TSTP Solution File: COL003-14 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL003-14 : TPTP v8.1.2. Released v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n005.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 10:34:47 EDT 2023

% Result   : Unsatisfiable 25.01s 14.28s
% Output   : CNFRefutation 25.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   25 (  20 unt;   5 typ;   0 def)
%            Number of atoms       :   20 (  19 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   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  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (;  28   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ apply > #nlpp > w > strong_fixed_point > fixed_pt > b

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(apply,type,
    apply: ( $i * $i ) > $i ).

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

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

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

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

tff(f_29,axiom,
    ! [X,Y,Z] : ( apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    strong_fixed_point = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b),
    file(unknown,unknown) ).

tff(f_31,axiom,
    ! [X,Y] : ( apply(apply(w,X),Y) = apply(apply(X,Y),Y) ),
    file(unknown,unknown) ).

tff(f_34,axiom,
    apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
    file(unknown,unknown) ).

tff(c_2,plain,
    ! [X_1,Y_2,Z_3] : ( apply(apply(apply(b,X_1),Y_2),Z_3) = apply(X_1,apply(Y_2,Z_3)) ),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_6,plain,
    apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,w),b))),b) = strong_fixed_point,
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_1719,plain,
    ! [Z_30] : ( apply(apply(apply(b,apply(w,w)),apply(apply(b,w),b)),apply(b,Z_30)) = apply(strong_fixed_point,Z_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_2]) ).

tff(c_1740,plain,
    ! [Z_30] : ( apply(apply(w,w),apply(apply(apply(b,w),b),apply(b,Z_30))) = apply(strong_fixed_point,Z_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_1719,c_2]) ).

tff(c_1757,plain,
    ! [Z_30] : ( apply(apply(w,w),apply(w,apply(b,apply(b,Z_30)))) = apply(strong_fixed_point,Z_30) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1740]) ).

tff(c_4,plain,
    ! [X_4,Y_5] : ( apply(apply(w,X_4),Y_5) = apply(apply(X_4,Y_5),Y_5) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_91,plain,
    ! [X_9,Y_10,Z_11] : ( apply(apply(apply(b,X_9),Y_10),Z_11) = apply(X_9,apply(Y_10,Z_11)) ),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_127,plain,
    ! [X_12,Y_13] : ( apply(apply(w,apply(b,X_12)),Y_13) = apply(X_12,apply(Y_13,Y_13)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_91]) ).

tff(c_5742,plain,
    ! [X_55,Y_56,Z_57] : ( apply(apply(apply(w,apply(b,apply(b,X_55))),Y_56),Z_57) = apply(X_55,apply(apply(Y_56,Y_56),Z_57)) ),
    inference(superposition,[status(thm),theory(equality)],[c_127,c_2]) ).

tff(c_38176,plain,
    ! [X_132,Y_133] : ( apply(apply(apply(w,apply(b,apply(b,X_132))),Y_133),Y_133) = apply(X_132,apply(apply(w,Y_133),Y_133)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_5742]) ).

tff(c_9,plain,
    ! [X_6,Y_7] : ( apply(apply(w,X_6),Y_7) = apply(apply(X_6,Y_7),Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_13,plain,
    ! [Y_7] : ( apply(apply(w,w),Y_7) = apply(apply(Y_7,Y_7),Y_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_9,c_4]) ).

tff(c_38349,plain,
    ! [X_132] : ( apply(X_132,apply(apply(w,apply(w,apply(b,apply(b,X_132)))),apply(w,apply(b,apply(b,X_132))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X_132)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_38176,c_13]) ).

tff(c_38610,plain,
    ! [X_132] : ( apply(X_132,apply(strong_fixed_point,X_132)) = apply(strong_fixed_point,X_132) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1757,c_1757,c_4,c_38349]) ).

tff(c_8,plain,
    apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_38654,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_38610,c_8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : COL003-14 : TPTP v8.1.2. Released v2.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 18:09:57 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 25.01/14.28  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.01/14.28  
% 25.01/14.28  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 25.01/14.31  
% 25.01/14.31  Inference rules
% 25.01/14.31  ----------------------
% 25.01/14.31  #Ref     : 0
% 25.01/14.31  #Sup     : 9392
% 25.01/14.31  #Fact    : 0
% 25.01/14.31  #Define  : 0
% 25.01/14.31  #Split   : 0
% 25.01/14.31  #Chain   : 0
% 25.01/14.31  #Close   : 0
% 25.01/14.31  
% 25.01/14.31  Ordering : KBO
% 25.01/14.31  
% 25.01/14.31  Simplification rules
% 25.01/14.31  ----------------------
% 25.01/14.31  #Subsume      : 421
% 25.01/14.31  #Demod        : 9087
% 25.01/14.31  #Tautology    : 1070
% 25.01/14.31  #SimpNegUnit  : 0
% 25.01/14.31  #BackRed      : 1
% 25.01/14.31  
% 25.01/14.31  #Partial instantiations: 0
% 25.01/14.31  #Strategies tried      : 1
% 25.01/14.31  
% 25.01/14.31  Timing (in seconds)
% 25.01/14.31  ----------------------
% 25.01/14.32  Preprocessing        : 0.40
% 25.01/14.32  Parsing              : 0.22
% 25.01/14.32  CNF conversion       : 0.02
% 25.01/14.32  Main loop            : 12.84
% 25.01/14.32  Inferencing          : 1.51
% 25.01/14.32  Reduction            : 9.79
% 25.01/14.32  Demodulation         : 9.50
% 25.01/14.32  BG Simplification    : 0.24
% 25.01/14.32  Subsumption          : 1.11
% 25.01/14.32  Abstraction          : 0.38
% 25.01/14.32  MUC search           : 0.00
% 25.01/14.32  Cooper               : 0.00
% 25.01/14.32  Total                : 13.29
% 25.01/14.32  Index Insertion      : 0.00
% 25.01/14.32  Index Deletion       : 0.00
% 25.01/14.32  Index Matching       : 0.00
% 25.01/14.32  BG Taut test         : 0.00
%------------------------------------------------------------------------------