TSTP Solution File: LCL157-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL157-1 : 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/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 : n029.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 10:47:29 EDT 2023

% Result   : Unsatisfiable 6.39s 2.60s
% Output   : CNFRefutation 6.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   63 (  54 unt;   9 typ;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    4 (   4   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   70 (;  70   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ xor > or > implies > and_star > and > #nlpp > not > 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(or,type,
    or: ( $i * $i ) > $i ).

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

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

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

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

tff(f_129,axiom,
    not(truth) = falsehood,
    file(unknown,unknown) ).

tff(f_48,axiom,
    ! [X] : ( implies(truth,X) = X ),
    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_81,axiom,
    ! [X,Y] : ( or(X,Y) = implies(not(X),Y) ),
    file(unknown,unknown) ).

tff(f_85,axiom,
    ! [X,Y] : ( or(X,Y) = or(Y,X) ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [X,Y] : ( implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
    file(unknown,unknown) ).

tff(f_87,axiom,
    ! [X,Y] : ( and(X,Y) = not(or(not(X),not(Y))) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ! [X,Y] : ( and_star(X,Y) = not(or(not(X),not(Y))) ),
    file(unknown,unknown) ).

tff(f_127,axiom,
    ! [X,Y] : ( and_star(X,Y) = and_star(Y,X) ),
    file(unknown,unknown) ).

tff(f_133,axiom,
    and_star(x,falsehood) != falsehood,
    file(unknown,unknown) ).

tff(c_32,plain,
    not(truth) = falsehood,
    inference(cnfTransformation,[status(thm)],[f_129]) ).

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

tff(c_919,plain,
    ! [X_68,Y_69,Z_70] : ( implies(implies(X_68,Y_69),implies(implies(Y_69,Z_70),implies(X_68,Z_70))) = truth ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_1070,plain,
    ! [X_1,Z_70] : ( implies(X_1,implies(implies(X_1,Z_70),implies(truth,Z_70))) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_919]) ).

tff(c_1098,plain,
    ! [X_71,Z_72] : ( implies(X_71,implies(implies(X_71,Z_72),Z_72)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1070]) ).

tff(c_1136,plain,
    ! [Z_72] : ( implies(implies(truth,Z_72),Z_72) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1098,c_2]) ).

tff(c_1205,plain,
    ! [Z_72] : ( implies(Z_72,Z_72) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1136]) ).

tff(c_516,plain,
    ! [Y_58,X_59] : ( implies(implies(Y_58,X_59),X_59) = implies(implies(X_59,Y_58),Y_58) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_555,plain,
    ! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_516]) ).

tff(c_1159,plain,
    ! [X_1] : ( implies(X_1,implies(X_1,X_1)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_555,c_1098]) ).

tff(c_1958,plain,
    ! [X_83] : ( implies(X_83,truth) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_1205,c_1159]) ).

tff(c_10,plain,
    ! [X_9,Y_10] : ( implies(not(X_9),Y_10) = or(X_9,Y_10) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_2002,plain,
    ! [X_9] : ( or(X_9,truth) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1958,c_10]) ).

tff(c_14,plain,
    ! [Y_15,X_14] : ( or(Y_15,X_14) = or(X_14,Y_15) ),
    inference(cnfTransformation,[status(thm)],[f_85]) ).

tff(c_163,plain,
    ! [X_43,Y_44] : ( implies(not(X_43),Y_44) = or(X_43,Y_44) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_175,plain,
    ! [Y_45] : ( or(truth,Y_45) = implies(falsehood,Y_45) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).

tff(c_191,plain,
    ! [Y_15] : ( or(Y_15,truth) = implies(falsehood,Y_15) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_175]) ).

tff(c_2047,plain,
    ! [Y_15] : ( implies(falsehood,Y_15) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2002,c_191]) ).

tff(c_172,plain,
    ! [Y_44] : ( or(truth,Y_44) = implies(falsehood,Y_44) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).

tff(c_1220,plain,
    ! [Z_73] : ( implies(Z_73,Z_73) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1136]) ).

tff(c_1347,plain,
    ! [X_76] : ( or(X_76,not(X_76)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_1220]) ).

tff(c_8,plain,
    ! [X_7,Y_8] : ( implies(implies(not(X_7),not(Y_8)),implies(Y_8,X_7)) = truth ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_305,plain,
    ! [X_50,Y_51] : ( implies(or(X_50,not(Y_51)),implies(Y_51,X_50)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_10,c_8]) ).

tff(c_339,plain,
    ! [X_1] : ( implies(or(X_1,not(truth)),X_1) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_305]) ).

tff(c_347,plain,
    ! [X_52] : ( implies(or(X_52,falsehood),X_52) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_339]) ).

tff(c_362,plain,
    ! [X_14] : ( implies(or(falsehood,X_14),X_14) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_347]) ).

tff(c_1372,plain,
    implies(truth,not(falsehood)) = truth,
    inference(superposition,[status(thm),theory(equality)],[c_1347,c_362]) ).

tff(c_1096,plain,
    ! [X_1,Z_70] : ( implies(X_1,implies(implies(X_1,Z_70),Z_70)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1070]) ).

tff(c_1617,plain,
    implies(truth,implies(truth,not(falsehood))) = truth,
    inference(superposition,[status(thm),theory(equality)],[c_1372,c_1096]) ).

tff(c_1647,plain,
    not(falsehood) = truth,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_1617]) ).

tff(c_198,plain,
    ! [X_46,Y_47] : ( not(or(not(X_46),not(Y_47))) = and(X_46,Y_47) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_222,plain,
    ! [Y_47,X_46] : ( not(or(not(Y_47),not(X_46))) = and(X_46,Y_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_198]) ).

tff(c_1682,plain,
    ! [Y_47] : ( not(or(not(Y_47),truth)) = and(falsehood,Y_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_1647,c_222]) ).

tff(c_1709,plain,
    ! [Y_47] : ( not(implies(falsehood,not(Y_47))) = and(falsehood,Y_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_172,c_14,c_1682]) ).

tff(c_7385,plain,
    ! [Y_47] : ( and(falsehood,Y_47) = falsehood ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_2047,c_1709]) ).

tff(c_16,plain,
    ! [X_16,Y_17] : ( not(or(not(X_16),not(Y_17))) = and(X_16,Y_17) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_26,plain,
    ! [X_27,Y_28] : ( not(or(not(X_27),not(Y_28))) = and_star(X_27,Y_28) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_36,plain,
    ! [X_27,Y_28] : ( and_star(X_27,Y_28) = and(X_27,Y_28) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_26]) ).

tff(c_30,plain,
    ! [Y_33,X_32] : ( and_star(Y_33,X_32) = and_star(X_32,Y_33) ),
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_34,plain,
    and_star(x,falsehood) != falsehood,
    inference(cnfTransformation,[status(thm)],[f_133]) ).

tff(c_35,plain,
    and_star(falsehood,x) != falsehood,
    inference(demodulation,[status(thm),theory(equality)],[c_30,c_34]) ).

tff(c_38,plain,
    and(falsehood,x) != falsehood,
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_35]) ).

tff(c_7390,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_7385,c_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL157-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % 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
% 0.13/0.35  % Computer : n029.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 14:38:37 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.39/2.60  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.39/2.61  
% 6.39/2.61  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.79/2.64  
% 6.79/2.64  Inference rules
% 6.79/2.64  ----------------------
% 6.79/2.64  #Ref     : 0
% 6.79/2.64  #Sup     : 1836
% 6.79/2.64  #Fact    : 0
% 6.79/2.64  #Define  : 0
% 6.79/2.64  #Split   : 0
% 6.79/2.64  #Chain   : 0
% 6.79/2.64  #Close   : 0
% 6.79/2.64  
% 6.79/2.64  Ordering : KBO
% 6.79/2.64  
% 6.79/2.64  Simplification rules
% 6.79/2.64  ----------------------
% 6.79/2.64  #Subsume      : 43
% 6.79/2.64  #Demod        : 1819
% 6.79/2.64  #Tautology    : 1176
% 6.79/2.64  #SimpNegUnit  : 0
% 6.79/2.64  #BackRed      : 18
% 6.79/2.64  
% 6.79/2.64  #Partial instantiations: 0
% 6.79/2.64  #Strategies tried      : 1
% 6.79/2.64  
% 6.79/2.64  Timing (in seconds)
% 6.79/2.64  ----------------------
% 6.79/2.65  Preprocessing        : 0.46
% 6.79/2.65  Parsing              : 0.25
% 6.79/2.65  CNF conversion       : 0.02
% 6.79/2.65  Main loop            : 1.13
% 6.79/2.65  Inferencing          : 0.32
% 6.79/2.65  Reduction            : 0.51
% 6.79/2.65  Demodulation         : 0.44
% 6.79/2.65  BG Simplification    : 0.04
% 6.79/2.65  Subsumption          : 0.18
% 6.79/2.65  Abstraction          : 0.05
% 6.79/2.65  MUC search           : 0.00
% 6.79/2.65  Cooper               : 0.00
% 6.79/2.65  Total                : 1.64
% 6.79/2.65  Index Insertion      : 0.00
% 6.79/2.65  Index Deletion       : 0.00
% 6.79/2.65  Index Matching       : 0.00
% 6.79/2.65  BG Taut test         : 0.00
%------------------------------------------------------------------------------