TSTP Solution File: LCL163-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL163-1 : 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 : 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 10:47:30 EDT 2023

% Result   : Unsatisfiable 36.19s 25.17s
% Output   : CNFRefutation 36.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   47 (  39 unt;   8 typ;   0 def)
%            Number of atoms       :   39 (  38 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   3 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   63 (;  63   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ xor > implies > and_star > #nlpp > not > y > x > truth > falsehood

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(f_50,axiom,
    ! [X] : ( xor(X,falsehood) = X ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [X] : ( xor(X,X) = falsehood ),
    file(unknown,unknown) ).

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

tff(f_60,axiom,
    ! [X,Y] : ( xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
    file(unknown,unknown) ).

tff(f_69,axiom,
    ! [X,Y] : ( xor(X,Y) = xor(Y,X) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ! [X,Y] : ( implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X,Y] : ( and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    implies(implies(x,y),y) != implies(implies(y,x),x),
    file(unknown,unknown) ).

tff(c_4,plain,
    ! [X_2] : ( xor(X_2,falsehood) = X_2 ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_6,plain,
    ! [X_3] : ( xor(X_3,X_3) = falsehood ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_2,plain,
    ! [X_1] : ( xor(X_1,truth) = not(X_1) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_14,plain,
    ! [X_7,Y_8] : ( xor(xor(X_7,truth),Y_8) = xor(X_7,xor(truth,Y_8)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_433,plain,
    ! [X_33,Y_34] : ( xor(not(X_33),Y_34) = xor(X_33,xor(truth,Y_34)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_14]) ).

tff(c_472,plain,
    ! [X_33] : ( xor(X_33,xor(truth,truth)) = not(not(X_33)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_433]) ).

tff(c_489,plain,
    ! [X_33] : ( not(not(X_33)) = X_33 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_6,c_472]) ).

tff(c_22,plain,
    ! [Y_17,X_16] : ( and_star(Y_17,X_16) = and_star(X_16,Y_17) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_136,plain,
    ! [Y_26,X_27] : ( xor(Y_26,X_27) = xor(X_27,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_187,plain,
    ! [X_1] : ( xor(truth,X_1) = not(X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_136]) ).

tff(c_26,plain,
    ! [X_18,Y_19] : ( xor(truth,and_star(X_18,xor(truth,Y_19))) = implies(X_18,Y_19) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1570,plain,
    ! [X_58,Y_59] : ( not(and_star(X_58,not(Y_59))) = implies(X_58,Y_59) ),
    inference(demodulation,[status(thm),theory(equality)],[c_187,c_187,c_26]) ).

tff(c_2452,plain,
    ! [X_76,Y_77] : ( and_star(X_76,not(Y_77)) = not(implies(X_76,Y_77)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1570,c_489]) ).

tff(c_2543,plain,
    ! [Y_77,Y_17] : ( and_star(not(Y_77),Y_17) = not(implies(Y_17,Y_77)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_2452]) ).

tff(c_1637,plain,
    ! [X_58,X_33] : ( implies(X_58,not(X_33)) = not(and_star(X_58,X_33)) ),
    inference(superposition,[status(thm),theory(equality)],[c_489,c_1570]) ).

tff(c_1611,plain,
    ! [X_58,Y_59] : ( and_star(X_58,not(Y_59)) = not(implies(X_58,Y_59)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1570,c_489]) ).

tff(c_698,plain,
    ! [X_18,Y_19] : ( not(and_star(X_18,not(Y_19))) = implies(X_18,Y_19) ),
    inference(demodulation,[status(thm),theory(equality)],[c_187,c_187,c_26]) ).

tff(c_2079,plain,
    ! [Y_68,Y_69] : ( not(and_star(not(Y_68),Y_69)) = implies(Y_69,Y_68) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_1570]) ).

tff(c_3693,plain,
    ! [Y_102,Y_101] : ( implies(not(Y_102),Y_101) = implies(not(Y_101),Y_102) ),
    inference(superposition,[status(thm),theory(equality)],[c_698,c_2079]) ).

tff(c_3834,plain,
    ! [Y_101,X_33] : ( implies(not(Y_101),not(X_33)) = implies(X_33,Y_101) ),
    inference(superposition,[status(thm),theory(equality)],[c_489,c_3693]) ).

tff(c_18,plain,
    ! [Y_12,X_11] : ( xor(Y_12,X_11) = xor(X_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_16,plain,
    ! [Y_10,X_9] : ( and_star(xor(and_star(xor(truth,Y_10),X_9),truth),X_9) = and_star(xor(and_star(xor(truth,X_9),Y_10),truth),Y_10) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_29,plain,
    ! [Y_10,X_9] : ( and_star(Y_10,xor(truth,and_star(xor(truth,X_9),Y_10))) = and_star(X_9,xor(truth,and_star(xor(truth,Y_10),X_9))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_18,c_22,c_18,c_16]) ).

tff(c_813,plain,
    ! [Y_10,X_9] : ( and_star(Y_10,not(and_star(not(X_9),Y_10))) = and_star(X_9,not(and_star(not(Y_10),X_9))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_187,c_187,c_187,c_187,c_29]) ).

tff(c_1623,plain,
    ! [Y_10,X_9] : ( not(and_star(Y_10,not(and_star(not(X_9),Y_10)))) = implies(X_9,and_star(not(Y_10),X_9)) ),
    inference(superposition,[status(thm),theory(equality)],[c_813,c_1570]) ).

tff(c_110663,plain,
    ! [Y_472,X_473] : ( not(and_star(Y_472,implies(Y_472,X_473))) = not(and_star(X_473,implies(X_473,Y_472))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1637,c_2543,c_1637,c_2543,c_489,c_1611,c_1623]) ).

tff(c_111428,plain,
    ! [Y_101,X_33] : ( not(and_star(not(Y_101),implies(X_33,Y_101))) = not(and_star(not(X_33),implies(not(X_33),not(Y_101)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_3834,c_110663]) ).

tff(c_111674,plain,
    ! [Y_101,X_33] : ( implies(implies(Y_101,X_33),X_33) = implies(implies(X_33,Y_101),Y_101) ),
    inference(demodulation,[status(thm),theory(equality)],[c_489,c_2543,c_1637,c_2543,c_489,c_2543,c_489,c_1611,c_1637,c_111428]) ).

tff(c_28,plain,
    implies(implies(y,x),x) != implies(implies(x,y),y),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_112470,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_111674,c_28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL163-1 : 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
% 0.14/0.35  % Computer : n016.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:47:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 36.19/25.17  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.21/25.18  
% 36.21/25.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.21/25.21  
% 36.21/25.21  Inference rules
% 36.21/25.21  ----------------------
% 36.21/25.21  #Ref     : 0
% 36.21/25.21  #Sup     : 28290
% 36.21/25.21  #Fact    : 0
% 36.21/25.21  #Define  : 0
% 36.21/25.21  #Split   : 0
% 36.21/25.21  #Chain   : 0
% 36.21/25.21  #Close   : 0
% 36.21/25.21  
% 36.21/25.21  Ordering : KBO
% 36.21/25.21  
% 36.21/25.21  Simplification rules
% 36.21/25.21  ----------------------
% 36.21/25.21  #Subsume      : 897
% 36.21/25.21  #Demod        : 63955
% 36.21/25.21  #Tautology    : 15318
% 36.21/25.21  #SimpNegUnit  : 0
% 36.21/25.21  #BackRed      : 12
% 36.21/25.21  
% 36.21/25.21  #Partial instantiations: 0
% 36.21/25.21  #Strategies tried      : 1
% 36.21/25.21  
% 36.21/25.21  Timing (in seconds)
% 36.21/25.21  ----------------------
% 36.21/25.22  Preprocessing        : 0.46
% 36.21/25.22  Parsing              : 0.23
% 36.21/25.22  CNF conversion       : 0.02
% 36.21/25.22  Main loop            : 23.68
% 36.21/25.22  Inferencing          : 1.80
% 36.21/25.22  Reduction            : 19.34
% 36.21/25.22  Demodulation         : 18.78
% 36.21/25.22  BG Simplification    : 0.24
% 36.21/25.22  Subsumption          : 1.85
% 36.21/25.22  Abstraction          : 0.45
% 36.21/25.22  MUC search           : 0.00
% 36.21/25.22  Cooper               : 0.00
% 36.21/25.22  Total                : 24.20
% 36.21/25.22  Index Insertion      : 0.00
% 36.21/25.22  Index Deletion       : 0.00
% 36.21/25.22  Index Matching       : 0.00
% 36.21/25.22  BG Taut test         : 0.00
%------------------------------------------------------------------------------