TSTP Solution File: LCL109-5 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL109-5 : 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 : n017.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 4.97s 2.14s
% Output   : CNFRefutation 4.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   56 (  33 unt;   8 typ;   0 def)
%            Number of atoms       :   63 (  27 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   34 (  19   ~;  15   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   75 (;  75   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ ordered > implies > big_hat > big_V > #nlpp > not > y > x > truth

%Foreground sorts:

%Background operators:

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

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

tff(ordered,type,
    ordered: ( $i * $i ) > $o ).

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

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

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

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

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

tff(f_48,axiom,
    ! [X] : ( implies(truth,X) = X ),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ! [X,Y] : ( big_V(X,Y) = implies(implies(X,Y),Y) ),
    file(unknown,unknown) ).

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

tff(f_52,axiom,
    ! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
    file(unknown,unknown) ).

tff(f_93,axiom,
    ! [X,Y] :
      ( ( implies(X,Y) != truth )
      | ordered(X,Y) ),
    file(unknown,unknown) ).

tff(f_116,axiom,
    ! [Y,X,Z] :
      ( ~ ordered(Y,implies(X,Z))
      | ordered(X,implies(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ! [X,Y,Z] :
      ( ~ ordered(X,Y)
      | ordered(implies(X,Z),implies(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_88,axiom,
    ! [X,Y] :
      ( ~ ordered(X,Y)
      | ( implies(X,Y) = truth ) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    big_V(implies(x,y),implies(y,x)) != truth,
    file(unknown,unknown) ).

tff(c_2,plain,
    ! [X_1] : ( implies(truth,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_10,plain,
    ! [X_9,Y_10] : ( implies(implies(X_9,Y_10),Y_10) = big_V(X_9,Y_10) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_885,plain,
    ! [X_80,Y_81,Z_82] : ( implies(implies(X_80,Y_81),implies(implies(Y_81,Z_82),implies(X_80,Z_82))) = truth ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_1007,plain,
    ! [X_1,Z_82] : ( implies(X_1,implies(implies(X_1,Z_82),implies(truth,Z_82))) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_885]) ).

tff(c_1027,plain,
    ! [X_83,Z_84] : ( implies(X_83,big_V(X_83,Z_84)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_2,c_1007]) ).

tff(c_1065,plain,
    ! [Z_84] : ( big_V(truth,Z_84) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1027,c_2]) ).

tff(c_94,plain,
    ! [X_48,Y_49] : ( implies(implies(X_48,Y_49),Y_49) = big_V(X_48,Y_49) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_109,plain,
    ! [X_1] : ( implies(X_1,X_1) = big_V(truth,X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_94]) ).

tff(c_1100,plain,
    ! [X_1] : ( implies(X_1,X_1) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_1065,c_109]) ).

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_52]) ).

tff(c_36,plain,
    ! [Y_6,X_5] : ( big_V(Y_6,X_5) = big_V(X_5,Y_6) ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_10,c_6]) ).

tff(c_1102,plain,
    ! [Z_85] : ( big_V(truth,Z_85) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1027,c_2]) ).

tff(c_1127,plain,
    ! [X_5] : ( big_V(X_5,truth) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_1102]) ).

tff(c_16,plain,
    ! [X_15,Y_16] :
      ( ordered(X_15,Y_16)
      | ( implies(X_15,Y_16) != truth ) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_244,plain,
    ! [X_57,Y_58,Z_59] :
      ( ordered(X_57,implies(Y_58,Z_59))
      | ~ ordered(Y_58,implies(X_57,Z_59)) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_259,plain,
    ! [Y_60,X_61] :
      ( ordered(truth,implies(Y_60,X_61))
      | ~ ordered(Y_60,X_61) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_244]) ).

tff(c_273,plain,
    ! [X_1] :
      ( ordered(truth,big_V(truth,X_1))
      | ~ ordered(X_1,X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_259]) ).

tff(c_1097,plain,
    ! [X_1] :
      ( ordered(truth,truth)
      | ~ ordered(X_1,X_1) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1065,c_273]) ).

tff(c_1658,plain,
    ! [X_97] : ~ ordered(X_97,X_97),
    inference(splitLeft,[status(thm)],[c_1097]) ).

tff(c_1670,plain,
    ! [Y_16] : ( implies(Y_16,Y_16) != truth ),
    inference(resolution,[status(thm)],[c_16,c_1658]) ).

tff(c_1676,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1100,c_1670]) ).

tff(c_1677,plain,
    ordered(truth,truth),
    inference(splitRight,[status(thm)],[c_1097]) ).

tff(c_770,plain,
    ! [X_77,Z_78,Y_79] :
      ( ordered(implies(X_77,Z_78),implies(Y_79,Z_78))
      | ~ ordered(X_77,Y_79) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_1678,plain,
    ! [X_98,X_99] :
      ( ordered(implies(X_98,X_99),X_99)
      | ~ ordered(X_98,truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_770]) ).

tff(c_1708,plain,
    ! [X_1] :
      ( ordered(X_1,X_1)
      | ~ ordered(truth,truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1678]) ).

tff(c_1826,plain,
    ! [X_102] : ordered(X_102,X_102),
    inference(demodulation,[status(thm),theory(equality)],[c_1677,c_1708]) ).

tff(c_24,plain,
    ! [X_27,Y_26,Z_28] :
      ( ordered(X_27,implies(Y_26,Z_28))
      | ~ ordered(Y_26,implies(X_27,Z_28)) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_1829,plain,
    ! [X_27,Z_28] : ordered(X_27,implies(implies(X_27,Z_28),Z_28)),
    inference(resolution,[status(thm)],[c_1826,c_24]) ).

tff(c_1837,plain,
    ! [X_103,Z_104] : ordered(X_103,big_V(X_103,Z_104)),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_1829]) ).

tff(c_1843,plain,
    ! [X_5] : ordered(X_5,truth),
    inference(superposition,[status(thm),theory(equality)],[c_1127,c_1837]) ).

tff(c_820,plain,
    ! [X_77,X_1] :
      ( ordered(implies(X_77,X_1),X_1)
      | ~ ordered(X_77,truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_770]) ).

tff(c_1907,plain,
    ! [X_108,X_109] : ordered(implies(X_108,X_109),X_109),
    inference(demodulation,[status(thm),theory(equality)],[c_1843,c_820]) ).

tff(c_1947,plain,
    ! [X_110] : ordered(truth,X_110),
    inference(superposition,[status(thm),theory(equality)],[c_1100,c_1907]) ).

tff(c_14,plain,
    ! [X_13,Y_14] :
      ( ( implies(X_13,Y_14) = truth )
      | ~ ordered(X_13,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_1974,plain,
    ! [X_113] : ( implies(truth,X_113) = truth ),
    inference(resolution,[status(thm)],[c_1947,c_14]) ).

tff(c_2015,plain,
    ! [X_113] : ( implies(truth,X_113) = big_V(truth,X_113) ),
    inference(superposition,[status(thm),theory(equality)],[c_1974,c_10]) ).

tff(c_2054,plain,
    ! [X_114] : ( truth = X_114 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1065,c_2015]) ).

tff(c_34,plain,
    big_V(implies(x,y),implies(y,x)) != truth,
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_2147,plain,
    $false,
    inference(superposition,[status(thm),theory(equality)],[c_2054,c_34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : LCL109-5 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.10  % 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
% 0.09/0.29  % Computer : n017.cluster.edu
% 0.09/0.29  % Model    : x86_64 x86_64
% 0.09/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29  % Memory   : 8042.1875MB
% 0.09/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29  % CPULimit : 300
% 0.09/0.29  % WCLimit  : 300
% 0.09/0.29  % DateTime : Thu Aug  3 12:50:36 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 4.97/2.14  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.97/2.15  
% 4.97/2.15  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.97/2.18  
% 4.97/2.18  Inference rules
% 4.97/2.18  ----------------------
% 4.97/2.18  #Ref     : 0
% 4.97/2.18  #Sup     : 589
% 4.97/2.18  #Fact    : 0
% 4.97/2.18  #Define  : 0
% 4.97/2.18  #Split   : 1
% 4.97/2.18  #Chain   : 0
% 4.97/2.18  #Close   : 0
% 4.97/2.18  
% 4.97/2.18  Ordering : KBO
% 4.97/2.18  
% 4.97/2.18  Simplification rules
% 4.97/2.18  ----------------------
% 4.97/2.18  #Subsume      : 38
% 4.97/2.18  #Demod        : 257
% 4.97/2.18  #Tautology    : 214
% 4.97/2.18  #SimpNegUnit  : 0
% 4.97/2.18  #BackRed      : 8
% 4.97/2.18  
% 4.97/2.18  #Partial instantiations: 0
% 4.97/2.18  #Strategies tried      : 1
% 4.97/2.18  
% 4.97/2.18  Timing (in seconds)
% 4.97/2.18  ----------------------
% 4.97/2.19  Preprocessing        : 0.46
% 4.97/2.19  Parsing              : 0.23
% 4.97/2.19  CNF conversion       : 0.02
% 4.97/2.19  Main loop            : 0.80
% 4.97/2.19  Inferencing          : 0.27
% 4.97/2.19  Reduction            : 0.29
% 4.97/2.19  Demodulation         : 0.23
% 4.97/2.19  BG Simplification    : 0.04
% 4.97/2.19  Subsumption          : 0.13
% 4.97/2.19  Abstraction          : 0.03
% 4.97/2.19  MUC search           : 0.00
% 4.97/2.19  Cooper               : 0.00
% 4.97/2.19  Total                : 1.32
% 4.97/2.19  Index Insertion      : 0.00
% 4.97/2.19  Index Deletion       : 0.00
% 4.97/2.19  Index Matching       : 0.00
% 4.97/2.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------