TSTP Solution File: NUN059+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 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 : n011.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 10:53:20 EDT 2023

% Result   : Theorem 60.08s 46.72s
% Output   : CNFRefutation 60.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   82 (  20 unt;  25 typ;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  166 (  80   ~;  67   |;  19   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   40 (  24   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   1 con; 0-2 aty)
%            Number of variables   :  140 (; 126   !;  14   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ r4 > r3 > r2 > id > r1 > #nlpp > #skF_11 > #skF_16 > #skF_6 > #skF_2 > #skF_18 > #skF_19 > #skF_3 > #skF_15 > #skF_12 > #skF_10 > #skF_1 > #skF_8 > #skF_13 > #skF_17 > #skF_14 > #skF_7 > #skF_9 > #skF_5 > #skF_4 > #skF_20

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_2',type,
    '#skF_2': $i > $i ).

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_19',type,
    '#skF_19': $i > $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff(r2,type,
    r2: ( $i * $i ) > $o ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i ) > $i ).

tff(r3,type,
    r3: ( $i * $i * $i ) > $o ).

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

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

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff(r4,type,
    r4: ( $i * $i * $i ) > $o ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff('#skF_14',type,
    '#skF_14': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff(r1,type,
    r1: $i > $o ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

tff(f_102,axiom,
    ! [X20] : id(X20,X20),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).

tff(f_232,axiom,
    ! [X4] :
    ? [Y9] :
      ( id(Y9,X4)
      & ? [Y16] :
          ( r1(Y16)
          & r3(X4,Y16,Y9) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).

tff(f_64,axiom,
    ? [Y24] :
    ! [X19] :
      ( ( id(X19,Y24)
        & r1(X19) )
      | ( ~ r1(X19)
        & ~ id(X19,Y24) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).

tff(f_107,axiom,
    ! [X21,X22] :
      ( ~ id(X21,X22)
      | id(X22,X21) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).

tff(f_163,axiom,
    ! [X32,X33,X34,X35,X36,X37] :
      ( ~ id(X32,X35)
      | ~ id(X33,X36)
      | ~ id(X34,X37)
      | ( ~ r3(X32,X33,X34)
        & ~ r3(X35,X36,X37) )
      | ( r3(X32,X33,X34)
        & r3(X35,X36,X37) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_10) ).

tff(f_88,axiom,
    ! [X13,X14] :
    ? [Y22] :
    ! [X15] :
      ( ( id(X15,Y22)
        & r3(X13,X14,X15) )
      | ( ~ r3(X13,X14,X15)
        & ~ id(X15,Y22) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3) ).

tff(f_115,axiom,
    ! [X23,X24,X25] :
      ( ~ id(X23,X24)
      | id(X23,X25)
      | ~ id(X24,X25) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).

tff(f_243,axiom,
    ! [X5] :
    ? [Y8] :
      ( ? [Y17] :
          ( r1(Y17)
          & r4(X5,Y17,Y8) )
      & ? [Y18] :
          ( id(Y8,Y18)
          & r1(Y18) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5a) ).

tff(f_128,axiom,
    ! [X26,X27] :
      ( ~ id(X26,X27)
      | ( ~ r1(X26)
        & ~ r1(X27) )
      | ( r1(X26)
        & r1(X27) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).

tff(f_182,axiom,
    ! [X38,X39,X40,X41,X42,X43] :
      ( ~ id(X38,X41)
      | ~ id(X39,X42)
      | ~ id(X40,X43)
      | ( ~ r4(X38,X39,X40)
        & ~ r4(X41,X42,X43) )
      | ( r4(X38,X39,X40)
        & r4(X41,X42,X43) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_11) ).

tff(f_279,negated_conjecture,
    ~ ? [Y1,Y3,Y2,Y4] :
        ( ? [Y5] :
            ( id(Y4,Y5)
            & r4(Y2,Y2,Y5) )
        & ? [Y6] :
            ( r4(Y3,Y3,Y6)
            & ? [Y7] :
                ( r4(Y1,Y1,Y7)
                & r3(Y7,Y6,Y4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).

tff(c_34,plain,
    ! [X20_23] : id(X20_23,X20_23),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_96,plain,
    ! [X4_87] : r1('#skF_14'(X4_87)),
    inference(cnfTransformation,[status(thm)],[f_232]) ).

tff(c_8,plain,
    ! [X19_2] :
      ( id(X19_2,'#skF_1')
      | ~ r1(X19_2) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_145,plain,
    ! [X22_140,X21_141] :
      ( id(X22_140,X21_141)
      | ~ id(X21_141,X22_140) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_154,plain,
    ! [X19_2] :
      ( id('#skF_1',X19_2)
      | ~ r1(X19_2) ),
    inference(resolution,[status(thm)],[c_8,c_145]) ).

tff(c_98,plain,
    ! [X4_87] : id('#skF_13'(X4_87),X4_87),
    inference(cnfTransformation,[status(thm)],[f_232]) ).

tff(c_156,plain,
    ! [X4_87] : id(X4_87,'#skF_13'(X4_87)),
    inference(resolution,[status(thm)],[c_98,c_145]) ).

tff(c_94,plain,
    ! [X4_87] : r3(X4_87,'#skF_14'(X4_87),'#skF_13'(X4_87)),
    inference(cnfTransformation,[status(thm)],[f_232]) ).

tff(c_2272,plain,
    ! [X32_415,X34_411,X33_410,X36_414,X37_413,X35_412] :
      ( ~ r3(X35_412,X36_414,X37_413)
      | r3(X32_415,X33_410,X34_411)
      | ~ id(X34_411,X37_413)
      | ~ id(X33_410,X36_414)
      | ~ id(X32_415,X35_412) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_18343,plain,
    ! [X32_1027,X33_1028,X34_1029,X4_1030] :
      ( r3(X32_1027,X33_1028,X34_1029)
      | ~ id(X34_1029,'#skF_13'(X4_1030))
      | ~ id(X33_1028,'#skF_14'(X4_1030))
      | ~ id(X32_1027,X4_1030) ),
    inference(resolution,[status(thm)],[c_94,c_2272]) ).

tff(c_258788,plain,
    ! [X32_5136,X33_5137,X4_5138] :
      ( r3(X32_5136,X33_5137,X4_5138)
      | ~ id(X33_5137,'#skF_14'(X4_5138))
      | ~ id(X32_5136,X4_5138) ),
    inference(resolution,[status(thm)],[c_156,c_18343]) ).

tff(c_258935,plain,
    ! [X32_5136,X4_5138] :
      ( r3(X32_5136,'#skF_1',X4_5138)
      | ~ id(X32_5136,X4_5138)
      | ~ r1('#skF_14'(X4_5138)) ),
    inference(resolution,[status(thm)],[c_154,c_258788]) ).

tff(c_259019,plain,
    ! [X32_5136,X4_5138] :
      ( r3(X32_5136,'#skF_1',X4_5138)
      | ~ id(X32_5136,X4_5138) ),
    inference(demodulation,[status(thm),theory(equality)],[c_96,c_258935]) ).

tff(c_1241,plain,
    ! [X15_313,X13_314,X14_315] :
      ( id(X15_313,'#skF_3'(X13_314,X14_315))
      | ~ r3(X13_314,X14_315,X15_313) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_36,plain,
    ! [X22_25,X21_24] :
      ( id(X22_25,X21_24)
      | ~ id(X21_24,X22_25) ),
    inference(cnfTransformation,[status(thm)],[f_107]) ).

tff(c_1259,plain,
    ! [X13_314,X14_315,X15_313] :
      ( id('#skF_3'(X13_314,X14_315),X15_313)
      | ~ r3(X13_314,X14_315,X15_313) ),
    inference(resolution,[status(thm)],[c_1241,c_36]) ).

tff(c_38,plain,
    ! [X24_27,X25_28,X23_26] :
      ( ~ id(X24_27,X25_28)
      | id(X23_26,X25_28)
      | ~ id(X23_26,X24_27) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_11477,plain,
    ! [X23_851,X13_852,X14_853,X15_854] :
      ( id(X23_851,'#skF_3'(X13_852,X14_853))
      | ~ id(X23_851,X15_854)
      | ~ r3(X13_852,X14_853,X15_854) ),
    inference(resolution,[status(thm)],[c_1241,c_38]) ).

tff(c_68561,plain,
    ! [X4_1859,X13_1860,X14_1861] :
      ( id(X4_1859,'#skF_3'(X13_1860,X14_1861))
      | ~ r3(X13_1860,X14_1861,'#skF_13'(X4_1859)) ),
    inference(resolution,[status(thm)],[c_156,c_11477]) ).

tff(c_68575,plain,
    ! [X4_87] : id(X4_87,'#skF_3'(X4_87,'#skF_14'(X4_87))),
    inference(resolution,[status(thm)],[c_94,c_68561]) ).

tff(c_106,plain,
    ! [X5_92] : r1('#skF_16'(X5_92)),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_100,plain,
    ! [X5_92] : r1('#skF_17'(X5_92)),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_102,plain,
    ! [X5_92] : id('#skF_15'(X5_92),'#skF_17'(X5_92)),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_155,plain,
    ! [X5_92] : id('#skF_17'(X5_92),'#skF_15'(X5_92)),
    inference(resolution,[status(thm)],[c_102,c_145]) ).

tff(c_214,plain,
    ! [X26_158,X27_159] :
      ( ~ r1(X26_158)
      | r1(X27_159)
      | ~ id(X26_158,X27_159) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_223,plain,
    ! [X5_92] :
      ( ~ r1('#skF_17'(X5_92))
      | r1('#skF_15'(X5_92)) ),
    inference(resolution,[status(thm)],[c_155,c_214]) ).

tff(c_246,plain,
    ! [X5_92] : r1('#skF_15'(X5_92)),
    inference(demodulation,[status(thm),theory(equality)],[c_100,c_223]) ).

tff(c_104,plain,
    ! [X5_92] : r4(X5_92,'#skF_16'(X5_92),'#skF_15'(X5_92)),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_2632,plain,
    ! [X40_449,X41_452,X38_453,X42_450,X43_448,X39_451] :
      ( ~ r4(X41_452,X42_450,X43_448)
      | r4(X38_453,X39_451,X40_449)
      | ~ id(X40_449,X43_448)
      | ~ id(X39_451,X42_450)
      | ~ id(X38_453,X41_452) ),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_25752,plain,
    ! [X38_1163,X39_1164,X40_1165,X5_1166] :
      ( r4(X38_1163,X39_1164,X40_1165)
      | ~ id(X40_1165,'#skF_15'(X5_1166))
      | ~ id(X39_1164,'#skF_16'(X5_1166))
      | ~ id(X38_1163,X5_1166) ),
    inference(resolution,[status(thm)],[c_104,c_2632]) ).

tff(c_25859,plain,
    ! [X38_1163,X39_1164,X5_1166] :
      ( r4(X38_1163,X39_1164,'#skF_1')
      | ~ id(X39_1164,'#skF_16'(X5_1166))
      | ~ id(X38_1163,X5_1166)
      | ~ r1('#skF_15'(X5_1166)) ),
    inference(resolution,[status(thm)],[c_154,c_25752]) ).

tff(c_260250,plain,
    ! [X38_5168,X39_5169,X5_5170] :
      ( r4(X38_5168,X39_5169,'#skF_1')
      | ~ id(X39_5169,'#skF_16'(X5_5170))
      | ~ id(X38_5168,X5_5170) ),
    inference(demodulation,[status(thm),theory(equality)],[c_246,c_25859]) ).

tff(c_260397,plain,
    ! [X38_5168,X5_5170] :
      ( r4(X38_5168,'#skF_1','#skF_1')
      | ~ id(X38_5168,X5_5170)
      | ~ r1('#skF_16'(X5_5170)) ),
    inference(resolution,[status(thm)],[c_154,c_260250]) ).

tff(c_260484,plain,
    ! [X38_5171,X5_5172] :
      ( r4(X38_5171,'#skF_1','#skF_1')
      | ~ id(X38_5171,X5_5172) ),
    inference(demodulation,[status(thm),theory(equality)],[c_106,c_260397]) ).

tff(c_261139,plain,
    ! [X4_87] : r4(X4_87,'#skF_1','#skF_1'),
    inference(resolution,[status(thm)],[c_68575,c_260484]) ).

tff(c_261362,plain,
    ! [X4_5173] : r4(X4_5173,'#skF_1','#skF_1'),
    inference(resolution,[status(thm)],[c_68575,c_260484]) ).

tff(c_921,plain,
    ! [X13_279,X14_280,X15_281] :
      ( r3(X13_279,X14_280,X15_281)
      | ~ id(X15_281,'#skF_3'(X13_279,X14_280)) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_957,plain,
    ! [X13_282,X14_283] : r3(X13_282,X14_283,'#skF_3'(X13_282,X14_283)),
    inference(resolution,[status(thm)],[c_34,c_921]) ).

tff(c_118,plain,
    ! [Y3_109,Y4_111,Y7_119,Y2_110,Y5_116,Y1_108,Y6_117] :
      ( ~ r3(Y7_119,Y6_117,Y4_111)
      | ~ r4(Y1_108,Y1_108,Y7_119)
      | ~ r4(Y3_109,Y3_109,Y6_117)
      | ~ r4(Y2_110,Y2_110,Y5_116)
      | ~ id(Y4_111,Y5_116) ),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_960,plain,
    ! [Y3_109,Y2_110,X14_283,X13_282,Y5_116,Y1_108] :
      ( ~ r4(Y1_108,Y1_108,X13_282)
      | ~ r4(Y3_109,Y3_109,X14_283)
      | ~ r4(Y2_110,Y2_110,Y5_116)
      | ~ id('#skF_3'(X13_282,X14_283),Y5_116) ),
    inference(resolution,[status(thm)],[c_957,c_118]) ).

tff(c_261762,plain,
    ! [Y3_5174,X14_5175,Y2_5176,Y5_5177] :
      ( ~ r4(Y3_5174,Y3_5174,X14_5175)
      | ~ r4(Y2_5176,Y2_5176,Y5_5177)
      | ~ id('#skF_3'('#skF_1',X14_5175),Y5_5177) ),
    inference(resolution,[status(thm)],[c_261362,c_960]) ).

tff(c_264853,plain,
    ! [Y2_5274,Y5_5275] :
      ( ~ r4(Y2_5274,Y2_5274,Y5_5275)
      | ~ id('#skF_3'('#skF_1','#skF_1'),Y5_5275) ),
    inference(resolution,[status(thm)],[c_261139,c_261762]) ).

tff(c_264872,plain,
    ~ id('#skF_3'('#skF_1','#skF_1'),'#skF_1'),
    inference(resolution,[status(thm)],[c_261139,c_264853]) ).

tff(c_264890,plain,
    ~ r3('#skF_1','#skF_1','#skF_1'),
    inference(resolution,[status(thm)],[c_1259,c_264872]) ).

tff(c_264902,plain,
    ~ id('#skF_1','#skF_1'),
    inference(resolution,[status(thm)],[c_259019,c_264890]) ).

tff(c_264909,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_264902]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUN059+1 : TPTP v8.1.2. Bugfixed v7.4.0.
% 0.00/0.15  % 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
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu Aug  3 18:39:51 EDT 2023
% 0.16/0.37  % CPUTime  : 
% 60.08/46.72  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 60.12/46.73  
% 60.12/46.73  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 60.16/46.77  
% 60.16/46.77  Inference rules
% 60.16/46.77  ----------------------
% 60.16/46.77  #Ref     : 0
% 60.16/46.77  #Sup     : 56201
% 60.16/46.77  #Fact    : 0
% 60.16/46.77  #Define  : 0
% 60.16/46.77  #Split   : 28
% 60.16/46.77  #Chain   : 0
% 60.16/46.77  #Close   : 0
% 60.16/46.77  
% 60.16/46.77  Ordering : KBO
% 60.16/46.77  
% 60.16/46.77  Simplification rules
% 60.16/46.77  ----------------------
% 60.16/46.77  #Subsume      : 17311
% 60.16/46.77  #Demod        : 35106
% 60.16/46.77  #Tautology    : 19883
% 60.16/46.77  #SimpNegUnit  : 2198
% 60.16/46.77  #BackRed      : 1
% 60.16/46.77  
% 60.16/46.77  #Partial instantiations: 0
% 60.16/46.77  #Strategies tried      : 1
% 60.16/46.77  
% 60.16/46.77  Timing (in seconds)
% 60.16/46.77  ----------------------
% 60.16/46.78  Preprocessing        : 0.55
% 60.16/46.78  Parsing              : 0.29
% 60.16/46.78  CNF conversion       : 0.05
% 60.16/46.78  Main loop            : 45.13
% 60.16/46.78  Inferencing          : 5.83
% 60.16/46.78  Reduction            : 21.15
% 60.16/46.78  Demodulation         : 15.59
% 60.16/46.78  BG Simplification    : 0.15
% 60.16/46.78  Subsumption          : 15.52
% 60.16/46.78  Abstraction          : 0.31
% 60.16/46.78  MUC search           : 0.00
% 60.16/46.78  Cooper               : 0.00
% 60.16/46.78  Total                : 45.74
% 60.16/46.78  Index Insertion      : 0.00
% 60.16/46.78  Index Deletion       : 0.00
% 60.16/46.78  Index Matching       : 0.00
% 60.16/46.78  BG Taut test         : 0.00
%------------------------------------------------------------------------------