TSTP Solution File: LCL158-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL158-1 : 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 : n010.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 6.68s 2.78s
% Output   : CNFRefutation 6.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   24
% Syntax   : Number of formulae    :  102 (  93 unt;   9 typ;   0 def)
%            Number of atoms       :   93 (  92 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   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   :  123 (; 123   !;   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_81,axiom,
    ! [X,Y] : ( or(X,Y) = implies(not(X),Y) ),
    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_87,axiom,
    ! [X,Y] : ( and(X,Y) = not(or(not(X),not(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_52,axiom,
    ! [X,Y] : ( implies(implies(X,Y),Y) = implies(implies(Y,X),X) ),
    file(unknown,unknown) ).

tff(f_89,axiom,
    ! [X,Y,Z] : ( and(and(X,Y),Z) = and(X,and(Y,Z)) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X,Y] : ( and(X,Y) = and(Y,X) ),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [X,Y] : ( xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ),
    file(unknown,unknown) ).

tff(f_120,axiom,
    ! [X,Y] : ( xor(X,Y) = xor(Y,X) ),
    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(xor(truth,x),x) != falsehood,
    file(unknown,unknown) ).

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

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_2,plain,
    ! [X_1] : ( implies(truth,X_1) = X_1 ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_1142,plain,
    ! [X_72,Y_73,Z_74] : ( implies(implies(X_72,Y_73),implies(implies(Y_73,Z_74),implies(X_72,Z_74))) = truth ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_1308,plain,
    ! [Y_73,X_1] : ( implies(implies(truth,Y_73),implies(implies(Y_73,X_1),X_1)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_1142]) ).

tff(c_1480,plain,
    ! [Y_76,X_77] : ( implies(Y_76,implies(implies(Y_76,X_77),X_77)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1308]) ).

tff(c_1518,plain,
    ! [X_77] : ( implies(implies(truth,X_77),X_77) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1480,c_2]) ).

tff(c_1597,plain,
    ! [X_78] : ( implies(X_78,X_78) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1518]) ).

tff(c_1735,plain,
    ! [X_80] : ( or(X_80,not(X_80)) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_1597]) ).

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_1763,plain,
    ! [X_16] : ( and(X_16,not(X_16)) = not(truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_1735,c_16]) ).

tff(c_1799,plain,
    ! [X_16] : ( and(X_16,not(X_16)) = falsehood ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_1763]) ).

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_172,plain,
    ! [Y_44] : ( or(truth,Y_44) = implies(falsehood,Y_44) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_163]) ).

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_358,plain,
    implies(implies(falsehood,falsehood),truth) = truth,
    inference(superposition,[status(thm),theory(equality)],[c_172,c_347]) ).

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_402,plain,
    ! [Y_54,X_55] : ( implies(implies(Y_54,X_55),X_55) = implies(implies(X_55,Y_54),Y_54) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_480,plain,
    ! [X_56] : ( implies(implies(X_56,truth),truth) = implies(X_56,X_56) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_402]) ).

tff(c_505,plain,
    ! [X_9] : ( or(X_9,not(X_9)) = implies(implies(not(X_9),truth),truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_480,c_10]) ).

tff(c_1063,plain,
    ! [X_71] : ( or(X_71,not(X_71)) = implies(implies(falsehood,X_71),truth) ),
    inference(demodulation,[status(thm),theory(equality)],[c_191,c_10,c_505]) ).

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_1089,plain,
    implies(implies(implies(falsehood,falsehood),truth),not(falsehood)) = truth,
    inference(superposition,[status(thm),theory(equality)],[c_1063,c_362]) ).

tff(c_1136,plain,
    not(falsehood) = truth,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_358,c_1089]) ).

tff(c_1370,plain,
    ! [Y_10] : ( or(falsehood,Y_10) = implies(truth,Y_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_1136,c_10]) ).

tff(c_1424,plain,
    ! [Y_75] : ( or(falsehood,Y_75) = Y_75 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1370]) ).

tff(c_1471,plain,
    ! [X_14] : ( or(X_14,falsehood) = X_14 ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1424]) ).

tff(c_1584,plain,
    ! [X_77] : ( implies(X_77,X_77) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1518]) ).

tff(c_441,plain,
    ! [X_1] : ( implies(implies(X_1,truth),truth) = implies(X_1,X_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_402]) ).

tff(c_1928,plain,
    ! [X_84] : ( implies(implies(X_84,truth),truth) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_1584,c_441]) ).

tff(c_1330,plain,
    ! [Y_73,X_1] : ( implies(Y_73,implies(implies(Y_73,X_1),X_1)) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1308]) ).

tff(c_2015,plain,
    ! [X_85] : ( implies(X_85,truth) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_1928,c_1330]) ).

tff(c_2059,plain,
    ! [X_9] : ( or(X_9,truth) = truth ),
    inference(superposition,[status(thm),theory(equality)],[c_2015,c_10]) ).

tff(c_2247,plain,
    ! [Y_90] : ( implies(falsehood,Y_90) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2059,c_191]) ).

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_2279,plain,
    ! [Y_90] : ( implies(implies(Y_90,falsehood),falsehood) = implies(truth,Y_90) ),
    inference(superposition,[status(thm),theory(equality)],[c_2247,c_6]) ).

tff(c_3018,plain,
    ! [Y_101] : ( implies(implies(Y_101,falsehood),falsehood) = Y_101 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2279]) ).

tff(c_3088,plain,
    ! [X_9] : ( implies(or(X_9,falsehood),falsehood) = not(X_9) ),
    inference(superposition,[status(thm),theory(equality)],[c_10,c_3018]) ).

tff(c_3111,plain,
    ! [X_9] : ( implies(X_9,falsehood) = not(X_9) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1471,c_3088]) ).

tff(c_2104,plain,
    ! [Y_15] : ( implies(falsehood,Y_15) = truth ),
    inference(demodulation,[status(thm),theory(equality)],[c_2059,c_191]) ).

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_225,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_1349,plain,
    ! [Y_47] : ( not(or(not(Y_47),truth)) = and(falsehood,Y_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_1136,c_225]) ).

tff(c_1376,plain,
    ! [Y_47] : ( not(implies(falsehood,not(Y_47))) = and(falsehood,Y_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_172,c_14,c_1349]) ).

tff(c_7369,plain,
    ! [Y_47] : ( and(falsehood,Y_47) = falsehood ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_2104,c_1376]) ).

tff(c_7370,plain,
    ! [Y_155] : ( and(falsehood,Y_155) = falsehood ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_2104,c_1376]) ).

tff(c_692,plain,
    ! [X_61,Y_62,Z_63] : ( and(and(X_61,Y_62),Z_63) = and(X_61,and(Y_62,Z_63)) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_20,plain,
    ! [Y_22,X_21] : ( and(Y_22,X_21) = and(X_21,Y_22) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_701,plain,
    ! [Z_63,X_61,Y_62] : ( and(Z_63,and(X_61,Y_62)) = and(X_61,and(Y_62,Z_63)) ),
    inference(superposition,[status(thm),theory(equality)],[c_692,c_20]) ).

tff(c_7375,plain,
    ! [Y_155,Z_63] : ( and(falsehood,and(Y_155,Z_63)) = and(Z_63,falsehood) ),
    inference(superposition,[status(thm),theory(equality)],[c_7370,c_701]) ).

tff(c_7436,plain,
    ! [Z_63] : ( and(Z_63,falsehood) = falsehood ),
    inference(demodulation,[status(thm),theory(equality)],[c_7369,c_7375]) ).

tff(c_2304,plain,
    ! [Y_90] : ( implies(implies(Y_90,falsehood),falsehood) = Y_90 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2279]) ).

tff(c_3226,plain,
    ! [Y_103] : ( not(not(Y_103)) = Y_103 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3111,c_3111,c_2304]) ).

tff(c_3268,plain,
    ! [Y_103,Y_10] : ( or(not(Y_103),Y_10) = implies(Y_103,Y_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_3226,c_10]) ).

tff(c_3113,plain,
    ! [Y_90] : ( not(not(Y_90)) = Y_90 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3111,c_3111,c_2304]) ).

tff(c_1383,plain,
    ! [Y_10] : ( or(falsehood,Y_10) = Y_10 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1370]) ).

tff(c_228,plain,
    ! [Y_47] : ( not(or(falsehood,not(Y_47))) = and(truth,Y_47) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_198]) ).

tff(c_1422,plain,
    ! [Y_47] : ( not(not(Y_47)) = and(truth,Y_47) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1383,c_228]) ).

tff(c_3224,plain,
    ! [Y_47] : ( and(truth,Y_47) = Y_47 ),
    inference(demodulation,[status(thm),theory(equality)],[c_3113,c_1422]) ).

tff(c_919,plain,
    ! [X_68,Y_69] : ( or(and(X_68,not(Y_69)),and(not(X_68),Y_69)) = xor(X_68,Y_69) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_981,plain,
    ! [X_68] : ( or(and(X_68,falsehood),and(not(X_68),truth)) = xor(X_68,truth) ),
    inference(superposition,[status(thm),theory(equality)],[c_32,c_919]) ).

tff(c_992,plain,
    ! [X_68] : ( or(and(X_68,falsehood),and(truth,not(X_68))) = xor(X_68,truth) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_981]) ).

tff(c_8119,plain,
    ! [X_164] : ( xor(X_164,truth) = not(X_164) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3111,c_7436,c_3268,c_14,c_3224,c_992]) ).

tff(c_24,plain,
    ! [Y_26,X_25] : ( xor(Y_26,X_25) = xor(X_25,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_8133,plain,
    ! [X_164] : ( xor(truth,X_164) = not(X_164) ),
    inference(superposition,[status(thm),theory(equality)],[c_8119,c_24]) ).

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(xor(truth,x),x) != falsehood,
    inference(cnfTransformation,[status(thm)],[f_133]) ).

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

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

tff(c_8162,plain,
    and(x,not(x)) != falsehood,
    inference(demodulation,[status(thm),theory(equality)],[c_8133,c_38]) ).

tff(c_8165,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1799,c_8162]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LCL158-1 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13  % 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
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 13:20:29 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 6.68/2.78  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.68/2.79  
% 6.68/2.79  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.68/2.83  
% 6.68/2.83  Inference rules
% 6.68/2.83  ----------------------
% 6.68/2.83  #Ref     : 0
% 6.68/2.83  #Sup     : 2022
% 6.68/2.83  #Fact    : 0
% 6.68/2.83  #Define  : 0
% 6.68/2.83  #Split   : 0
% 6.68/2.83  #Chain   : 0
% 6.68/2.83  #Close   : 0
% 6.68/2.83  
% 6.68/2.83  Ordering : KBO
% 6.68/2.83  
% 6.68/2.83  Simplification rules
% 6.68/2.83  ----------------------
% 6.68/2.83  #Subsume      : 47
% 6.68/2.83  #Demod        : 2031
% 6.68/2.83  #Tautology    : 1308
% 6.68/2.83  #SimpNegUnit  : 0
% 6.68/2.83  #BackRed      : 21
% 6.68/2.83  
% 6.68/2.83  #Partial instantiations: 0
% 6.68/2.83  #Strategies tried      : 1
% 6.68/2.83  
% 6.68/2.83  Timing (in seconds)
% 6.68/2.83  ----------------------
% 6.68/2.83  Preprocessing        : 0.48
% 6.68/2.83  Parsing              : 0.25
% 6.68/2.83  CNF conversion       : 0.02
% 6.68/2.84  Main loop            : 1.26
% 6.68/2.84  Inferencing          : 0.38
% 6.68/2.84  Reduction            : 0.57
% 6.68/2.84  Demodulation         : 0.48
% 6.68/2.84  BG Simplification    : 0.04
% 6.68/2.84  Subsumption          : 0.18
% 6.68/2.84  Abstraction          : 0.05
% 6.68/2.84  MUC search           : 0.00
% 6.68/2.84  Cooper               : 0.00
% 6.68/2.84  Total                : 1.80
% 6.68/2.84  Index Insertion      : 0.00
% 6.68/2.84  Index Deletion       : 0.00
% 6.68/2.84  Index Matching       : 0.00
% 6.68/2.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------