TSTP Solution File: LCL672+1.001 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL672+1.001 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 10:48:44 EDT 2023

% Result   : Theorem 6.27s 2.51s
% Output   : CNFRefutation 6.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   69 (  21 unt;  14 typ;   0 def)
%            Number of atoms       :  189 (   0 equ)
%            Maximal formula atoms :   49 (   3 avg)
%            Number of connectives :  273 ( 139   ~; 121   |;  12   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   25 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   95 (;  94   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ r1 > p2 > p1 > #nlpp > #skF_11 > #skF_7 > #skF_10 > #skF_1 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_5 > #skF_6 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

tff(p2,type,
    p2: $i > $o ).

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

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

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

tff(p1,type,
    p1: $i > $o ).

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

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

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

tff(f_223,negated_conjecture,
    ~ ~ ? [X] :
          ~ ( ( ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p2(Y) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | ~ ( ~ ! [X] :
                              ( ~ r1(Y,X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ p1(Y) ) )
                        & p1(Y) ) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p1(Y) ) )
            | ( ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p2(Y) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | ! [X] :
                        ( ~ r1(Y,X)
                        | ~ ( ~ ! [Y] :
                                  ( ~ r1(X,Y)
                                  | ~ ! [X] :
                                        ( ~ r1(Y,X)
                                        | p1(X) ) )
                            & ~ ! [Y] :
                                  ( ~ r1(X,Y)
                                  | p1(Y) ) ) ) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p1(Y) ) )
            | ( ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p2(Y) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | ~ ( ~ ! [X] :
                              ( ~ r1(Y,X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | ~ ! [X] :
                                          ( ~ r1(Y,X)
                                          | p1(X) ) ) )
                        & ~ ! [X] :
                              ( ~ r1(Y,X)
                              | ~ ! [Y] :
                                    ( ~ r1(X,Y)
                                    | p1(Y) ) ) ) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p1(Y) ) )
            | ( ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p2(Y) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | ~ ! [X] :
                          ( ~ r1(Y,X)
                          | $false ) )
              & ~ ! [Y] :
                    ( ~ r1(X,Y)
                    | p1(Y) ) )
            | ! [Y] :
                ( ~ r1(X,Y)
                | p2(Y) )
            | ! [Y] :
                ( ~ r1(X,Y)
                | ! [X] :
                    ( ~ r1(Y,X)
                    | ~ ! [Y] :
                          ( ~ r1(X,Y)
                          | p1(Y) ) )
                | ! [X] :
                    ( ~ r1(Y,X)
                    | p1(X) ) )
            | ! [Y] :
                ( ~ r1(X,Y)
                | p1(Y) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).

tff(f_28,axiom,
    ! [X] : r1(X,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).

tff(f_34,axiom,
    ! [X,Y,Z] :
      ( ( r1(X,Y)
        & r1(Y,Z) )
     => r1(X,Z) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).

tff(c_10,plain,
    ~ p1('#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_2,plain,
    ! [X_1] : r1(X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_12,plain,
    r1('#skF_8','#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_48,plain,
    ! [X_135,Z_136,Y_137] :
      ( r1(X_135,Z_136)
      | ~ r1(Y_137,Z_136)
      | ~ r1(X_135,Y_137) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_63,plain,
    ! [X_135] :
      ( r1(X_135,'#skF_10')
      | ~ r1(X_135,'#skF_8') ),
    inference(resolution,[status(thm)],[c_12,c_48]) ).

tff(c_18,plain,
    r1('#skF_1','#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_16,plain,
    r1('#skF_8','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_84,plain,
    ! [X_140] :
      ( r1(X_140,'#skF_10')
      | ~ r1(X_140,'#skF_8') ),
    inference(resolution,[status(thm)],[c_12,c_48]) ).

tff(c_4,plain,
    ! [X_2,Z_4,Y_3] :
      ( r1(X_2,Z_4)
      | ~ r1(Y_3,Z_4)
      | ~ r1(X_2,Y_3) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_440,plain,
    ! [X_154,X_155] :
      ( r1(X_154,'#skF_10')
      | ~ r1(X_154,X_155)
      | ~ r1(X_155,'#skF_8') ),
    inference(resolution,[status(thm)],[c_84,c_4]) ).

tff(c_454,plain,
    ( r1('#skF_1','#skF_10')
    | ~ r1('#skF_8','#skF_8') ),
    inference(resolution,[status(thm)],[c_18,c_440]) ).

tff(c_473,plain,
    r1('#skF_1','#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_454]) ).

tff(c_495,plain,
    ! [X_2] :
      ( r1(X_2,'#skF_10')
      | ~ r1(X_2,'#skF_1') ),
    inference(resolution,[status(thm)],[c_473,c_4]) ).

tff(c_20,plain,
    ~ p2('#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_22,plain,
    r1('#skF_1','#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_65,plain,
    ! [X_135] :
      ( r1(X_135,'#skF_7')
      | ~ r1(X_135,'#skF_1') ),
    inference(resolution,[status(thm)],[c_22,c_48]) ).

tff(c_36,plain,
    ! [Y_98,Y_82,Y_83,X_93,Y_100,Y_101] :
      ( r1(Y_98,'#skF_3'(Y_83,X_93,Y_98))
      | p1(Y_101)
      | ~ r1('#skF_1',Y_101)
      | p1(Y_100)
      | ~ r1(X_93,Y_100)
      | ~ r1(X_93,Y_98)
      | ~ r1(Y_83,X_93)
      | ~ r1('#skF_1',Y_83)
      | p2(Y_82)
      | ~ r1('#skF_1',Y_82) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_1416,plain,
    ! [Y_206] :
      ( p2(Y_206)
      | ~ r1('#skF_1',Y_206) ),
    inference(splitLeft,[status(thm)],[c_36]) ).

tff(c_1473,plain,
    ( p2('#skF_7')
    | ~ r1('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_65,c_1416]) ).

tff(c_1524,plain,
    p2('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_1473]) ).

tff(c_1526,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_1524]) ).

tff(c_1527,plain,
    ! [Y_98,Y_83,X_93,Y_100,Y_101] :
      ( r1(Y_98,'#skF_3'(Y_83,X_93,Y_98))
      | p1(Y_100)
      | ~ r1(X_93,Y_100)
      | ~ r1(X_93,Y_98)
      | ~ r1(Y_83,X_93)
      | ~ r1('#skF_1',Y_83)
      | p1(Y_101)
      | ~ r1('#skF_1',Y_101) ),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_2353,plain,
    ! [Y_242] :
      ( p1(Y_242)
      | ~ r1('#skF_1',Y_242) ),
    inference(splitLeft,[status(thm)],[c_1527]) ).

tff(c_2431,plain,
    ( p1('#skF_10')
    | ~ r1('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_495,c_2353]) ).

tff(c_2510,plain,
    p1('#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2431]) ).

tff(c_2512,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_2510]) ).

tff(c_3582,plain,
    ! [Y_266,Y_267,X_268,Y_269] :
      ( r1(Y_266,'#skF_3'(Y_267,X_268,Y_266))
      | p1(Y_269)
      | ~ r1(X_268,Y_269)
      | ~ r1(X_268,Y_266)
      | ~ r1(Y_267,X_268)
      | ~ r1('#skF_1',Y_267) ),
    inference(splitRight,[status(thm)],[c_1527]) ).

tff(c_3660,plain,
    ! [Y_266,Y_267] :
      ( r1(Y_266,'#skF_3'(Y_267,'#skF_8',Y_266))
      | p1('#skF_10')
      | ~ r1('#skF_8',Y_266)
      | ~ r1(Y_267,'#skF_8')
      | ~ r1('#skF_1',Y_267) ),
    inference(resolution,[status(thm)],[c_12,c_3582]) ).

tff(c_3767,plain,
    ! [Y_270,Y_271] :
      ( r1(Y_270,'#skF_3'(Y_271,'#skF_8',Y_270))
      | ~ r1('#skF_8',Y_270)
      | ~ r1(Y_271,'#skF_8')
      | ~ r1('#skF_1',Y_271) ),
    inference(negUnitSimplification,[status(thm)],[c_10,c_3660]) ).

tff(c_14,plain,
    ! [Y_132] :
      ( p1(Y_132)
      | ~ r1('#skF_9',Y_132) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_3806,plain,
    ! [Y_271] :
      ( p1('#skF_3'(Y_271,'#skF_8','#skF_9'))
      | ~ r1('#skF_8','#skF_9')
      | ~ r1(Y_271,'#skF_8')
      | ~ r1('#skF_1',Y_271) ),
    inference(resolution,[status(thm)],[c_3767,c_14]) ).

tff(c_4101,plain,
    ! [Y_274] :
      ( p1('#skF_3'(Y_274,'#skF_8','#skF_9'))
      | ~ r1(Y_274,'#skF_8')
      | ~ r1('#skF_1',Y_274) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_3806]) ).

tff(c_34,plain,
    ! [Y_98,Y_82,Y_83,X_93,Y_100,Y_101] :
      ( ~ p1('#skF_3'(Y_83,X_93,Y_98))
      | p1(Y_101)
      | ~ r1('#skF_1',Y_101)
      | p1(Y_100)
      | ~ r1(X_93,Y_100)
      | ~ r1(X_93,Y_98)
      | ~ r1(Y_83,X_93)
      | ~ r1('#skF_1',Y_83)
      | p2(Y_82)
      | ~ r1('#skF_1',Y_82) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_755,plain,
    ! [Y_168] :
      ( p2(Y_168)
      | ~ r1('#skF_1',Y_168) ),
    inference(splitLeft,[status(thm)],[c_34]) ).

tff(c_781,plain,
    ( p2('#skF_7')
    | ~ r1('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_65,c_755]) ).

tff(c_817,plain,
    p2('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_781]) ).

tff(c_819,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_20,c_817]) ).

tff(c_820,plain,
    ! [Y_98,Y_83,X_93,Y_100,Y_101] :
      ( ~ p1('#skF_3'(Y_83,X_93,Y_98))
      | p1(Y_100)
      | ~ r1(X_93,Y_100)
      | ~ r1(X_93,Y_98)
      | ~ r1(Y_83,X_93)
      | ~ r1('#skF_1',Y_83)
      | p1(Y_101)
      | ~ r1('#skF_1',Y_101) ),
    inference(splitRight,[status(thm)],[c_34]) ).

tff(c_2061,plain,
    ! [Y_229] :
      ( p1(Y_229)
      | ~ r1('#skF_1',Y_229) ),
    inference(splitLeft,[status(thm)],[c_820]) ).

tff(c_2128,plain,
    ( p1('#skF_10')
    | ~ r1('#skF_1','#skF_1') ),
    inference(resolution,[status(thm)],[c_495,c_2061]) ).

tff(c_2201,plain,
    p1('#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2128]) ).

tff(c_2203,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_2201]) ).

tff(c_2204,plain,
    ! [Y_83,X_93,Y_98,Y_100] :
      ( ~ p1('#skF_3'(Y_83,X_93,Y_98))
      | p1(Y_100)
      | ~ r1(X_93,Y_100)
      | ~ r1(X_93,Y_98)
      | ~ r1(Y_83,X_93)
      | ~ r1('#skF_1',Y_83) ),
    inference(splitRight,[status(thm)],[c_820]) ).

tff(c_4103,plain,
    ! [Y_100,Y_274] :
      ( p1(Y_100)
      | ~ r1('#skF_8',Y_100)
      | ~ r1('#skF_8','#skF_9')
      | ~ r1(Y_274,'#skF_8')
      | ~ r1('#skF_1',Y_274) ),
    inference(resolution,[status(thm)],[c_4101,c_2204]) ).

tff(c_4106,plain,
    ! [Y_100,Y_274] :
      ( p1(Y_100)
      | ~ r1('#skF_8',Y_100)
      | ~ r1(Y_274,'#skF_8')
      | ~ r1('#skF_1',Y_274) ),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_4103]) ).

tff(c_4169,plain,
    ! [Y_277] :
      ( ~ r1(Y_277,'#skF_8')
      | ~ r1('#skF_1',Y_277) ),
    inference(splitLeft,[status(thm)],[c_4106]) ).

tff(c_4171,plain,
    ~ r1('#skF_1','#skF_1'),
    inference(resolution,[status(thm)],[c_18,c_4169]) ).

tff(c_4178,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4171]) ).

tff(c_4180,plain,
    ! [Y_278] :
      ( p1(Y_278)
      | ~ r1('#skF_8',Y_278) ),
    inference(splitRight,[status(thm)],[c_4106]) ).

tff(c_4286,plain,
    ( p1('#skF_10')
    | ~ r1('#skF_8','#skF_8') ),
    inference(resolution,[status(thm)],[c_63,c_4180]) ).

tff(c_4347,plain,
    p1('#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_4286]) ).

tff(c_4349,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_10,c_4347]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : LCL672+1.001 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % 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
% 0.15/0.35  % Computer : n025.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 14:35:49 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 6.27/2.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.59/2.52  
% 6.59/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.59/2.56  
% 6.59/2.56  Inference rules
% 6.59/2.56  ----------------------
% 6.59/2.56  #Ref     : 0
% 6.59/2.56  #Sup     : 985
% 6.59/2.56  #Fact    : 0
% 6.59/2.56  #Define  : 0
% 6.59/2.56  #Split   : 30
% 6.59/2.56  #Chain   : 0
% 6.59/2.56  #Close   : 0
% 6.59/2.56  
% 6.59/2.56  Ordering : KBO
% 6.59/2.56  
% 6.59/2.56  Simplification rules
% 6.59/2.56  ----------------------
% 6.59/2.56  #Subsume      : 223
% 6.59/2.56  #Demod        : 299
% 6.59/2.56  #Tautology    : 124
% 6.59/2.56  #SimpNegUnit  : 33
% 6.59/2.56  #BackRed      : 0
% 6.59/2.56  
% 6.59/2.56  #Partial instantiations: 0
% 6.59/2.56  #Strategies tried      : 1
% 6.59/2.56  
% 6.59/2.56  Timing (in seconds)
% 6.59/2.56  ----------------------
% 6.59/2.56  Preprocessing        : 0.50
% 6.59/2.56  Parsing              : 0.27
% 6.59/2.56  CNF conversion       : 0.05
% 6.59/2.56  Main loop            : 0.99
% 6.59/2.56  Inferencing          : 0.35
% 6.59/2.56  Reduction            : 0.27
% 6.59/2.56  Demodulation         : 0.19
% 6.59/2.56  BG Simplification    : 0.04
% 6.59/2.56  Subsumption          : 0.27
% 6.59/2.56  Abstraction          : 0.04
% 6.59/2.56  MUC search           : 0.00
% 6.59/2.56  Cooper               : 0.00
% 6.59/2.56  Total                : 1.55
% 6.59/2.56  Index Insertion      : 0.00
% 6.59/2.56  Index Deletion       : 0.00
% 6.59/2.56  Index Matching       : 0.00
% 6.59/2.56  BG Taut test         : 0.00
%------------------------------------------------------------------------------