TSTP Solution File: SYO617-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SYO617-1 : TPTP v8.1.2. Released v7.1.0.
% 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 : n003.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 11:18:15 EDT 2023

% Result   : Unsatisfiable 6.53s 2.63s
% Output   : CNFRefutation 6.53s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   82 (  34 unt;   8 typ;   0 def)
%            Number of atoms       :  130 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :  133 (  77   ~;  56   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  143 (; 143   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ le > eq > max > #nlpp > s > f > a2 > a1 > a0

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(a1,type,
    a1: $i ).

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

tff(s,type,
    s: $i > $i ).

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

tff(a0,type,
    a0: $i ).

tff(a2,type,
    a2: $i ).

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

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

tff(f_41,axiom,
    ! [A] :
      ( eq(f(A),a0)
      | eq(f(A),a1)
      | eq(f(A),a2) ),
    file(unknown,unknown) ).

tff(f_25,axiom,
    ! [A] : le(A,A),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [A,B,C] :
      ( ~ le(max(A,B),C)
      | le(A,C) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [A0,A1] :
      ( ~ eq(f(A0),a2)
      | ~ eq(f(A1),a2)
      | ~ le(s(A0),A1) ),
    file(unknown,unknown) ).

tff(f_35,axiom,
    ! [A,B,C] :
      ( ~ le(max(A,B),C)
      | le(B,C) ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [A0,A1] :
      ( ~ eq(f(A0),a1)
      | ~ eq(f(A1),a1)
      | ~ le(s(A0),A1) ),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ! [A0,A1] :
      ( ~ eq(f(A0),a0)
      | ~ eq(f(A1),a0)
      | ~ le(s(A0),A1) ),
    file(unknown,unknown) ).

tff(c_8,plain,
    ! [A_8] :
      ( eq(f(A_8),a2)
      | eq(f(A_8),a1)
      | eq(f(A_8),a0) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2,plain,
    ! [A_1] : le(A_1,A_1),
    inference(cnfTransformation,[status(thm)],[f_25]) ).

tff(c_16,plain,
    ! [A_16,C_17,B_18] :
      ( le(A_16,C_17)
      | ~ le(max(A_16,B_18),C_17) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_21,plain,
    ! [A_16,B_18] : le(A_16,max(A_16,B_18)),
    inference(resolution,[status(thm)],[c_2,c_16]) ).

tff(c_114,plain,
    ! [A0_37,A1_38] :
      ( ~ le(s(A0_37),A1_38)
      | ~ eq(f(A1_38),a2)
      | ~ eq(f(A0_37),a2) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_423,plain,
    ! [A0_82,B_83] :
      ( ~ eq(f(max(s(A0_82),B_83)),a2)
      | ~ eq(f(A0_82),a2) ),
    inference(resolution,[status(thm)],[c_21,c_114]) ).

tff(c_1249,plain,
    ! [A0_291,B_292] :
      ( ~ eq(f(A0_291),a2)
      | eq(f(max(s(A0_291),B_292)),a1)
      | eq(f(max(s(A0_291),B_292)),a0) ),
    inference(resolution,[status(thm)],[c_8,c_423]) ).

tff(c_34,plain,
    ! [B_24,C_25,A_26] :
      ( le(B_24,C_25)
      | ~ le(max(A_26,B_24),C_25) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_66,plain,
    ! [B_29,A_30] : le(B_29,max(A_30,B_29)),
    inference(resolution,[status(thm)],[c_2,c_34]) ).

tff(c_6,plain,
    ! [B_6,C_7,A_5] :
      ( le(B_6,C_7)
      | ~ le(max(A_5,B_6),C_7) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_98,plain,
    ! [B_34,A_35,A_36] : le(B_34,max(A_35,max(A_36,B_34))),
    inference(resolution,[status(thm)],[c_66,c_6]) ).

tff(c_12,plain,
    ! [A0_11,A1_12] :
      ( ~ le(s(A0_11),A1_12)
      | ~ eq(f(A1_12),a1)
      | ~ eq(f(A0_11),a1) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_111,plain,
    ! [A_35,A_36,A0_11] :
      ( ~ eq(f(max(A_35,max(A_36,s(A0_11)))),a1)
      | ~ eq(f(A0_11),a1) ),
    inference(resolution,[status(thm)],[c_98,c_12]) ).

tff(c_2706,plain,
    ! [A0_676,A0_677,A_678] :
      ( ~ eq(f(A0_676),a1)
      | ~ eq(f(A0_677),a2)
      | eq(f(max(s(A0_677),max(A_678,s(A0_676)))),a0) ),
    inference(resolution,[status(thm)],[c_1249,c_111]) ).

tff(c_4,plain,
    ! [A_2,C_4,B_3] :
      ( le(A_2,C_4)
      | ~ le(max(A_2,B_3),C_4) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_145,plain,
    ! [A_39,A_40,B_41] : le(A_39,max(A_40,max(A_39,B_41))),
    inference(resolution,[status(thm)],[c_66,c_4]) ).

tff(c_366,plain,
    ! [A_72,A_73,B_74,B_75] : le(A_72,max(A_73,max(max(A_72,B_74),B_75))),
    inference(resolution,[status(thm)],[c_145,c_4]) ).

tff(c_10,plain,
    ! [A0_9,A1_10] :
      ( ~ le(s(A0_9),A1_10)
      | ~ eq(f(A1_10),a0)
      | ~ eq(f(A0_9),a0) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_387,plain,
    ! [A_73,A0_9,B_74,B_75] :
      ( ~ eq(f(max(A_73,max(max(s(A0_9),B_74),B_75))),a0)
      | ~ eq(f(A0_9),a0) ),
    inference(resolution,[status(thm)],[c_366,c_10]) ).

tff(c_2722,plain,
    ! [A0_9,A0_676,A0_677] :
      ( ~ eq(f(A0_9),a0)
      | ~ eq(f(A0_676),a1)
      | ~ eq(f(A0_677),a2) ),
    inference(resolution,[status(thm)],[c_2706,c_387]) ).

tff(c_2727,plain,
    ! [A0_677] : ~ eq(f(A0_677),a2),
    inference(splitLeft,[status(thm)],[c_2722]) ).

tff(c_2730,plain,
    ! [A_680] :
      ( eq(f(A_680),a1)
      | eq(f(A_680),a0) ),
    inference(negUnitSimplification,[status(thm)],[c_2727,c_8]) ).

tff(c_50,plain,
    ! [A0_27,A1_28] :
      ( ~ le(s(A0_27),A1_28)
      | ~ eq(f(A1_28),a1)
      | ~ eq(f(A0_27),a1) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_64,plain,
    ! [A0_27,B_18] :
      ( ~ eq(f(max(s(A0_27),B_18)),a1)
      | ~ eq(f(A0_27),a1) ),
    inference(resolution,[status(thm)],[c_21,c_50]) ).

tff(c_2821,plain,
    ! [A0_689,B_690] :
      ( ~ eq(f(A0_689),a1)
      | eq(f(max(s(A0_689),B_690)),a0) ),
    inference(resolution,[status(thm)],[c_2730,c_64]) ).

tff(c_81,plain,
    ! [A_2,A_30,B_3] : le(A_2,max(A_30,max(A_2,B_3))),
    inference(resolution,[status(thm)],[c_66,c_4]) ).

tff(c_278,plain,
    ! [A0_65,A1_66] :
      ( ~ le(s(A0_65),A1_66)
      | ~ eq(f(A1_66),a0)
      | ~ eq(f(A0_65),a0) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_332,plain,
    ! [A_30,A0_65,B_3] :
      ( ~ eq(f(max(A_30,max(s(A0_65),B_3))),a0)
      | ~ eq(f(A0_65),a0) ),
    inference(resolution,[status(thm)],[c_81,c_278]) ).

tff(c_2850,plain,
    ! [A0_65,A0_689] :
      ( ~ eq(f(A0_65),a0)
      | ~ eq(f(A0_689),a1) ),
    inference(resolution,[status(thm)],[c_2821,c_332]) ).

tff(c_2854,plain,
    ! [A0_689] : ~ eq(f(A0_689),a1),
    inference(splitLeft,[status(thm)],[c_2850]) ).

tff(c_2728,plain,
    ! [A_8] :
      ( eq(f(A_8),a1)
      | eq(f(A_8),a0) ),
    inference(negUnitSimplification,[status(thm)],[c_2727,c_8]) ).

tff(c_2855,plain,
    ! [A_8] : eq(f(A_8),a0),
    inference(negUnitSimplification,[status(thm)],[c_2854,c_2728]) ).

tff(c_22,plain,
    ! [A_19,B_20] : le(A_19,max(A_19,B_20)),
    inference(resolution,[status(thm)],[c_2,c_16]) ).

tff(c_28,plain,
    ! [A_21,B_22,B_23] : le(A_21,max(max(A_21,B_22),B_23)),
    inference(resolution,[status(thm)],[c_22,c_4]) ).

tff(c_340,plain,
    ! [A_68,B_69,B_70,B_71] : le(A_68,max(max(max(A_68,B_69),B_70),B_71)),
    inference(resolution,[status(thm)],[c_28,c_4]) ).

tff(c_361,plain,
    ! [A0_9,B_69,B_70,B_71] :
      ( ~ eq(f(max(max(max(s(A0_9),B_69),B_70),B_71)),a0)
      | ~ eq(f(A0_9),a0) ),
    inference(resolution,[status(thm)],[c_340,c_10]) ).

tff(c_2889,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2855,c_2855,c_361]) ).

tff(c_2890,plain,
    ! [A0_65] : ~ eq(f(A0_65),a0),
    inference(splitRight,[status(thm)],[c_2850]) ).

tff(c_2927,plain,
    ! [A_8] : eq(f(A_8),a1),
    inference(negUnitSimplification,[status(thm)],[c_2890,c_2728]) ).

tff(c_82,plain,
    ! [B_31,A_32,B_33] : le(B_31,max(max(A_32,B_31),B_33)),
    inference(resolution,[status(thm)],[c_21,c_34]) ).

tff(c_189,plain,
    ! [A_48,A_49,B_50,B_51] : le(A_48,max(max(A_49,max(A_48,B_50)),B_51)),
    inference(resolution,[status(thm)],[c_82,c_4]) ).

tff(c_207,plain,
    ! [A_49,A0_11,B_50,B_51] :
      ( ~ eq(f(max(max(A_49,max(s(A0_11),B_50)),B_51)),a1)
      | ~ eq(f(A0_11),a1) ),
    inference(resolution,[status(thm)],[c_189,c_12]) ).

tff(c_2961,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2927,c_2927,c_207]) ).

tff(c_2962,plain,
    ! [A0_9,A0_676] :
      ( ~ eq(f(A0_9),a0)
      | ~ eq(f(A0_676),a1) ),
    inference(splitRight,[status(thm)],[c_2722]) ).

tff(c_2963,plain,
    ! [A0_676] : ~ eq(f(A0_676),a1),
    inference(splitLeft,[status(thm)],[c_2962]) ).

tff(c_427,plain,
    ! [A0_82,B_83] :
      ( ~ eq(f(A0_82),a2)
      | eq(f(max(s(A0_82),B_83)),a1)
      | eq(f(max(s(A0_82),B_83)),a0) ),
    inference(resolution,[status(thm)],[c_8,c_423]) ).

tff(c_3065,plain,
    ! [A0_705,B_706] :
      ( ~ eq(f(A0_705),a2)
      | eq(f(max(s(A0_705),B_706)),a0) ),
    inference(negUnitSimplification,[status(thm)],[c_2963,c_427]) ).

tff(c_3094,plain,
    ! [A0_65,A0_705] :
      ( ~ eq(f(A0_65),a0)
      | ~ eq(f(A0_705),a2) ),
    inference(resolution,[status(thm)],[c_3065,c_332]) ).

tff(c_3098,plain,
    ! [A0_705] : ~ eq(f(A0_705),a2),
    inference(splitLeft,[status(thm)],[c_3094]) ).

tff(c_2993,plain,
    ! [A_8] :
      ( eq(f(A_8),a2)
      | eq(f(A_8),a0) ),
    inference(negUnitSimplification,[status(thm)],[c_2963,c_8]) ).

tff(c_3099,plain,
    ! [A_8] : eq(f(A_8),a0),
    inference(negUnitSimplification,[status(thm)],[c_3098,c_2993]) ).

tff(c_3133,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3099,c_3099,c_361]) ).

tff(c_3134,plain,
    ! [A0_65] : ~ eq(f(A0_65),a0),
    inference(splitRight,[status(thm)],[c_3094]) ).

tff(c_3158,plain,
    ! [A_8] : eq(f(A_8),a2),
    inference(negUnitSimplification,[status(thm)],[c_3134,c_2993]) ).

tff(c_14,plain,
    ! [A0_13,A1_14] :
      ( ~ le(s(A0_13),A1_14)
      | ~ eq(f(A1_14),a2)
      | ~ eq(f(A0_13),a2) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_206,plain,
    ! [A_49,A0_13,B_50,B_51] :
      ( ~ eq(f(max(max(A_49,max(s(A0_13),B_50)),B_51)),a2)
      | ~ eq(f(A0_13),a2) ),
    inference(resolution,[status(thm)],[c_189,c_14]) ).

tff(c_3192,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3158,c_3158,c_206]) ).

tff(c_3193,plain,
    ! [A0_9] : ~ eq(f(A0_9),a0),
    inference(splitRight,[status(thm)],[c_2962]) ).

tff(c_1266,plain,
    ! [A0_11,A0_291,A_36] :
      ( ~ eq(f(A0_11),a1)
      | ~ eq(f(A0_291),a2)
      | eq(f(max(s(A0_291),max(A_36,s(A0_11)))),a0) ),
    inference(resolution,[status(thm)],[c_1249,c_111]) ).

tff(c_3194,plain,
    ! [A0_11,A0_291] :
      ( ~ eq(f(A0_11),a1)
      | ~ eq(f(A0_291),a2) ),
    inference(negUnitSimplification,[status(thm)],[c_3193,c_1266]) ).

tff(c_3267,plain,
    ! [A0_291] : ~ eq(f(A0_291),a2),
    inference(splitLeft,[status(thm)],[c_3194]) ).

tff(c_3200,plain,
    ! [A_8] :
      ( eq(f(A_8),a2)
      | eq(f(A_8),a1) ),
    inference(negUnitSimplification,[status(thm)],[c_3193,c_8]) ).

tff(c_3273,plain,
    ! [A_8] : eq(f(A_8),a1),
    inference(negUnitSimplification,[status(thm)],[c_3267,c_3200]) ).

tff(c_3307,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3273,c_3273,c_207]) ).

tff(c_3308,plain,
    ! [A0_11] : ~ eq(f(A0_11),a1),
    inference(splitRight,[status(thm)],[c_3194]) ).

tff(c_3309,plain,
    ! [A_8] : eq(f(A_8),a2),
    inference(negUnitSimplification,[status(thm)],[c_3308,c_3200]) ).

tff(c_3359,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3309,c_3309,c_206]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SYO617-1 : TPTP v8.1.2. Released v7.1.0.
% 0.07/0.14  % 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
% 0.14/0.35  % Computer : n003.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:07:53 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.53/2.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.53/2.63  
% 6.53/2.63  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.53/2.67  
% 6.53/2.67  Inference rules
% 6.53/2.67  ----------------------
% 6.53/2.67  #Ref     : 0
% 6.53/2.67  #Sup     : 601
% 6.53/2.67  #Fact    : 0
% 6.53/2.67  #Define  : 0
% 6.53/2.67  #Split   : 9
% 6.53/2.67  #Chain   : 0
% 6.53/2.67  #Close   : 0
% 6.53/2.67  
% 6.53/2.67  Ordering : KBO
% 6.53/2.67  
% 6.53/2.67  Simplification rules
% 6.53/2.67  ----------------------
% 6.53/2.67  #Subsume      : 251
% 6.53/2.67  #Demod        : 256
% 6.53/2.67  #Tautology    : 10
% 6.53/2.67  #SimpNegUnit  : 29
% 6.53/2.67  #BackRed      : 157
% 6.53/2.67  
% 6.53/2.67  #Partial instantiations: 0
% 6.53/2.67  #Strategies tried      : 1
% 6.53/2.67  
% 6.53/2.67  Timing (in seconds)
% 6.53/2.67  ----------------------
% 6.53/2.68  Preprocessing        : 0.46
% 6.53/2.68  Parsing              : 0.25
% 6.53/2.68  CNF conversion       : 0.02
% 6.53/2.68  Main loop            : 1.12
% 6.53/2.68  Inferencing          : 0.42
% 6.53/2.68  Reduction            : 0.27
% 6.53/2.68  Demodulation         : 0.20
% 6.53/2.68  BG Simplification    : 0.03
% 6.53/2.68  Subsumption          : 0.32
% 6.53/2.68  Abstraction          : 0.03
% 6.53/2.68  MUC search           : 0.00
% 6.53/2.68  Cooper               : 0.00
% 6.53/2.68  Total                : 1.64
% 6.53/2.68  Index Insertion      : 0.00
% 6.53/2.68  Index Deletion       : 0.00
% 6.53/2.68  Index Matching       : 0.00
% 6.53/2.68  BG Taut test         : 0.00
%------------------------------------------------------------------------------