TSTP Solution File: LAT394-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LAT394-2 : TPTP v8.1.2. Released v5.4.0.
% 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 : n024.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 10:47:07 EDT 2023

% Result   : Unsatisfiable 71.41s 37.13s
% Output   : CNFRefutation 71.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   57 (  54 unt;   3 typ;   0 def)
%            Number of atoms       :   54 (  53 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :   11 (   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    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :  132 (; 132   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ f > #nlpp > x1 > x0

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(x1,type,
    x1: $i ).

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

tff(x0,type,
    x0: $i ).

tff(f_23,axiom,
    ! [A,B,C,D] : ( f(f(f(f(A,B),f(B,C)),D),f(B,f(f(B,f(f(A,A),A)),C))) = B ),
    file(unknown,unknown) ).

tff(f_25,axiom,
    f(x0,f(x0,x0)) != f(x1,f(x1,x1)),
    file(unknown,unknown) ).

tff(c_5,plain,
    ! [A_5,B_6,C_7,D_8] : ( f(f(f(f(A_5,B_6),f(B_6,C_7)),D_8),f(B_6,f(f(B_6,f(f(A_5,A_5),A_5)),C_7))) = B_6 ),
    inference(cnfTransformation,[status(thm)],[f_23]) ).

tff(c_2,plain,
    ! [A_1,B_2,C_3,D_4] : ( f(f(f(f(A_1,B_2),f(B_2,C_3)),D_4),f(B_2,f(f(B_2,f(f(A_1,A_1),A_1)),C_3))) = B_2 ),
    inference(cnfTransformation,[status(thm)],[f_23]) ).

tff(c_1137,plain,
    ! [B_29,D_30,A_31,C_32] : ( f(f(B_29,D_30),f(B_29,f(f(B_29,f(f(f(f(A_31,B_29),f(B_29,C_32)),f(f(A_31,B_29),f(B_29,C_32))),f(f(A_31,B_29),f(B_29,C_32)))),f(f(B_29,f(f(A_31,A_31),A_31)),C_32)))) = B_29 ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_1304,plain,
    ! [A_1,B_2,C_3] : ( f(f(A_1,B_2),f(B_2,f(f(B_2,f(f(A_1,A_1),A_1)),C_3))) = B_2 ),
    inference(superposition,[status(thm),theory(equality)],[c_1137,c_2]) ).

tff(c_2336,plain,
    ! [A_37,B_38,C_39] : ( f(f(A_37,B_38),f(B_38,f(f(B_38,f(f(A_37,A_37),A_37)),C_39))) = B_38 ),
    inference(superposition,[status(thm),theory(equality)],[c_1137,c_2]) ).

tff(c_19,plain,
    ! [B_6,C_7,A_5,C_3] : ( f(B_6,f(f(B_6,C_7),f(f(f(B_6,C_7),f(f(f(A_5,B_6),f(A_5,B_6)),f(A_5,B_6))),C_3))) = f(B_6,C_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_1290,plain,
    ! [B_6,C_7] : ( f(B_6,f(f(B_6,C_7),f(B_6,C_7))) = f(B_6,C_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_1137,c_19]) ).

tff(c_2352,plain,
    ! [A_37,B_38,C_39] : ( f(f(A_37,B_38),f(B_38,f(f(A_37,B_38),f(B_38,f(f(B_38,f(f(A_37,A_37),A_37)),C_39))))) = f(f(A_37,B_38),f(B_38,f(f(B_38,f(f(A_37,A_37),A_37)),C_39))) ),
    inference(superposition,[status(thm),theory(equality)],[c_2336,c_1290]) ).

tff(c_2579,plain,
    ! [A_37,B_38] : ( f(f(A_37,B_38),f(B_38,B_38)) = B_38 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1304,c_1304,c_2352]) ).

tff(c_50,plain,
    ! [B_9,C_10,A_11,C_12] : ( f(B_9,f(f(B_9,C_10),f(f(f(B_9,C_10),f(f(f(A_11,B_9),f(A_11,B_9)),f(A_11,B_9))),C_12))) = f(B_9,C_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_284,plain,
    ! [A_16,B_17,C_18] : ( f(f(A_16,B_17),f(f(f(A_16,B_17),f(B_17,C_18)),B_17)) = f(f(A_16,B_17),f(B_17,C_18)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_50]) ).

tff(c_392,plain,
    ! [A_1,B_2,C_3] : ( f(f(f(f(A_1,B_2),f(B_2,C_3)),B_2),f(B_2,f(f(B_2,f(f(A_1,A_1),A_1)),C_3))) = f(f(f(f(A_1,B_2),f(B_2,C_3)),B_2),f(B_2,B_2)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_284]) ).

tff(c_423,plain,
    ! [A_19,B_20,C_21] : ( f(f(f(f(A_19,B_20),f(B_20,C_21)),B_20),f(B_20,B_20)) = B_20 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_392]) ).

tff(c_422,plain,
    ! [A_1,B_2,C_3] : ( f(f(f(f(A_1,B_2),f(B_2,C_3)),B_2),f(B_2,B_2)) = B_2 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_392]) ).

tff(c_546,plain,
    ! [B_22] : ( f(f(B_22,B_22),f(B_22,B_22)) = B_22 ),
    inference(superposition,[status(thm),theory(equality)],[c_423,c_422]) ).

tff(c_73,plain,
    ! [B_6,C_7,A_5] : ( f(B_6,f(f(B_6,C_7),f(f(f(A_5,B_6),f(A_5,B_6)),f(A_5,B_6)))) = f(B_6,C_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_50,c_19]) ).

tff(c_591,plain,
    ! [B_22,C_7] : ( f(B_22,f(f(B_22,C_7),f(B_22,f(B_22,B_22)))) = f(B_22,C_7) ),
    inference(superposition,[status(thm),theory(equality)],[c_546,c_73]) ).

tff(c_5896,plain,
    ! [A_61,B_62] : ( f(f(A_61,B_62),f(B_62,f(f(A_61,A_61),A_61))) = B_62 ),
    inference(superposition,[status(thm),theory(equality)],[c_19,c_2336]) ).

tff(c_15,plain,
    ! [B_6,D_4,A_5,C_7] : ( f(f(B_6,D_4),f(B_6,f(f(B_6,f(f(f(f(A_5,B_6),f(B_6,C_7)),f(f(A_5,B_6),f(B_6,C_7))),f(f(A_5,B_6),f(B_6,C_7)))),f(f(B_6,f(f(A_5,A_5),A_5)),C_7)))) = B_6 ),
    inference(superposition,[status(thm),theory(equality)],[c_5,c_2]) ).

tff(c_1787,plain,
    ! [B_33,C_34] : ( f(B_33,f(f(B_33,C_34),f(B_33,C_34))) = f(B_33,C_34) ),
    inference(superposition,[status(thm),theory(equality)],[c_1137,c_19]) ).

tff(c_1911,plain,
    ! [B_6,D_4,A_5,C_7] : ( f(f(B_6,D_4),f(B_6,f(f(B_6,D_4),f(B_6,f(f(B_6,f(f(f(f(A_5,B_6),f(B_6,C_7)),f(f(A_5,B_6),f(B_6,C_7))),f(f(A_5,B_6),f(B_6,C_7)))),f(f(B_6,f(f(A_5,A_5),A_5)),C_7)))))) = f(f(B_6,D_4),f(B_6,f(f(B_6,f(f(f(f(A_5,B_6),f(B_6,C_7)),f(f(A_5,B_6),f(B_6,C_7))),f(f(A_5,B_6),f(B_6,C_7)))),f(f(B_6,f(f(A_5,A_5),A_5)),C_7)))) ),
    inference(superposition,[status(thm),theory(equality)],[c_15,c_1787]) ).

tff(c_2019,plain,
    ! [B_6,D_4] : ( f(f(B_6,D_4),f(B_6,B_6)) = B_6 ),
    inference(demodulation,[status(thm),theory(equality)],[c_15,c_15,c_1911]) ).

tff(c_6320,plain,
    ! [B_63,A_64] : ( f(B_63,f(f(A_64,B_63),f(A_64,B_63))) = f(A_64,B_63) ),
    inference(superposition,[status(thm),theory(equality)],[c_5896,c_2019]) ).

tff(c_2044,plain,
    ! [B_35,D_36] : ( f(f(B_35,D_36),f(B_35,B_35)) = B_35 ),
    inference(demodulation,[status(thm),theory(equality)],[c_15,c_15,c_1911]) ).

tff(c_139,plain,
    ! [A_1,B_2,C_3] : ( f(f(A_1,B_2),f(f(f(A_1,B_2),f(B_2,C_3)),B_2)) = f(f(A_1,B_2),f(B_2,C_3)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_50]) ).

tff(c_2167,plain,
    ! [B_35,D_36,C_3] : ( f(f(f(B_35,D_36),f(B_35,B_35)),f(f(B_35,f(f(B_35,B_35),C_3)),f(B_35,B_35))) = f(f(f(B_35,D_36),f(B_35,B_35)),f(f(B_35,B_35),C_3)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2044,c_139]) ).

tff(c_2310,plain,
    ! [B_35,C_3] : ( f(B_35,f(f(B_35,B_35),C_3)) = f(B_35,B_35) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2019,c_2019,c_2019,c_2167]) ).

tff(c_6387,plain,
    ! [B_35,A_64] : ( f(B_35,f(A_64,f(B_35,B_35))) = f(B_35,B_35) ),
    inference(superposition,[status(thm),theory(equality)],[c_6320,c_2310]) ).

tff(c_46284,plain,
    ! [A_185,D_183,A_182,B_184,C_186] : ( f(f(f(f(A_185,B_184),f(B_184,f(f(f(B_184,f(f(A_185,A_185),A_185)),f(f(f(A_182,B_184),f(A_182,B_184)),f(A_182,B_184))),C_186))),D_183),f(B_184,f(f(A_185,A_185),A_185))) = B_184 ),
    inference(superposition,[status(thm),theory(equality)],[c_50,c_2]) ).

tff(c_47722,plain,
    ! [A_185,B_35,D_183] : ( f(f(f(f(A_185,B_35),f(B_35,B_35)),D_183),f(B_35,f(f(A_185,A_185),A_185))) = B_35 ),
    inference(superposition,[status(thm),theory(equality)],[c_6387,c_46284]) ).

tff(c_48656,plain,
    ! [B_187,D_188,A_189] : ( f(f(B_187,D_188),f(B_187,f(f(A_189,A_189),A_189))) = B_187 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2579,c_47722]) ).

tff(c_2617,plain,
    ! [A_40,B_41] : ( f(f(A_40,B_41),f(B_41,B_41)) = B_41 ),
    inference(demodulation,[status(thm),theory(equality)],[c_1304,c_1304,c_2352]) ).

tff(c_5445,plain,
    ! [B_58,D_59,A_60] : ( f(f(B_58,D_59),f(B_58,f(f(B_58,f(f(A_60,A_60),A_60)),B_58))) = B_58 ),
    inference(superposition,[status(thm),theory(equality)],[c_2617,c_2]) ).

tff(c_2892,plain,
    ! [B_42,D_43] : ( f(f(f(B_42,B_42),D_43),B_42) = f(B_42,B_42) ),
    inference(superposition,[status(thm),theory(equality)],[c_2019,c_2044]) ).

tff(c_2987,plain,
    ! [B_42,C_3] : ( f(f(B_42,B_42),f(B_42,C_3)) = f(f(B_42,B_42),f(B_42,B_42)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2892,c_139]) ).

tff(c_3129,plain,
    ! [B_42,C_3] : ( f(f(B_42,B_42),f(B_42,C_3)) = B_42 ),
    inference(demodulation,[status(thm),theory(equality)],[c_2019,c_2987]) ).

tff(c_5535,plain,
    ! [B_58,D_59] : ( f(f(f(B_58,D_59),f(B_58,D_59)),B_58) = f(B_58,D_59) ),
    inference(superposition,[status(thm),theory(equality)],[c_5445,c_3129]) ).

tff(c_50289,plain,
    ! [B_190,A_191] : ( f(B_190,f(f(A_191,A_191),A_191)) = f(B_190,B_190) ),
    inference(superposition,[status(thm),theory(equality)],[c_48656,c_5535]) ).

tff(c_6394,plain,
    ! [B_63,A_64] : ( f(f(B_63,B_63),f(A_64,B_63)) = B_63 ),
    inference(superposition,[status(thm),theory(equality)],[c_6320,c_3129]) ).

tff(c_51250,plain,
    ! [B_63,A_191] : ( f(f(B_63,B_63),f(f(A_191,A_191),A_191)) = B_63 ),
    inference(superposition,[status(thm),theory(equality)],[c_50289,c_6394]) ).

tff(c_52096,plain,
    ! [B_192,A_193] : ( f(f(B_192,B_192),f(f(A_193,A_193),A_193)) = B_192 ),
    inference(superposition,[status(thm),theory(equality)],[c_50289,c_6394]) ).

tff(c_6015,plain,
    ! [B_62,A_61] : ( f(B_62,f(f(A_61,B_62),f(A_61,B_62))) = f(A_61,B_62) ),
    inference(superposition,[status(thm),theory(equality)],[c_5896,c_2019]) ).

tff(c_52572,plain,
    ! [A_193,B_192] : ( f(f(f(A_193,A_193),A_193),f(B_192,f(f(B_192,B_192),f(f(A_193,A_193),A_193)))) = f(f(B_192,B_192),f(f(A_193,A_193),A_193)) ),
    inference(superposition,[status(thm),theory(equality)],[c_52096,c_6015]) ).

tff(c_59809,plain,
    ! [A_206,B_207] : ( f(f(f(A_206,A_206),A_206),f(B_207,B_207)) = B_207 ),
    inference(demodulation,[status(thm),theory(equality)],[c_51250,c_2310,c_52572]) ).

tff(c_67362,plain,
    ! [A_222,A_223] : ( f(f(f(A_222,A_222),A_222),A_223) = f(A_223,A_223) ),
    inference(superposition,[status(thm),theory(equality)],[c_6394,c_59809]) ).

tff(c_6208,plain,
    ! [B_38,B_62] : ( f(f(f(B_38,B_38),B_62),f(B_62,f(B_38,f(B_38,B_38)))) = B_62 ),
    inference(superposition,[status(thm),theory(equality)],[c_2579,c_5896]) ).

tff(c_68421,plain,
    ! [B_38,A_222] : ( f(f(f(B_38,B_38),f(f(A_222,A_222),A_222)),f(f(B_38,f(B_38,B_38)),f(B_38,f(B_38,B_38)))) = f(f(A_222,A_222),A_222) ),
    inference(superposition,[status(thm),theory(equality)],[c_67362,c_6208]) ).

tff(c_73261,plain,
    ! [A_231,B_232] : ( f(f(A_231,A_231),A_231) = f(B_232,f(B_232,B_232)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_591,c_51250,c_68421]) ).

tff(c_77050,plain,
    ! [B_242,B_241] : ( f(B_242,f(B_242,B_242)) = f(B_241,f(B_241,B_241)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2579,c_73261]) ).

tff(c_4,plain,
    f(x1,f(x1,x1)) != f(x0,f(x0,x0)),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_77668,plain,
    ! [B_241] : ( f(x0,f(x0,x0)) != f(B_241,f(B_241,B_241)) ),
    inference(superposition,[status(thm),theory(equality)],[c_77050,c_4]) ).

tff(c_81087,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_77668]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : LAT394-2 : TPTP v8.1.2. Released v5.4.0.
% 0.08/0.14  % 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
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 12:40:00 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 71.41/37.13  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 71.41/37.15  
% 71.41/37.15  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 71.53/37.18  
% 71.53/37.18  Inference rules
% 71.53/37.18  ----------------------
% 71.53/37.18  #Ref     : 1
% 71.53/37.18  #Sup     : 19318
% 71.53/37.18  #Fact    : 0
% 71.53/37.18  #Define  : 0
% 71.53/37.18  #Split   : 0
% 71.53/37.18  #Chain   : 0
% 71.53/37.18  #Close   : 0
% 71.53/37.18  
% 71.53/37.18  Ordering : KBO
% 71.53/37.18  
% 71.53/37.18  Simplification rules
% 71.53/37.18  ----------------------
% 71.53/37.18  #Subsume      : 213
% 71.53/37.18  #Demod        : 37047
% 71.53/37.18  #Tautology    : 8069
% 71.53/37.18  #SimpNegUnit  : 0
% 71.53/37.18  #BackRed      : 25
% 71.53/37.18  
% 71.53/37.18  #Partial instantiations: 0
% 71.53/37.18  #Strategies tried      : 1
% 71.53/37.18  
% 71.53/37.18  Timing (in seconds)
% 71.53/37.18  ----------------------
% 71.53/37.19  Preprocessing        : 0.39
% 71.53/37.19  Parsing              : 0.20
% 71.53/37.19  CNF conversion       : 0.02
% 71.53/37.19  Main loop            : 35.71
% 71.53/37.19  Inferencing          : 4.23
% 71.53/37.19  Reduction            : 29.59
% 71.53/37.19  Demodulation         : 28.72
% 71.53/37.19  BG Simplification    : 0.58
% 71.53/37.19  Subsumption          : 0.98
% 71.53/37.19  Abstraction          : 2.18
% 71.53/37.19  MUC search           : 0.00
% 71.53/37.19  Cooper               : 0.00
% 71.53/37.19  Total                : 36.16
% 71.53/37.19  Index Insertion      : 0.00
% 71.53/37.19  Index Deletion       : 0.00
% 71.53/37.19  Index Matching       : 0.00
% 71.53/37.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------