z_407)))) = multiply(X_405,add(Z_407,Y_406)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_8536]) ).

tff(c_95367,plain,
    ! [X_405,Z_407] : ( multiply(X_405,add(Z_407,additive_inverse(multiply(X_405,multiply(X_405,Z_407))))) = multiply(X_405,additive_identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_94758]) ).

tff(c_96753,plain,
    ! [X_411,Z_412] : ( multiply(X_411,add(Z_412,additive_inverse(multiply(X_411,multiply(X_411,Z_412))))) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_10483,c_95367]) ).

tff(c_97214,plain,
    multiply(a,add(additive_inverse(b),additive_inverse(multiply(a,additive_inverse(c))))) = additive_identity,
    inference(superposition,[status(thm),theory(equality)],[c_5828,c_96753]) ).

tff(c_97394,plain,
    multiply(a,add(additive_inverse(b),multiply(a,c))) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_1686,c_49071,c_12,c_1689,c_97214]) ).

tff(c_97668,plain,
    ! [Z_12] : ( multiply(a,multiply(add(additive_inverse(b),multiply(a,c)),Z_12)) = multiply(additive_identity,Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_97394,c_14]) ).

tff(c_264108,plain,
    ! [Z_654] : ( multiply(a,multiply(add(additive_inverse(b),multiply(a,c)),Z_654)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_12449,c_97668]) ).

tff(c_235,plain,
    ! [X_27,Y_28] : ( multiply(X_27,multiply(Y_28,multiply(X_27,multiply(Y_28,multiply(X_27,Y_28))))) = multiply(X_27,Y_28) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_225]) ).

tff(c_264255,plain,
    multiply(add(additive_inverse(b),multiply(a,c)),multiply(a,multiply(add(additive_inverse(b),multiply(a,c)),additive_identity))) = multiply(add(additive_inverse(b),multiply(a,c)),a),
    inference(superposition,[status(thm),theory(equality)],[c_264108,c_235]) ).

tff(c_264512,plain,
    multiply(add(additive_inverse(b),multiply(a,c)),a) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10483,c_10483,c_10483,c_264255]) ).

tff(c_264732,plain,
    ! [Z_12] : ( multiply(add(additive_inverse(b),multiply(a,c)),multiply(a,Z_12)) = multiply(additive_identity,Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_264512,c_14]) ).

tff(c_286550,plain,
    ! [Z_687] : ( multiply(add(additive_inverse(b),multiply(a,c)),multiply(a,Z_687)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_12449,c_264732]) ).

tff(c_286996,plain,
    multiply(add(additive_inverse(b),multiply(a,c)),c) = additive_identity,
    inference(superposition,[status(thm),theory(equality)],[c_2224,c_286550]) ).

tff(c_458,plain,
    ! [X_38,Z_39,Y_40] : ( add(additive_inverse(multiply(X_38,Z_39)),multiply(add(X_38,Y_40),Z_39)) = multiply(Y_40,Z_39) ),
    inference(superposition,[status(thm),theory(equality)],[c_452,c_328]) ).

tff(c_287218,plain,
    add(additive_inverse(multiply(additive_inverse(b),c)),additive_identity) = multiply(multiply(a,c),c),
    inference(superposition,[status(thm),theory(equality)],[c_286996,c_458]) ).

tff(c_287335,plain,
    multiply(a,multiply(c,c)) = multiply(b,c),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_4,c_45064,c_14,c_287218]) ).

tff(c_311365,plain,
    ! [Z_714] : ( multiply(add(additive_inverse(b),multiply(a,c)),multiply(c,Z_714)) = additive_identity ),
    inference(superposition,[status(thm),theory(equality)],[c_228,c_286550]) ).

tff(c_311566,plain,
    multiply(c,multiply(add(additive_inverse(b),multiply(a,c)),multiply(c,additive_identity))) = multiply(c,add(additive_inverse(b),multiply(a,c))),
    inference(superposition,[status(thm),theory(equality)],[c_311365,c_235]) ).

tff(c_311883,plain,
    multiply(c,add(additive_inverse(b),multiply(a,c))) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10483,c_10483,c_10483,c_311566]) ).

tff(c_312074,plain,
    add(additive_inverse(multiply(c,additive_inverse(b))),additive_identity) = multiply(c,multiply(a,c)),
    inference(superposition,[status(thm),theory(equality)],[c_311883,c_527]) ).

tff(c_312196,plain,
    multiply(c,multiply(a,c)) = multiply(c,b),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_4,c_49071,c_312074]) ).

tff(c_2185,plain,
    ! [Z_29] : ( multiply(a,multiply(a,multiply(c,Z_29))) = multiply(a,multiply(b,Z_29)) ),
    inference(superposition,[status(thm),theory(equality)],[c_228,c_2138]) ).

tff(c_20430,plain,
    ! [Z_192] : ( multiply(a,multiply(a,multiply(c,Z_192))) = multiply(c,Z_192) ),
    inference(demodulation,[status(thm),theory(equality)],[c_228,c_2185]) ).

tff(c_20533,plain,
    multiply(c,multiply(a,multiply(c,multiply(a,c)))) = multiply(a,multiply(a,c)),
    inference(superposition,[status(thm),theory(equality)],[c_235,c_20430]) ).

tff(c_20592,plain,
    multiply(c,multiply(a,multiply(c,multiply(a,c)))) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_2224,c_20533]) ).

tff(c_312223,plain,
    multiply(c,multiply(a,multiply(c,b))) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_312196,c_20592]) ).

tff(c_334111,plain,
    multiply(c,multiply(multiply(c,a),multiply(c,multiply(multiply(c,a),multiply(c,b))))) = multiply(c,multiply(c,a)),
    inference(superposition,[status(thm),theory(equality)],[c_331260,c_235]) ).

tff(c_334186,plain,
    multiply(c,multiply(c,multiply(b,c))) = multiply(c,b),
    inference(demodulation,[status(thm),theory(equality)],[c_331260,c_287335,c_312223,c_14,c_14,c_334111]) ).

tff(c_338659,plain,
    multiply(c,multiply(c,b)) = multiply(c,multiply(b,c)),
    inference(superposition,[status(thm),theory(equality)],[c_334186,c_234]) ).

tff(c_338718,plain,
    multiply(c,multiply(b,c)) = multiply(c,a),
    inference(demodulation,[status(thm),theory(equality)],[c_331010,c_338659]) ).

tff(c_330960,plain,
    ! [Z_12] : ( multiply(c,multiply(add(additive_inverse(a),multiply(c,b)),Z_12)) = multiply(additive_identity,Z_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_330669,c_14]) ).

tff(c_360063,plain,
    ! [Z_761] : ( multiply(c,multiply(add(additive_inverse(a),multiply(c,b)),Z_761)) = additive_identity ),
    inference(demodulation,[status(thm),theory(equality)],[c_12449,c_330960]) ).

tff(c_360287,plain,
    multiply(add(additive_inverse(a),multiply(c,b)),multiply(c,multiply(add(additive_inverse(a),multiply(c,b)),additive_identity))) = multiply(add(additive_inverse(a),multiply(c,b)),c),
    inference(superposition,[status(thm),theory(equality)],[c_360063,c_235]) ).

tff(c_360613,plain,
    multiply(add(additive_inverse(a),multiply(c,b)),c) = additive_identity,
    inference(demodulation,[status(thm),theory(equality)],[c_10483,c_10483,c_10483,c_360287]) ).

tff(c_360813,plain,
    add(additive_inverse(multiply(additive_inverse(a),c)),additive_identity) = multiply(multiply(c,b),c),
    inference(superposition,[status(thm),theory(equality)],[c_360613,c_458]) ).

tff(c_360939,plain,
    multiply(c,a) = multiply(a,c),
    inference(demodulation,[status(thm),theory(equality)],[c_338718,c_398,c_4,c_45064,c_14,c_360813]) ).

tff(c_264651,plain,
    add(additive_inverse(multiply(additive_inverse(b),a)),additive_identity) = multiply(multiply(a,c),a),
    inference(superposition,[status(thm),theory(equality)],[c_264512,c_458]) ).

tff(c_264761,plain,
    multiply(a,multiply(c,a)) = multiply(b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_4,c_45064,c_14,c_264651]) ).

tff(c_360973,plain,
    multiply(a,multiply(a,c)) = multiply(b,a),
    inference(demodulation,[status(thm),theory(equality)],[c_360939,c_264761]) ).

tff(c_360978,plain,
    multiply(b,a) = c,
    inference(demodulation,[status(thm),theory(equality)],[c_2224,c_360973]) ).

tff(c_360980,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_360978]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : RNG009-7 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 17:58:56 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 168.45/137.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 168.45/137.20  
% 168.45/137.20  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 168.71/137.25  
% 168.71/137.25  Inference rules
% 168.71/137.25  ----------------------
% 168.71/137.25  #Ref     : 0
% 168.71/137.25  #Sup     : 90454
% 168.71/137.25  #Fact    : 0
% 168.71/137.25  #Define  : 0
% 168.71/137.25  #Split   : 0
% 168.71/137.25  #Chain   : 0
% 168.71/137.25  #Close   : 0
% 168.71/137.25  
% 168.71/137.25  Ordering : KBO
% 168.71/137.25  
% 168.71/137.25  Simplification rules
% 168.71/137.25  ----------------------
% 168.71/137.25  #Subsume      : 7464
% 168.71/137.25  #Demod        : 167283
% 168.71/137.25  #Tautology    : 22334
% 168.71/137.25  #SimpNegUnit  : 1
% 168.71/137.25  #BackRed      : 65
% 168.71/137.25  
% 168.71/137.25  #Partial instantiations: 0
% 168.71/137.25  #Strategies tried      : 1
% 168.71/137.25  
% 168.71/137.25  Timing (in seconds)
% 168.71/137.25  ----------------------
% 168.71/137.25  Preprocessing        : 0.43
% 168.71/137.25  Parsing              : 0.22
% 168.71/137.25  CNF conversion       : 0.02
% 168.71/137.25  Main loop            : 135.62
% 168.71/137.25  Inferencing          : 8.12
% 168.71/137.25  Reduction            : 106.83
% 168.71/137.25  Demodulation         : 103.94
% 168.71/137.25  BG Simplification    : 1.30
% 168.71/137.25  Subsumption          : 13.58
% 168.71/137.25  Abstraction          : 3.26
% 168.71/137.25  MUC search           : 0.00
% 168.71/137.25  Cooper               : 0.00
% 168.71/137.25  Total                : 136.13
% 168.71/137.25  Index Insertion      : 0.00
% 168.71/137.25  Index Deletion       : 0.00
% 168.71/137.25  Index Matching       : 0.00
% 168.71/137.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------