TSTP Solution File: GRP095-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP095-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n016.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 10:39:49 EDT 2023

% Result   : Unsatisfiable 18.79s 8.91s
% Output   : CNFRefutation 18.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   86 (  69 unt;  13 typ;   0 def)
%            Number of atoms       :   82 (  80 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   27 (  18   ~;   9   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    5 (   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    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :  110 (; 110   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > divide > #nlpp > inverse > identity > c3 > b4 > b3 > b2 > b1 > a4 > a3 > a2 > a1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a1,type,
    a1: $i ).

tff(a3,type,
    a3: $i ).

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

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

tff(b2,type,
    b2: $i ).

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

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

tff(b1,type,
    b1: $i ).

tff(b4,type,
    b4: $i ).

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

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

tff(a4,type,
    a4: $i ).

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

tff(f_33,axiom,
    ! [X] : ( inverse(X) = divide(identity,X) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [X,Y] : ( multiply(X,Y) = divide(X,divide(identity,Y)) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [X] : ( identity = divide(X,X) ),
    file(unknown,unknown) ).

tff(f_27,axiom,
    ! [X,Y,Z] : ( divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y)) = Z ),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ( ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(a4,b4) != multiply(b4,a4) ) ),
    file(unknown,unknown) ).

tff(c_6,plain,
    ! [X_6] : ( divide(identity,X_6) = inverse(X_6) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_4,plain,
    ! [X_4,Y_5] : ( divide(X_4,divide(identity,Y_5)) = multiply(X_4,Y_5) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_11,plain,
    ! [X_4,Y_5] : ( divide(X_4,inverse(Y_5)) = multiply(X_4,Y_5) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).

tff(c_8,plain,
    ! [X_7] : ( divide(X_7,X_7) = identity ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_20,plain,
    ! [X_9] : ( divide(identity,X_9) = inverse(X_9) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_27,plain,
    inverse(identity) = identity,
    inference(superposition,[status(thm),theory(equality)],[c_20,c_8]) ).

tff(c_2,plain,
    ! [X_1,Y_2,Z_3] : ( divide(divide(identity,X_1),divide(divide(divide(Y_2,X_1),Z_3),Y_2)) = Z_3 ),
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_70,plain,
    ! [X_12,Y_13,Z_14] : ( divide(inverse(X_12),divide(divide(divide(Y_13,X_12),Z_14),Y_13)) = Z_14 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).

tff(c_106,plain,
    ! [X_12,Y_13] : ( divide(inverse(X_12),divide(identity,Y_13)) = divide(Y_13,X_12) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_70]) ).

tff(c_727,plain,
    ! [X_35,Y_36] : ( multiply(inverse(X_35),Y_36) = divide(Y_36,X_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_106]) ).

tff(c_754,plain,
    ! [Y_36] : ( multiply(identity,Y_36) = divide(Y_36,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_727]) ).

tff(c_42,plain,
    ! [X_10,Y_11] : ( divide(X_10,inverse(Y_11)) = multiply(X_10,Y_11) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4]) ).

tff(c_63,plain,
    ! [Y_11] : ( inverse(inverse(Y_11)) = multiply(identity,Y_11) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_42]) ).

tff(c_762,plain,
    ! [Y_11] : ( inverse(inverse(Y_11)) = divide(Y_11,identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_754,c_63]) ).

tff(c_59,plain,
    ! [X_10] : ( multiply(X_10,identity) = divide(X_10,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_42]) ).

tff(c_745,plain,
    ! [X_35] : ( divide(inverse(X_35),identity) = divide(identity,X_35) ),
    inference(superposition,[status(thm),theory(equality)],[c_59,c_727]) ).

tff(c_759,plain,
    ! [X_35] : ( divide(inverse(X_35),identity) = inverse(X_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_745]) ).

tff(c_957,plain,
    ! [X_43,Z_44] : ( divide(inverse(X_43),divide(divide(inverse(X_43),Z_44),identity)) = Z_44 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_70]) ).

tff(c_1001,plain,
    ! [Z_44] : ( divide(identity,divide(divide(inverse(identity),Z_44),identity)) = Z_44 ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_957]) ).

tff(c_1017,plain,
    ! [Z_44] : ( divide(Z_44,identity) = Z_44 ),
    inference(demodulation,[status(thm),theory(equality)],[c_762,c_759,c_6,c_6,c_27,c_1001]) ).

tff(c_1023,plain,
    ! [Y_11] : ( inverse(inverse(Y_11)) = Y_11 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1017,c_762]) ).

tff(c_85,plain,
    ! [Y_5,X_4,Z_14] : ( divide(inverse(inverse(Y_5)),divide(divide(multiply(X_4,Y_5),Z_14),X_4)) = Z_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_11,c_70]) ).

tff(c_1404,plain,
    ! [Y_56,X_57,Z_58] : ( divide(Y_56,divide(divide(multiply(X_57,Y_56),Z_58),X_57)) = Z_58 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1023,c_85]) ).

tff(c_1482,plain,
    ! [Y_56,X_57] : ( divide(Y_56,divide(identity,X_57)) = multiply(X_57,Y_56) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1404]) ).

tff(c_1493,plain,
    ! [Y_56,X_57] : ( multiply(Y_56,X_57) = multiply(X_57,Y_56) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_1482]) ).

tff(c_102,plain,
    ! [X_7,Z_14] : ( divide(inverse(X_7),divide(divide(identity,Z_14),X_7)) = Z_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_70]) ).

tff(c_111,plain,
    ! [X_7,Z_14] : ( divide(inverse(X_7),divide(inverse(Z_14),X_7)) = Z_14 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_102]) ).

tff(c_928,plain,
    ! [X_42] : ( divide(inverse(X_42),identity) = inverse(X_42) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_745]) ).

tff(c_12,plain,
    ! [X_1,Y_2,Z_3] : ( divide(inverse(X_1),divide(divide(divide(Y_2,X_1),Z_3),Y_2)) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2]) ).

tff(c_940,plain,
    ! [X_42,Z_3] : ( divide(inverse(identity),divide(divide(inverse(X_42),Z_3),inverse(X_42))) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_928,c_12]) ).

tff(c_953,plain,
    ! [X_42,Z_3] : ( inverse(multiply(divide(inverse(X_42),Z_3),X_42)) = Z_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_27,c_11,c_940]) ).

tff(c_4067,plain,
    ! [X_102,Z_103] : ( inverse(multiply(X_102,divide(inverse(X_102),Z_103))) = Z_103 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1493,c_953]) ).

tff(c_4189,plain,
    ! [Z_14,X_7] : ( divide(inverse(Z_14),X_7) = inverse(multiply(X_7,Z_14)) ),
    inference(superposition,[status(thm),theory(equality)],[c_111,c_4067]) ).

tff(c_1075,plain,
    ! [Y_46] : ( inverse(inverse(Y_46)) = Y_46 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1017,c_762]) ).

tff(c_112,plain,
    ! [X_12,Y_13] : ( multiply(inverse(X_12),Y_13) = divide(Y_13,X_12) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_106]) ).

tff(c_1783,plain,
    ! [Y_65,Y_66] : ( divide(Y_65,inverse(Y_66)) = multiply(Y_66,Y_65) ),
    inference(superposition,[status(thm),theory(equality)],[c_1075,c_112]) ).

tff(c_1084,plain,
    ! [Y_46,Z_14] : ( divide(Y_46,divide(inverse(Z_14),inverse(Y_46))) = Z_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_1075,c_111]) ).

tff(c_1111,plain,
    ! [Y_46,Z_14] : ( divide(Y_46,divide(Y_46,Z_14)) = Z_14 ),
    inference(demodulation,[status(thm),theory(equality)],[c_112,c_11,c_1084]) ).

tff(c_1808,plain,
    ! [Y_65,Y_66] : ( divide(Y_65,multiply(Y_66,Y_65)) = inverse(Y_66) ),
    inference(superposition,[status(thm),theory(equality)],[c_1783,c_1111]) ).

tff(c_1822,plain,
    ! [Y_66,Y_65,Z_3] : ( divide(inverse(inverse(Y_66)),divide(divide(multiply(Y_66,Y_65),Z_3),Y_65)) = Z_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_1783,c_12]) ).

tff(c_20369,plain,
    ! [Y_232,Y_233,Z_234] : ( divide(Y_232,divide(divide(multiply(Y_232,Y_233),Z_234),Y_233)) = Z_234 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1023,c_1822]) ).

tff(c_20695,plain,
    ! [Y_232,Y_66,Y_233] : ( divide(Y_232,divide(inverse(Y_66),Y_233)) = multiply(Y_66,multiply(Y_232,Y_233)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1808,c_20369]) ).

tff(c_20826,plain,
    ! [Y_66,Y_232,Y_233] : ( multiply(Y_66,multiply(Y_232,Y_233)) = multiply(Y_232,multiply(Y_233,Y_66)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_4189,c_20695]) ).

tff(c_1090,plain,
    ! [Y_13,Y_46] : ( divide(Y_13,inverse(Y_46)) = multiply(Y_46,Y_13) ),
    inference(superposition,[status(thm),theory(equality)],[c_1075,c_112]) ).

tff(c_21261,plain,
    ! [X_238,Y_239,Z_240] : ( divide(multiply(X_238,Y_239),Z_240) = divide(Y_239,divide(Z_240,X_238)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1111,c_1404]) ).

tff(c_21587,plain,
    ! [Y_239,Y_46,X_238] : ( divide(Y_239,divide(inverse(Y_46),X_238)) = multiply(Y_46,multiply(X_238,Y_239)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1090,c_21261]) ).

tff(c_21694,plain,
    ! [Y_46,X_238,Y_239] : ( multiply(Y_46,multiply(X_238,Y_239)) = multiply(Y_239,multiply(X_238,Y_46)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_4189,c_21587]) ).

tff(c_339,plain,
    ! [X_24,Z_25] : ( divide(inverse(X_24),divide(divide(inverse(X_24),Z_25),identity)) = Z_25 ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_70]) ).

tff(c_381,plain,
    ! [X_24] : ( divide(inverse(X_24),divide(identity,identity)) = inverse(X_24) ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_339]) ).

tff(c_389,plain,
    ! [X_24] : ( divide(inverse(X_24),identity) = inverse(X_24) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_381]) ).

tff(c_374,plain,
    ! [Z_25] : ( divide(identity,divide(divide(inverse(identity),Z_25),identity)) = Z_25 ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_339]) ).

tff(c_387,plain,
    ! [Z_25] : ( inverse(divide(inverse(Z_25),identity)) = Z_25 ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_6,c_27,c_374]) ).

tff(c_492,plain,
    ! [Z_25] : ( inverse(inverse(Z_25)) = Z_25 ),
    inference(demodulation,[status(thm),theory(equality)],[c_389,c_387]) ).

tff(c_188,plain,
    ! [X_18,Y_19] : ( multiply(inverse(X_18),Y_19) = divide(Y_19,X_18) ),
    inference(demodulation,[status(thm),theory(equality)],[c_11,c_6,c_106]) ).

tff(c_215,plain,
    ! [Y_19] : ( multiply(identity,Y_19) = divide(Y_19,identity) ),
    inference(superposition,[status(thm),theory(equality)],[c_27,c_188]) ).

tff(c_269,plain,
    ! [Y_11] : ( inverse(inverse(Y_11)) = divide(Y_11,identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_215,c_63]) ).

tff(c_526,plain,
    ! [Y_11] : ( divide(Y_11,identity) = Y_11 ),
    inference(demodulation,[status(thm),theory(equality)],[c_492,c_269]) ).

tff(c_53,plain,
    ! [Y_11] : ( multiply(inverse(Y_11),Y_11) = identity ),
    inference(superposition,[status(thm),theory(equality)],[c_42,c_8]) ).

tff(c_10,plain,
    ( ( multiply(b4,a4) != multiply(a4,b4) )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(multiply(inverse(b2),b2),a2) != a2 )
    | ( multiply(inverse(b1),b1) != multiply(inverse(a1),a1) ) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_129,plain,
    ( ( multiply(b4,a4) != multiply(a4,b4) )
    | ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(identity,a2) != a2 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_53,c_53,c_53,c_10]) ).

tff(c_130,plain,
    multiply(identity,a2) != a2,
    inference(splitLeft,[status(thm)],[c_129]) ).

tff(c_270,plain,
    divide(a2,identity) != a2,
    inference(demodulation,[status(thm),theory(equality)],[c_215,c_130]) ).

tff(c_663,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_526,c_270]) ).

tff(c_664,plain,
    ( ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) )
    | ( multiply(b4,a4) != multiply(a4,b4) ) ),
    inference(splitRight,[status(thm)],[c_129]) ).

tff(c_3392,plain,
    multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_1493,c_1493,c_664]) ).

tff(c_29870,plain,
    multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_21694,c_3392]) ).

tff(c_50712,plain,
    multiply(a3,multiply(c3,b3)) != multiply(a3,multiply(b3,c3)),
    inference(demodulation,[status(thm),theory(equality)],[c_20826,c_29870]) ).

tff(c_50715,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1493,c_50712]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : GRP095-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.16  % 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
% 0.17/0.38  % Computer : n016.cluster.edu
% 0.17/0.38  % Model    : x86_64 x86_64
% 0.17/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38  % Memory   : 8042.1875MB
% 0.17/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38  % CPULimit : 300
% 0.17/0.38  % WCLimit  : 300
% 0.17/0.38  % DateTime : Thu Aug  3 22:54:38 EDT 2023
% 0.24/0.38  % CPUTime  : 
% 18.79/8.91  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.79/8.92  
% 18.79/8.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.79/8.96  
% 18.79/8.96  Inference rules
% 18.79/8.96  ----------------------
% 18.79/8.96  #Ref     : 0
% 18.79/8.96  #Sup     : 12748
% 18.79/8.96  #Fact    : 0
% 18.79/8.96  #Define  : 0
% 18.79/8.96  #Split   : 1
% 18.79/8.96  #Chain   : 0
% 18.79/8.96  #Close   : 0
% 18.79/8.96  
% 18.79/8.96  Ordering : KBO
% 18.79/8.96  
% 18.79/8.96  Simplification rules
% 18.79/8.96  ----------------------
% 18.79/8.96  #Subsume      : 856
% 18.79/8.96  #Demod        : 26322
% 18.79/8.96  #Tautology    : 5780
% 18.79/8.96  #SimpNegUnit  : 0
% 18.79/8.96  #BackRed      : 55
% 18.79/8.96  
% 18.79/8.96  #Partial instantiations: 0
% 18.79/8.96  #Strategies tried      : 1
% 18.79/8.96  
% 18.79/8.96  Timing (in seconds)
% 18.79/8.96  ----------------------
% 18.79/8.97  Preprocessing        : 0.44
% 18.79/8.97  Parsing              : 0.23
% 18.79/8.97  CNF conversion       : 0.02
% 18.79/8.97  Main loop            : 7.35
% 18.79/8.97  Inferencing          : 1.27
% 18.79/8.97  Reduction            : 4.74
% 18.79/8.97  Demodulation         : 4.44
% 18.79/8.97  BG Simplification    : 0.17
% 18.79/8.97  Subsumption          : 0.75
% 18.79/8.97  Abstraction          : 0.32
% 18.79/8.97  MUC search           : 0.00
% 18.79/8.97  Cooper               : 0.00
% 18.79/8.97  Total                : 7.86
% 18.79/8.97  Index Insertion      : 0.00
% 18.79/8.97  Index Deletion       : 0.00
% 18.79/8.97  Index Matching       : 0.00
% 18.79/8.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------