TSTP Solution File: LCL109-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL109-3 : 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/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 : n026.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 10:47:23 EDT 2023

% Result   : Unsatisfiable 195.70s 170.04s
% Output   : CNFRefutation 195.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   72 (  38 unt;   5 typ;   0 def)
%            Number of atoms       :   97 (  96 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   64 (  34   ~;  30   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  123 (; 123   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ implies > #nlpp > not > truth > b > a

%Foreground sorts:

%Background operators:

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

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

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

tff(not,type,
    not: $i > $i ).

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

tff(f_70,axiom,
    ! [X,Y] : ( implies(X,implies(Y,X)) = truth ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [X] : ( implies(truth,X) = X ),
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [X,Y,Z] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
    file(unknown,unknown) ).

tff(f_77,axiom,
    ! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [X] : ( not(not(X)) = X ),
    file(unknown,unknown) ).

tff(f_85,axiom,
    ! [X,Y] : ( implies(not(X),not(Y)) = implies(Y,X) ),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ! [X,Y,Z] :
      ( ( implies(X,Y) != implies(Y,Z) )
      | ( implies(X,Z) = truth ) ),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [X,Y] :
      ( ( implies(X,Y) != implies(Y,X) )
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_81,axiom,
    ! [X] : ( implies(X,not(truth)) = not(X) ),
    file(unknown,unknown) ).

tff(f_87,axiom,
    implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    file(unknown,unknown) ).

tff(c_16,plain,
    ! [X_13,Y_14] : ( implies(X_13,implies(Y_14,X_13)) = truth ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_6,plain,
    ! [Y_6,X_5] : ( implies(implies(Y_6,X_5),X_5) = implies(implies(X_5,Y_6),Y_6) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_2,plain,
    ! [X_1] : ( implies(truth,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_526,plain,
    ! [Y_50,X_51] : ( implies(implies(Y_50,X_51),X_51) = implies(implies(X_51,Y_50),Y_50) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_628,plain,
    ! [Y_14,X_13] : ( implies(implies(implies(Y_14,X_13),X_13),X_13) = implies(truth,implies(Y_14,X_13)) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_526]) ).

tff(c_3936,plain,
    ! [Y_93,X_94] : ( implies(implies(implies(Y_93,X_94),X_94),X_94) = implies(Y_93,X_94) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_628]) ).

tff(c_4147,plain,
    ! [Y_6,X_5] : ( implies(implies(implies(Y_6,X_5),X_5),Y_6) = implies(X_5,Y_6) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_3936]) ).

tff(c_22,plain,
    ! [Y_22,X_21,Z_23] : ( implies(Y_22,implies(X_21,Z_23)) = implies(X_21,implies(Y_22,Z_23)) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_20,plain,
    ! [X_18,Y_19,Z_20] : ( implies(implies(X_18,Y_19),implies(implies(Z_20,X_18),implies(Z_20,Y_19))) = truth ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_1669,plain,
    ! [X_67,Y_68,Z_69] : ( implies(implies(X_67,Y_68),implies(Z_69,implies(implies(Z_69,X_67),Y_68))) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_20]) ).

tff(c_1827,plain,
    ! [Y_6,X_5,Z_69] : ( implies(implies(implies(Y_6,X_5),X_5),implies(Z_69,implies(implies(Z_69,implies(X_5,Y_6)),Y_6))) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_1669]) ).

tff(c_26,plain,
    ! [X_25] : ( not(not(X_25)) = X_25 ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_285,plain,
    ! [X_39,Y_40] : ( implies(not(X_39),not(Y_40)) = implies(Y_40,X_39) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_301,plain,
    ! [Y_40,X_39] : ( implies(not(Y_40),implies(Y_40,X_39)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_285,c_16]) ).

tff(c_28,plain,
    ! [X_26,Y_27] : ( implies(not(X_26),not(Y_27)) = implies(Y_27,X_26) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_396,plain,
    ! [X_43,Z_44,Y_45] :
      ( ( implies(X_43,Z_44) = truth )
      | ( implies(Y_45,Z_44) != implies(X_43,Y_45) ) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_14886,plain,
    ! [X_197,Z_198,Y_199] :
      ( ( implies(not(X_197),Z_198) = truth )
      | ( implies(not(Y_199),Z_198) != implies(Y_199,X_197) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_396]) ).

tff(c_15012,plain,
    ! [Y_40,X_39,Z_198] :
      ( ( implies(not(implies(Y_40,X_39)),Z_198) = truth )
      | ( implies(not(not(Y_40)),Z_198) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_301,c_14886]) ).

tff(c_15079,plain,
    ! [Y_40,X_39,Z_198] :
      ( ( implies(not(implies(Y_40,X_39)),Z_198) = truth )
      | ( implies(Y_40,Z_198) != truth ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_15012]) ).

tff(c_573,plain,
    ! [Y_50,X_51] : ( implies(Y_50,implies(implies(Y_50,X_51),X_51)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_526,c_16]) ).

tff(c_76342,plain,
    ! [Y_449,X_450] : ( implies(implies(implies(Y_449,X_450),X_450),Y_449) = implies(X_450,Y_449) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_3936]) ).

tff(c_12,plain,
    ! [Y_11,X_10] :
      ( ( Y_11 = X_10 )
      | ( implies(Y_11,X_10) != implies(X_10,Y_11) ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_77075,plain,
    ! [Y_449,X_450] :
      ( ( implies(implies(Y_449,X_450),X_450) = Y_449 )
      | ( implies(Y_449,implies(implies(Y_449,X_450),X_450)) != implies(X_450,Y_449) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_76342,c_12]) ).

tff(c_77620,plain,
    ! [Y_449,X_450] :
      ( ( implies(implies(Y_449,X_450),X_450) = Y_449 )
      | ( implies(X_450,Y_449) != truth ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_573,c_77075]) ).

tff(c_24,plain,
    ! [X_24] : ( implies(X_24,not(truth)) = not(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_410,plain,
    ! [X_43,X_24] :
      ( ( implies(X_43,not(truth)) = truth )
      | ( implies(X_43,X_24) != not(X_24) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_396]) ).

tff(c_427,plain,
    ! [X_43,X_24] :
      ( ( not(X_43) = truth )
      | ( implies(X_43,X_24) != not(X_24) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_410]) ).

tff(c_466681,plain,
    ! [Y_1068,X_1069] :
      ( ( not(implies(implies(Y_1068,X_1069),X_1069)) = truth )
      | ( implies(Y_1068,X_1069) != not(X_1069) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3936,c_427]) ).

tff(c_3278,plain,
    ! [X_84,X_83] : ( implies(not(X_84),X_83) = implies(not(X_83),X_84) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_285]) ).

tff(c_416,plain,
    ! [Z_44,X_1] :
      ( ( implies(truth,Z_44) = truth )
      | ( implies(X_1,Z_44) != X_1 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_396]) ).

tff(c_430,plain,
    ! [Z_44,X_1] :
      ( ( truth = Z_44 )
      | ( implies(X_1,Z_44) != X_1 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_416]) ).

tff(c_3850,plain,
    ! [X_91,X_92] :
      ( ( truth = X_91 )
      | ( implies(not(X_91),X_92) != not(X_92) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3278,c_430]) ).

tff(c_3915,plain,
    ! [X_91,Y_14] :
      ( ( truth = X_91 )
      | ( not(implies(Y_14,not(X_91))) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_3850]) ).

tff(c_467501,plain,
    ! [X_91,Y_1068] :
      ( ( truth = X_91 )
      | ( implies(Y_1068,not(X_91)) != not(not(X_91)) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_466681,c_3915]) ).

tff(c_469013,plain,
    ! [X_1070,Y_1071] :
      ( ( truth = X_1070 )
      | ( implies(Y_1071,not(X_1070)) != X_1070 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_467501]) ).

tff(c_470016,plain,
    ! [Y_1074] :
      ( ( truth = Y_1074 )
      | ( implies(not(Y_1074),Y_1074) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_77620,c_469013]) ).

tff(c_661034,plain,
    ! [Y_1422,X_1423] :
      ( ( implies(Y_1422,X_1423) = truth )
      | ( implies(Y_1422,implies(Y_1422,X_1423)) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15079,c_470016]) ).

tff(c_661411,plain,
    ! [Y_6,X_5] : ( implies(implies(implies(Y_6,X_5),X_5),implies(implies(implies(implies(Y_6,X_5),X_5),implies(X_5,Y_6)),Y_6)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1827,c_661034]) ).

tff(c_662337,plain,
    ! [X_1424,Y_1425] : ( implies(implies(implies(X_1424,Y_1425),X_1424),X_1424) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_4147,c_22,c_4147,c_22,c_661411]) ).

tff(c_83390,plain,
    ! [Y_466,X_467] :
      ( ( implies(implies(Y_466,X_467),X_467) = Y_466 )
      | ( implies(X_467,Y_466) != truth ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_573,c_77075]) ).

tff(c_131,plain,
    ! [X_33,Y_34] : ( implies(X_33,implies(Y_34,X_33)) = truth ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_171,plain,
    ! [X_35] : ( implies(not(truth),not(X_35)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_131]) ).

tff(c_194,plain,
    ! [X_25] : ( implies(not(truth),X_25) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_171]) ).

tff(c_252,plain,
    ! [Y_37,X_38] :
      ( ( Y_37 = X_38 )
      | ( implies(Y_37,X_38) != implies(X_38,Y_37) ) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_264,plain,
    ! [X_24] :
      ( ( not(truth) = X_24 )
      | ( implies(not(truth),X_24) != not(X_24) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_252]) ).

tff(c_341,plain,
    ! [X_41] :
      ( ( not(truth) = X_41 )
      | ( not(X_41) != truth ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_194,c_264]) ).

tff(c_345,plain,
    ! [X_42] :
      ( ( not(truth) = not(X_42) )
      | ( truth != X_42 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_341]) ).

tff(c_359,plain,
    ! [X_26,X_42] :
      ( ( implies(not(X_26),not(truth)) = implies(X_42,X_26) )
      | ( truth != X_42 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_345,c_28]) ).

tff(c_386,plain,
    ! [X_42,X_26] :
      ( ( implies(X_42,X_26) = X_26 )
      | ( truth != X_42 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_24,c_359]) ).

tff(c_84121,plain,
    ! [Y_466,X_467] :
      ( ( Y_466 = X_467 )
      | ( implies(Y_466,X_467) != truth )
      | ( implies(X_467,Y_466) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_83390,c_386]) ).

tff(c_663049,plain,
    ! [X_1424,Y_1425] :
      ( ( implies(implies(X_1424,Y_1425),X_1424) = X_1424 )
      | ( implies(X_1424,implies(implies(X_1424,Y_1425),X_1424)) != truth ) ),
    inference(superposition,[status(thm),theory(equality)],[c_662337,c_84121]) ).

tff(c_665850,plain,
    ! [X_1424,Y_1425] : ( implies(implies(X_1424,Y_1425),X_1424) = X_1424 ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_663049]) ).

tff(c_30,plain,
    implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_31,plain,
    implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_22,c_30]) ).

tff(c_666523,plain,
    implies(b,implies(implies(b,a),a)) != truth,
    inference(demodulation,[status(thm),theory(equality)],[c_665850,c_31]) ).

tff(c_666528,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_6,c_666523]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL109-3 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 14:15:16 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 195.70/170.04  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 195.74/170.05  
% 195.74/170.05  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 195.74/170.09  
% 195.74/170.09  Inference rules
% 195.74/170.09  ----------------------
% 195.74/170.09  #Ref     : 51
% 195.74/170.09  #Sup     : 178116
% 195.74/170.09  #Fact    : 0
% 195.74/170.09  #Define  : 0
% 195.74/170.09  #Split   : 2
% 195.74/170.09  #Chain   : 0
% 195.74/170.09  #Close   : 0
% 195.74/170.09  
% 195.74/170.09  Ordering : KBO
% 195.74/170.09  
% 195.74/170.09  Simplification rules
% 195.74/170.09  ----------------------
% 195.74/170.09  #Subsume      : 70416
% 195.74/170.09  #Demod        : 145852
% 195.74/170.09  #Tautology    : 40307
% 195.74/170.09  #SimpNegUnit  : 1443
% 195.74/170.09  #BackRed      : 28
% 195.74/170.09  
% 195.74/170.09  #Partial instantiations: 0
% 195.74/170.09  #Strategies tried      : 1
% 195.74/170.09  
% 195.74/170.09  Timing (in seconds)
% 195.74/170.09  ----------------------
% 195.74/170.09  Preprocessing        : 0.46
% 195.74/170.10  Parsing              : 0.22
% 195.74/170.10  CNF conversion       : 0.02
% 195.74/170.10  Main loop            : 168.53
% 195.74/170.10  Inferencing          : 7.07
% 195.74/170.10  Reduction            : 105.75
% 195.74/170.10  Demodulation         : 95.92
% 195.74/170.10  BG Simplification    : 0.78
% 195.74/170.10  Subsumption          : 43.71
% 195.74/170.10  Abstraction          : 1.57
% 195.74/170.10  MUC search           : 0.00
% 195.74/170.10  Cooper               : 0.00
% 195.74/170.10  Total                : 169.06
% 195.74/170.10  Index Insertion      : 0.00
% 195.74/170.10  Index Deletion       : 0.00
% 195.74/170.10  Index Matching       : 0.00
% 195.74/170.10  BG Taut test         : 0.00
%------------------------------------------------------------------------------