TSTP Solution File: GRP048-10 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% 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 : n003.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 10:39:44 EDT 2023

% Result   : Unsatisfiable 20.09s 9.91s
% Output   : CNFRefutation 20.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   67 (  58 unt;   9 typ;   0 def)
%            Number of atoms       :   58 (  57 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   12 (   5   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-4 aty)
%            Number of variables   :  110 (; 110   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ifeq > product > multiply > equalish > #nlpp > inverse > true > identity > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(f_41,axiom,
    equalish(inverse(a),inverse(b)) != true,
    file(unknown,unknown) ).

tff(f_28,axiom,
    ! [X] : ( product(inverse(X),X,identity) = true ),
    file(unknown,unknown) ).

tff(f_24,axiom,
    ! [A,B,C] : ( ifeq(A,A,B,C) = B ),
    file(unknown,unknown) ).

tff(f_26,axiom,
    ! [X] : ( product(identity,X,X) = true ),
    file(unknown,unknown) ).

tff(f_34,axiom,
    ! [W,U,Z,X,Y,V] : ( ifeq(product(U,Z,W),true,ifeq(product(Y,Z,V),true,ifeq(product(X,Y,U),true,product(X,V,W),true),true),true) = true ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [W,U,Z,X,Y,V] : ( ifeq(product(Y,Z,V),true,ifeq(product(X,V,W),true,ifeq(product(X,Y,U),true,product(U,Z,W),true),true),true) = true ),
    file(unknown,unknown) ).

tff(f_39,axiom,
    equalish(a,b) = true,
    file(unknown,unknown) ).

tff(f_38,axiom,
    ! [X,Y,W,Z] : ( ifeq(equalish(X,Y),true,ifeq(product(W,Z,X),true,product(W,Z,Y),true),true) = true ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [X,Y,W,Z] : ( ifeq(product(X,Y,W),true,ifeq(product(X,Y,Z),true,equalish(Z,W),true),true) = true ),
    file(unknown,unknown) ).

tff(c_20,plain,
    equalish(inverse(a),inverse(b)) != true,
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_6,plain,
    ! [X_5] : ( product(inverse(X_5),X_5,identity) = true ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3] : ( ifeq(A_1,A_1,B_2,C_3) = B_2 ),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_4,plain,
    ! [X_4] : ( product(identity,X_4,X_4) = true ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_312,plain,
    ! [W_58,V_60,U_57,Z_61,X_62,Y_59] : ( ifeq(product(U_57,Z_61,W_58),true,ifeq(product(Y_59,Z_61,V_60),true,ifeq(product(X_62,Y_59,U_57),true,product(X_62,V_60,W_58),true),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_8564,plain,
    ! [Y_289,X_290,V_291,X_292] : ( ifeq(true,true,ifeq(product(Y_289,X_290,V_291),true,ifeq(product(X_292,Y_289,identity),true,product(X_292,V_291,X_290),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_312]) ).

tff(c_8720,plain,
    ! [X_292,X_5] : ( ifeq(true,true,ifeq(true,true,ifeq(product(X_292,inverse(X_5),identity),true,product(X_292,identity,X_5),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_8564]) ).

tff(c_15322,plain,
    ! [X_375,X_376] : ( ifeq(product(X_375,inverse(X_376),identity),true,product(X_375,identity,X_376),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_8720]) ).

tff(c_15438,plain,
    ! [X_377] : ( ifeq(true,true,product(inverse(inverse(X_377)),identity,X_377),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_15322]) ).

tff(c_15443,plain,
    ! [X_377] : ( product(inverse(inverse(X_377)),identity,X_377) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_15438,c_2]) ).

tff(c_210,plain,
    ! [V_53,Y_54,Z_50,X_52,W_51,U_49] : ( ifeq(product(Y_54,Z_50,V_53),true,ifeq(product(X_52,V_53,W_51),true,ifeq(product(X_52,Y_54,U_49),true,product(U_49,Z_50,W_51),true),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_9434,plain,
    ! [X_297,X_298,W_299,U_300] : ( ifeq(true,true,ifeq(product(X_297,X_298,W_299),true,ifeq(product(X_297,identity,U_300),true,product(U_300,X_298,W_299),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_210]) ).

tff(c_9631,plain,
    ! [X_5,U_300] : ( ifeq(true,true,ifeq(true,true,ifeq(product(inverse(X_5),identity,U_300),true,product(U_300,X_5,identity),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_9434]) ).

tff(c_20155,plain,
    ! [X_406,U_407] : ( ifeq(product(inverse(X_406),identity,U_407),true,product(U_407,X_406,identity),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_9631]) ).

tff(c_20739,plain,
    ! [X_409] : ( ifeq(true,true,product(X_409,inverse(X_409),identity),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_15443,c_20155]) ).

tff(c_20760,plain,
    ! [X_410] : ( product(X_410,inverse(X_410),identity) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_20739,c_2]) ).

tff(c_18,plain,
    equalish(a,b) = true,
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_55,plain,
    ! [X_35,Y_36,W_37,Z_38] : ( ifeq(equalish(X_35,Y_36),true,ifeq(product(W_37,Z_38,X_35),true,product(W_37,Z_38,Y_36),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_74,plain,
    ! [X_4,Y_36] : ( ifeq(equalish(X_4,Y_36),true,ifeq(true,true,product(identity,X_4,Y_36),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_55]) ).

tff(c_86,plain,
    ! [X_39,Y_40] : ( ifeq(equalish(X_39,Y_40),true,product(identity,X_39,Y_40),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_74]) ).

tff(c_100,plain,
    ifeq(true,true,product(identity,a,b),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_18,c_86]) ).

tff(c_144,plain,
    product(identity,a,b) = true,
    inference(superposition,[status(thm),theory(equality)],[c_100,c_2]) ).

tff(c_256,plain,
    ! [Y_54,Z_50,X_4,U_49] : ( ifeq(product(Y_54,Z_50,X_4),true,ifeq(true,true,ifeq(product(identity,Y_54,U_49),true,product(U_49,Z_50,X_4),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_210]) ).

tff(c_3672,plain,
    ! [Y_148,Z_149,X_150,U_151] : ( ifeq(product(Y_148,Z_149,X_150),true,ifeq(product(identity,Y_148,U_151),true,product(U_151,Z_149,X_150),true),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_256]) ).

tff(c_3778,plain,
    ! [Z_149,X_150] : ( ifeq(product(a,Z_149,X_150),true,ifeq(true,true,product(b,Z_149,X_150),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_144,c_3672]) ).

tff(c_3822,plain,
    ! [Z_149,X_150] : ( ifeq(product(a,Z_149,X_150),true,product(b,Z_149,X_150),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_3778]) ).

tff(c_21022,plain,
    ifeq(true,true,product(b,inverse(a),identity),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_20760,c_3822]) ).

tff(c_22451,plain,
    product(b,inverse(a),identity) = true,
    inference(superposition,[status(thm),theory(equality)],[c_21022,c_2]) ).

tff(c_8723,plain,
    ! [X_5,X_290,V_291] : ( ifeq(true,true,ifeq(product(X_5,X_290,V_291),true,ifeq(true,true,product(inverse(X_5),V_291,X_290),true),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_8564]) ).

tff(c_8769,plain,
    ! [X_5,X_290,V_291] : ( ifeq(product(X_5,X_290,V_291),true,product(inverse(X_5),V_291,X_290),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_8723]) ).

tff(c_22466,plain,
    ifeq(true,true,product(inverse(b),identity,inverse(a)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_22451,c_8769]) ).

tff(c_25215,plain,
    product(inverse(b),identity,inverse(a)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_22466,c_2]) ).

tff(c_8768,plain,
    ! [X_292,X_5] : ( ifeq(product(X_292,inverse(X_5),identity),true,product(X_292,identity,X_5),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_8720]) ).

tff(c_21186,plain,
    ! [X_411] : ( ifeq(true,true,product(X_411,identity,X_411),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_20760,c_8768]) ).

tff(c_21211,plain,
    ! [X_412] : ( product(X_412,identity,X_412) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_21186,c_2]) ).

tff(c_10,plain,
    ! [X_8,Y_9,W_10,Z_11] : ( ifeq(product(X_8,Y_9,W_10),true,ifeq(product(X_8,Y_9,Z_11),true,equalish(Z_11,W_10),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_21671,plain,
    ! [X_412,W_10] : ( ifeq(product(X_412,identity,W_10),true,ifeq(true,true,equalish(X_412,W_10),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_21211,c_10]) ).

tff(c_27511,plain,
    ! [X_447,W_448] : ( ifeq(product(X_447,identity,W_448),true,equalish(X_447,W_448),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_21671]) ).

tff(c_27537,plain,
    ifeq(true,true,equalish(inverse(b),inverse(a)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_25215,c_27511]) ).

tff(c_27950,plain,
    equalish(inverse(b),inverse(a)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_27537,c_2]) ).

tff(c_85,plain,
    ! [X_4,Y_36] : ( ifeq(equalish(X_4,Y_36),true,product(identity,X_4,Y_36),true) = true ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_74]) ).

tff(c_28207,plain,
    ifeq(true,true,product(identity,inverse(b),inverse(a)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_27950,c_85]) ).

tff(c_40537,plain,
    product(identity,inverse(b),inverse(a)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_28207,c_2]) ).

tff(c_110,plain,
    ! [X_42,Y_43,W_44,Z_45] : ( ifeq(product(X_42,Y_43,W_44),true,ifeq(product(X_42,Y_43,Z_45),true,equalish(Z_45,W_44),true),true) = true ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_1254,plain,
    ! [X_88,Z_89] : ( ifeq(true,true,ifeq(product(identity,X_88,Z_89),true,equalish(Z_89,X_88),true),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_110]) ).

tff(c_1259,plain,
    ! [X_88,Z_89] : ( ifeq(product(identity,X_88,Z_89),true,equalish(Z_89,X_88),true) = true ),
    inference(superposition,[status(thm),theory(equality)],[c_1254,c_2]) ).

tff(c_40777,plain,
    ifeq(true,true,equalish(inverse(a),inverse(b)),true) = true,
    inference(superposition,[status(thm),theory(equality)],[c_40537,c_1259]) ).

tff(c_40877,plain,
    equalish(inverse(a),inverse(b)) = true,
    inference(superposition,[status(thm),theory(equality)],[c_40777,c_2]) ).

tff(c_40884,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_40877]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% 0.13/0.14  % 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 : n003.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 21:58:53 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 20.09/9.91  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.14/9.92  
% 20.14/9.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.14/9.96  
% 20.14/9.96  Inference rules
% 20.14/9.96  ----------------------
% 20.14/9.96  #Ref     : 0
% 20.14/9.96  #Sup     : 11153
% 20.14/9.96  #Fact    : 0
% 20.14/9.96  #Define  : 0
% 20.14/9.96  #Split   : 0
% 20.14/9.96  #Chain   : 0
% 20.14/9.96  #Close   : 0
% 20.14/9.96  
% 20.14/9.96  Ordering : KBO
% 20.14/9.96  
% 20.14/9.96  Simplification rules
% 20.14/9.96  ----------------------
% 20.14/9.96  #Subsume      : 0
% 20.14/9.96  #Demod        : 8430
% 20.14/9.96  #Tautology    : 4288
% 20.14/9.96  #SimpNegUnit  : 1
% 20.14/9.96  #BackRed      : 193
% 20.14/9.96  
% 20.14/9.96  #Partial instantiations: 0
% 20.14/9.96  #Strategies tried      : 1
% 20.14/9.96  
% 20.14/9.96  Timing (in seconds)
% 20.14/9.96  ----------------------
% 20.14/9.96  Preprocessing        : 0.43
% 20.14/9.96  Parsing              : 0.24
% 20.14/9.96  CNF conversion       : 0.02
% 20.14/9.96  Main loop            : 8.46
% 20.14/9.96  Inferencing          : 1.38
% 20.14/9.96  Reduction            : 4.80
% 20.14/9.97  Demodulation         : 4.38
% 20.14/9.97  BG Simplification    : 0.08
% 20.14/9.97  Subsumption          : 1.77
% 20.14/9.97  Abstraction          : 0.07
% 20.14/9.97  MUC search           : 0.00
% 20.14/9.97  Cooper               : 0.00
% 20.14/9.97  Total                : 8.95
% 20.14/9.97  Index Insertion      : 0.00
% 20.14/9.97  Index Deletion       : 0.00
% 20.14/9.97  Index Matching       : 0.00
% 20.14/9.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------