TSTP Solution File: SET975+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n001.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 10:57:26 EDT 2023

% Result   : Theorem 3.91s 2.09s
% Output   : CNFRefutation 3.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   66 (  26 unt;  18 typ;   0 def)
%            Number of atoms       :   78 (  17 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   62 (  32   ~;  24   |;   2   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-2 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > ordered_pair > cartesian_product2 > #nlpp > singleton > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_2 > #skF_1 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

tff(f_40,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_63,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))
      <=> ( ( A = C )
          & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t128_zfmisc_1) ).

tff(f_51,axiom,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(c_8,plain,
    ! [C_9] : in(C_9,singleton(C_9)),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_36,plain,
    ( ( '#skF_7' = '#skF_5' )
    | ~ in('#skF_10','#skF_12')
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_89,plain,
    '#skF_11' != '#skF_9',
    inference(splitLeft,[status(thm)],[c_36]) ).

tff(c_42,plain,
    ( ( '#skF_7' = '#skF_5' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_212,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')),
    inference(splitLeft,[status(thm)],[c_42]) ).

tff(c_26,plain,
    ! [A_14,C_16,B_15,D_17] :
      ( in(A_14,C_16)
      | ~ in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_218,plain,
    in('#skF_9',singleton('#skF_11')),
    inference(resolution,[status(thm)],[c_212,c_26]) ).

tff(c_6,plain,
    ! [C_9,A_5] :
      ( ( C_9 = A_5 )
      | ~ in(C_9,singleton(A_5)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_224,plain,
    '#skF_11' = '#skF_9',
    inference(resolution,[status(thm)],[c_218,c_6]) ).

tff(c_229,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_89,c_224]) ).

tff(c_231,plain,
    ~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')),
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_40,plain,
    ( in('#skF_6','#skF_8')
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_291,plain,
    in('#skF_6','#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_231,c_40]) ).

tff(c_22,plain,
    ! [A_14,B_15,C_16,D_17] :
      ( in(ordered_pair(A_14,B_15),cartesian_product2(C_16,D_17))
      | ~ in(B_15,D_17)
      | ~ in(A_14,C_16) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_230,plain,
    '#skF_7' = '#skF_5',
    inference(splitRight,[status(thm)],[c_42]) ).

tff(c_38,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),'#skF_8'))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_339,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8'))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_11'),'#skF_12')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_230,c_38]) ).

tff(c_340,plain,
    ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
    inference(negUnitSimplification,[status(thm)],[c_231,c_339]) ).

tff(c_343,plain,
    ( ~ in('#skF_6','#skF_8')
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_22,c_340]) ).

tff(c_347,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_291,c_343]) ).

tff(c_349,plain,
    '#skF_11' = '#skF_9',
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_348,plain,
    ( ~ in('#skF_10','#skF_12')
    | ( '#skF_7' = '#skF_5' ) ),
    inference(splitRight,[status(thm)],[c_36]) ).

tff(c_354,plain,
    ~ in('#skF_10','#skF_12'),
    inference(splitLeft,[status(thm)],[c_348]) ).

tff(c_530,plain,
    ( ( '#skF_7' = '#skF_5' )
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_349,c_42]) ).

tff(c_531,plain,
    in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')),
    inference(splitLeft,[status(thm)],[c_530]) ).

tff(c_543,plain,
    ! [B_76,D_77,A_78,C_79] :
      ( in(B_76,D_77)
      | ~ in(ordered_pair(A_78,B_76),cartesian_product2(C_79,D_77)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_546,plain,
    in('#skF_10','#skF_12'),
    inference(resolution,[status(thm)],[c_531,c_543]) ).

tff(c_550,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_354,c_546]) ).

tff(c_552,plain,
    ~ in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')),
    inference(splitRight,[status(thm)],[c_530]) ).

tff(c_558,plain,
    ( in('#skF_6','#skF_8')
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_349,c_40]) ).

tff(c_559,plain,
    in('#skF_6','#skF_8'),
    inference(negUnitSimplification,[status(thm)],[c_552,c_558]) ).

tff(c_551,plain,
    '#skF_7' = '#skF_5',
    inference(splitRight,[status(thm)],[c_530]) ).

tff(c_611,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8'))
    | in(ordered_pair('#skF_9','#skF_10'),cartesian_product2(singleton('#skF_9'),'#skF_12')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_349,c_551,c_38]) ).

tff(c_612,plain,
    ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
    inference(negUnitSimplification,[status(thm)],[c_552,c_611]) ).

tff(c_615,plain,
    ( ~ in('#skF_6','#skF_8')
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_22,c_612]) ).

tff(c_619,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_559,c_615]) ).

tff(c_621,plain,
    in('#skF_10','#skF_12'),
    inference(splitRight,[status(thm)],[c_348]) ).

tff(c_34,plain,
    ( in('#skF_6','#skF_8')
    | ~ in('#skF_10','#skF_12')
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_630,plain,
    in('#skF_6','#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_349,c_621,c_34]) ).

tff(c_829,plain,
    ! [A_128,B_129,C_130,D_131] :
      ( in(ordered_pair(A_128,B_129),cartesian_product2(C_130,D_131))
      | ~ in(B_129,D_131)
      | ~ in(A_128,C_130) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_620,plain,
    '#skF_7' = '#skF_5',
    inference(splitRight,[status(thm)],[c_348]) ).

tff(c_32,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_7'),'#skF_8'))
    | ~ in('#skF_10','#skF_12')
    | ( '#skF_11' != '#skF_9' ) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_817,plain,
    ~ in(ordered_pair('#skF_5','#skF_6'),cartesian_product2(singleton('#skF_5'),'#skF_8')),
    inference(demodulation,[status(thm),theory(equality)],[c_349,c_621,c_620,c_32]) ).

tff(c_832,plain,
    ( ~ in('#skF_6','#skF_8')
    | ~ in('#skF_5',singleton('#skF_5')) ),
    inference(resolution,[status(thm)],[c_829,c_817]) ).

tff(c_844,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_630,c_832]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SET975+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 17:06:10 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 3.91/2.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.91/2.10  
% 3.91/2.10  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.91/2.13  
% 3.91/2.13  Inference rules
% 3.91/2.13  ----------------------
% 3.91/2.13  #Ref     : 0
% 3.91/2.13  #Sup     : 197
% 3.91/2.13  #Fact    : 0
% 3.91/2.13  #Define  : 0
% 3.91/2.13  #Split   : 6
% 3.91/2.13  #Chain   : 0
% 3.91/2.13  #Close   : 0
% 3.91/2.13  
% 3.91/2.13  Ordering : KBO
% 3.91/2.13  
% 3.91/2.13  Simplification rules
% 3.91/2.13  ----------------------
% 3.91/2.13  #Subsume      : 5
% 3.91/2.13  #Demod        : 68
% 3.91/2.13  #Tautology    : 102
% 3.91/2.13  #SimpNegUnit  : 6
% 3.91/2.13  #BackRed      : 0
% 3.91/2.13  
% 3.91/2.13  #Partial instantiations: 0
% 3.91/2.13  #Strategies tried      : 1
% 3.91/2.13  
% 3.91/2.13  Timing (in seconds)
% 3.91/2.13  ----------------------
% 3.91/2.14  Preprocessing        : 0.50
% 3.91/2.14  Parsing              : 0.25
% 3.91/2.14  CNF conversion       : 0.04
% 3.91/2.14  Main loop            : 0.48
% 3.91/2.14  Inferencing          : 0.18
% 3.91/2.14  Reduction            : 0.14
% 3.91/2.14  Demodulation         : 0.11
% 3.91/2.14  BG Simplification    : 0.03
% 3.91/2.14  Subsumption          : 0.10
% 3.91/2.14  Abstraction          : 0.02
% 3.91/2.14  MUC search           : 0.00
% 3.91/2.14  Cooper               : 0.00
% 3.91/2.14  Total                : 1.03
% 3.91/2.14  Index Insertion      : 0.00
% 3.91/2.14  Index Deletion       : 0.00
% 3.91/2.14  Index Matching       : 0.00
% 3.91/2.14  BG Taut test         : 0.00
%------------------------------------------------------------------------------