TSTP Solution File: LCL109-10 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL109-10 : 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 : n009.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 88.40s 67.47s
% Output   : CNFRefutation 88.40s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (  33 unt;   6 typ;   0 def)
%            Number of atoms       :   33 (  32 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-4 aty)
%            Number of variables   :   57 (;  57   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ifeq > 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(ifeq,type,
    ifeq: ( $i * $i * $i * $i ) > $i ).

tff(f_46,axiom,
    ! [X,Y,Z] : ( implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ),
    file(unknown,unknown) ).

tff(f_26,axiom,
    ! [X] : ( implies(truth,X) = X ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [X,Y] : ( implies(not(X),not(Y)) = implies(Y,X) ),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [X,Y] : ( implies(X,implies(Y,X)) = truth ),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [X] : ( not(not(X)) = X ),
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [X] : ( implies(X,not(truth)) = not(X) ),
    file(unknown,unknown) ).

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

tff(f_28,axiom,
    ! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    file(unknown,unknown) ).

tff(c_24,plain,
    ! [Y_25,X_24,Z_26] : ( implies(Y_25,implies(X_24,Z_26)) = implies(X_24,implies(Y_25,Z_26)) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_4,plain,
    ! [X_4] : ( implies(truth,X_4) = X_4 ),
    inference(cnfTransformation,[status(thm)],[f_26]) ).

tff(c_259,plain,
    ! [X_43,Y_44] : ( implies(not(X_43),not(Y_44)) = implies(Y_44,X_43) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_18,plain,
    ! [X_16,Y_17] : ( implies(X_16,implies(Y_17,X_16)) = truth ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_269,plain,
    ! [Y_44,X_43] : ( implies(not(Y_44),implies(Y_44,X_43)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_259,c_18]) ).

tff(c_28,plain,
    ! [X_28] : ( not(not(X_28)) = X_28 ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_298,plain,
    ! [X_43,X_28] : ( implies(not(X_43),X_28) = implies(not(X_28),X_43) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_259]) ).

tff(c_30,plain,
    ! [X_29,Y_30] : ( implies(not(X_29),not(Y_30)) = implies(Y_30,X_29) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_26,plain,
    ! [X_27] : ( implies(X_27,not(truth)) = not(X_27) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_295,plain,
    ! [Y_44,X_28] : ( implies(Y_44,not(X_28)) = implies(X_28,not(Y_44)) ),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_259]) ).

tff(c_910,plain,
    ! [Y_55,X_56] : ( implies(implies(Y_55,X_56),X_56) = implies(implies(X_56,Y_55),Y_55) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_1045,plain,
    ! [Y_30,X_29] : ( implies(implies(not(Y_30),not(X_29)),not(X_29)) = implies(implies(Y_30,X_29),not(Y_30)) ),
    inference(superposition,[status(thm),theory(equality)],[c_30,c_910]) ).

tff(c_12681,plain,
    ! [Y_167,X_168] : ( implies(implies(Y_167,X_168),not(Y_167)) = implies(X_168,not(implies(X_168,Y_167))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_30,c_1045]) ).

tff(c_1115,plain,
    ! [Y_30,X_29] : ( implies(implies(Y_30,X_29),not(Y_30)) = implies(X_29,not(implies(X_29,Y_30))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_295,c_30,c_1045]) ).

tff(c_12687,plain,
    ! [Y_167,X_168] : ( implies(not(Y_167),not(implies(not(Y_167),implies(Y_167,X_168)))) = implies(implies(X_168,not(implies(X_168,Y_167))),not(implies(Y_167,X_168))) ),
    inference(superposition,[status(thm),theory(equality)],[c_12681,c_1115]) ).

tff(c_13202,plain,
    ! [X_168,Y_167] : ( implies(implies(X_168,not(implies(X_168,Y_167))),not(implies(Y_167,X_168))) = Y_167 ),
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_269,c_12687]) ).

tff(c_8,plain,
    ! [Y_9,X_8] : ( implies(implies(Y_9,X_8),X_8) = implies(implies(X_8,Y_9),Y_9) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_1956,plain,
    ! [X_67,Y_68,Z_69] : ( implies(implies(X_67,Y_68),implies(implies(Y_68,Z_69),implies(X_67,Z_69))) = truth ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_353034,plain,
    ! [Y_726,X_727,Y_728] : ( implies(implies(implies(Y_726,X_727),Y_728),implies(implies(Y_728,X_727),implies(implies(X_727,Y_726),Y_726))) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_8,c_1956]) ).

tff(c_354885,plain,
    ! [Y_167,X_168] : ( implies(Y_167,implies(implies(not(implies(Y_167,X_168)),not(implies(X_168,Y_167))),implies(implies(not(implies(X_168,Y_167)),X_168),X_168))) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_13202,c_353034]) ).

tff(c_357062,plain,
    ! [Y_167,X_168] : ( implies(Y_167,implies(implies(Y_167,implies(implies(X_168,Y_167),X_168)),X_168)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_4,c_269,c_298,c_30,c_354885]) ).

tff(c_32,plain,
    implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth,
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_33,plain,
    implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_24,c_32]) ).

tff(c_361182,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_357062,c_33]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL109-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n009.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 13:41:53 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 88.40/67.47  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 88.40/67.48  
% 88.40/67.48  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 88.40/67.51  
% 88.40/67.51  Inference rules
% 88.40/67.51  ----------------------
% 88.40/67.51  #Ref     : 0
% 88.40/67.51  #Sup     : 90711
% 88.40/67.51  #Fact    : 0
% 88.40/67.51  #Define  : 0
% 88.40/67.51  #Split   : 0
% 88.40/67.51  #Chain   : 0
% 88.40/67.51  #Close   : 0
% 88.40/67.51  
% 88.40/67.51  Ordering : KBO
% 88.40/67.51  
% 88.40/67.51  Simplification rules
% 88.40/67.51  ----------------------
% 88.40/67.51  #Subsume      : 425
% 88.40/67.51  #Demod        : 151626
% 88.40/67.51  #Tautology    : 49170
% 88.40/67.51  #SimpNegUnit  : 0
% 88.40/67.51  #BackRed      : 15
% 88.40/67.51  
% 88.40/67.51  #Partial instantiations: 0
% 88.40/67.51  #Strategies tried      : 1
% 88.40/67.51  
% 88.40/67.51  Timing (in seconds)
% 88.40/67.51  ----------------------
% 88.40/67.51  Preprocessing        : 0.46
% 88.40/67.51  Parsing              : 0.25
% 88.40/67.51  CNF conversion       : 0.02
% 88.40/67.51  Main loop            : 65.92
% 88.40/67.51  Inferencing          : 3.48
% 88.40/67.51  Reduction            : 51.45
% 88.40/67.51  Demodulation         : 49.82
% 88.40/67.52  BG Simplification    : 0.39
% 88.40/67.52  Subsumption          : 8.55
% 88.40/67.52  Abstraction          : 0.77
% 88.40/67.52  MUC search           : 0.00
% 88.40/67.52  Cooper               : 0.00
% 88.40/67.52  Total                : 66.43
% 88.40/67.52  Index Insertion      : 0.00
% 88.40/67.52  Index Deletion       : 0.00
% 88.40/67.52  Index Matching       : 0.00
% 88.40/67.52  BG Taut test         : 0.00
%------------------------------------------------------------------------------