TSTP Solution File: GRP590-1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP590-1 : 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 : n031.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 10:41:35 EDT 2023

% Result   : Unsatisfiable 3.51s 2.01s
% Output   : CNFRefutation 3.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   36 (  31 unt;   5 typ;   0 def)
%            Number of atoms       :   31 (  30 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    :    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   :   66 (;  66   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ multiply > double_divide > #nlpp > inverse > b2 > a2

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(b2,type,
    b2: $i ).

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

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

tff(f_27,axiom,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file(unknown,unknown) ).

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

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

tff(c_17,plain,
    ! [C_8,A_9,B_10] : ( double_divide(multiply(multiply(inverse(C_8),A_9),double_divide(A_9,B_10)),B_10) = C_8 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).

tff(c_26,plain,
    ! [B_10,C_8,A_9] : ( multiply(B_10,multiply(multiply(inverse(C_8),A_9),double_divide(A_9,B_10))) = inverse(C_8) ),
    inference(superposition,[status(thm),theory(equality)],[c_17,c_4]) ).

tff(c_7,plain,
    ! [C_3,A_1,B_2] : ( double_divide(multiply(multiply(inverse(C_3),A_1),double_divide(A_1,B_2)),B_2) = C_3 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_4,c_2]) ).

tff(c_102,plain,
    ! [C_18,C_19,A_20,B_21] : ( double_divide(multiply(multiply(inverse(C_18),multiply(multiply(inverse(C_19),A_20),double_divide(A_20,B_21))),C_19),B_21) = C_18 ),
    inference(superposition,[status(thm),theory(equality)],[c_17,c_7]) ).

tff(c_149,plain,
    ! [C_22,C_23] : ( double_divide(multiply(inverse(C_22),C_22),inverse(C_23)) = C_23 ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_102]) ).

tff(c_179,plain,
    ! [C_24,C_25] : ( multiply(inverse(C_24),multiply(inverse(C_25),C_25)) = inverse(C_24) ),
    inference(superposition,[status(thm),theory(equality)],[c_149,c_4]) ).

tff(c_137,plain,
    ! [C_8,C_18] : ( double_divide(multiply(inverse(C_8),C_8),inverse(C_18)) = C_18 ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_102]) ).

tff(c_220,plain,
    ! [C_26,C_27] : ( double_divide(inverse(multiply(inverse(C_26),C_26)),inverse(C_27)) = C_27 ),
    inference(superposition,[status(thm),theory(equality)],[c_179,c_137]) ).

tff(c_238,plain,
    ! [C_27,C_26] : ( multiply(inverse(C_27),inverse(multiply(inverse(C_26),C_26))) = inverse(C_27) ),
    inference(superposition,[status(thm),theory(equality)],[c_220,c_4]) ).

tff(c_190,plain,
    ! [C_25,C_18] : ( double_divide(inverse(multiply(inverse(C_25),C_25)),inverse(C_18)) = C_18 ),
    inference(superposition,[status(thm),theory(equality)],[c_179,c_137]) ).

tff(c_167,plain,
    ! [C_23,C_22] : ( multiply(inverse(C_23),multiply(inverse(C_22),C_22)) = inverse(C_23) ),
    inference(superposition,[status(thm),theory(equality)],[c_149,c_4]) ).

tff(c_348,plain,
    ! [C_32,A_33,B_34] : ( double_divide(multiply(inverse(C_32),C_32),multiply(A_33,B_34)) = double_divide(B_34,A_33) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_149]) ).

tff(c_363,plain,
    ! [C_3,C_32,B_34,A_33] : ( double_divide(multiply(multiply(inverse(C_3),multiply(inverse(C_32),C_32)),double_divide(B_34,A_33)),multiply(A_33,B_34)) = C_3 ),
    inference(superposition,[status(thm),theory(equality)],[c_348,c_7]) ).

tff(c_479,plain,
    ! [C_38,B_39,A_40] : ( double_divide(multiply(inverse(C_38),double_divide(B_39,A_40)),multiply(A_40,B_39)) = C_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_363]) ).

tff(c_532,plain,
    ! [C_38,C_18,C_25] : ( double_divide(multiply(inverse(C_38),C_18),multiply(inverse(C_18),inverse(multiply(inverse(C_25),C_25)))) = C_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_190,c_479]) ).

tff(c_564,plain,
    ! [C_41,C_42] : ( double_divide(multiply(inverse(C_41),C_42),inverse(C_42)) = C_41 ),
    inference(demodulation,[status(thm),theory(equality)],[c_238,c_532]) ).

tff(c_621,plain,
    ! [C_43,C_44] : ( multiply(inverse(C_43),multiply(inverse(C_44),C_43)) = inverse(C_44) ),
    inference(superposition,[status(thm),theory(equality)],[c_564,c_4]) ).

tff(c_559,plain,
    ! [C_38,C_18] : ( double_divide(multiply(inverse(C_38),C_18),inverse(C_18)) = C_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_238,c_532]) ).

tff(c_1089,plain,
    ! [C_55,C_56] : ( double_divide(inverse(C_55),inverse(multiply(inverse(C_55),C_56))) = C_56 ),
    inference(superposition,[status(thm),theory(equality)],[c_621,c_559]) ).

tff(c_1113,plain,
    ! [C_25,C_56] : ( multiply(inverse(multiply(inverse(C_25),C_25)),C_56) = C_56 ),
    inference(superposition,[status(thm),theory(equality)],[c_1089,c_190]) ).

tff(c_811,plain,
    ! [C_49,C_50] : ( double_divide(inverse(C_49),inverse(multiply(inverse(C_50),C_50))) = C_49 ),
    inference(superposition,[status(thm),theory(equality)],[c_167,c_564]) ).

tff(c_874,plain,
    ! [C_52,C_51] : ( multiply(inverse(C_52),C_52) = multiply(inverse(C_51),C_51) ),
    inference(superposition,[status(thm),theory(equality)],[c_811,c_190]) ).

tff(c_6,plain,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    inference(cnfTransformation,[status(thm)],[f_27]) ).

tff(c_1057,plain,
    ! [C_53] : ( multiply(multiply(inverse(C_53),C_53),a2) != a2 ),
    inference(superposition,[status(thm),theory(equality)],[c_874,c_6]) ).

tff(c_1069,plain,
    ! [C_22] : ( multiply(inverse(multiply(inverse(C_22),C_22)),a2) != a2 ),
    inference(superposition,[status(thm),theory(equality)],[c_167,c_1057]) ).

tff(c_1183,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1113,c_1069]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15  % Problem  : GRP590-1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.16  % 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
% 0.16/0.37  % Computer : n031.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 22:30:59 EDT 2023
% 0.16/0.38  % CPUTime  : 
% 3.51/2.01  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/2.01  
% 3.51/2.01  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.51/2.05  
% 3.51/2.05  Inference rules
% 3.51/2.05  ----------------------
% 3.51/2.05  #Ref     : 0
% 3.51/2.05  #Sup     : 330
% 3.51/2.05  #Fact    : 0
% 3.51/2.05  #Define  : 0
% 3.51/2.05  #Split   : 0
% 3.51/2.05  #Chain   : 0
% 3.51/2.05  #Close   : 0
% 3.51/2.05  
% 3.51/2.05  Ordering : KBO
% 3.51/2.05  
% 3.51/2.05  Simplification rules
% 3.51/2.05  ----------------------
% 3.51/2.05  #Subsume      : 15
% 3.51/2.05  #Demod        : 104
% 3.51/2.05  #Tautology    : 104
% 3.51/2.05  #SimpNegUnit  : 0
% 3.51/2.05  #BackRed      : 1
% 3.51/2.05  
% 3.51/2.05  #Partial instantiations: 0
% 3.51/2.05  #Strategies tried      : 1
% 3.51/2.05  
% 3.51/2.05  Timing (in seconds)
% 3.51/2.05  ----------------------
% 3.51/2.05  Preprocessing        : 0.39
% 3.51/2.05  Parsing              : 0.21
% 3.51/2.05  CNF conversion       : 0.02
% 3.51/2.05  Main loop            : 0.51
% 3.51/2.05  Inferencing          : 0.21
% 3.51/2.05  Reduction            : 0.15
% 3.51/2.05  Demodulation         : 0.11
% 3.51/2.05  BG Simplification    : 0.03
% 3.51/2.05  Subsumption          : 0.09
% 3.51/2.05  Abstraction          : 0.03
% 3.51/2.05  MUC search           : 0.00
% 3.51/2.05  Cooper               : 0.00
% 3.51/2.05  Total                : 0.95
% 3.51/2.05  Index Insertion      : 0.00
% 3.51/2.05  Index Deletion       : 0.00
% 3.51/2.06  Index Matching       : 0.00
% 3.51/2.06  BG Taut test         : 0.00
%------------------------------------------------------------------------------