TSTP Solution File: SET956+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET956+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/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 : n008.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 10:57:24 EDT 2023

% Result   : Theorem 6.15s 2.63s
% Output   : CNFRefutation 6.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   35 (   6 unt;  16 typ;   0 def)
%            Number of atoms       :   49 (   3 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   52 (  22   ~;  21   |;   5   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  10   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-4 aty)
%            Number of variables   :   47 (;  47   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_77,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( ( subset(A,cartesian_product2(B,C))
          & ! [E,F] :
              ( in(ordered_pair(E,F),A)
             => in(ordered_pair(E,F),D) ) )
       => subset(A,D) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t109_zfmisc_1) ).

tff(f_42,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_67,axiom,
    ! [A,B,C,D] :
      ~ ( subset(A,cartesian_product2(B,C))
        & in(D,A)
        & ! [E,F] :
            ~ ( in(E,B)
              & in(F,C)
              & ( D = ordered_pair(E,F) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t103_zfmisc_1) ).

tff(c_28,plain,
    ~ subset('#skF_6','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_10,plain,
    ! [A_5,B_6] :
      ( in('#skF_1'(A_5,B_6),A_5)
      | subset(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_22,plain,
    ! [A_16,B_17,C_18,D_19] :
      ( ( ordered_pair('#skF_4'(A_16,B_17,C_18,D_19),'#skF_5'(A_16,B_17,C_18,D_19)) = D_19 )
      | ~ in(D_19,A_16)
      | ~ subset(A_16,cartesian_product2(B_17,C_18)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_356,plain,
    ! [A_72,B_73,C_74,D_75] :
      ( ( ordered_pair('#skF_4'(A_72,B_73,C_74,D_75),'#skF_5'(A_72,B_73,C_74,D_75)) = D_75 )
      | ~ in(D_75,A_72)
      | ~ subset(A_72,cartesian_product2(B_73,C_74)) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_30,plain,
    ! [E_24,F_25] :
      ( in(ordered_pair(E_24,F_25),'#skF_9')
      | ~ in(ordered_pair(E_24,F_25),'#skF_6') ),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_429,plain,
    ! [A_86,B_87,C_88,D_89] :
      ( in(ordered_pair('#skF_4'(A_86,B_87,C_88,D_89),'#skF_5'(A_86,B_87,C_88,D_89)),'#skF_9')
      | ~ in(D_89,'#skF_6')
      | ~ in(D_89,A_86)
      | ~ subset(A_86,cartesian_product2(B_87,C_88)) ),
    inference(superposition,[status(thm),theory(equality)],[c_356,c_30]) ).

tff(c_2768,plain,
    ! [D_218,A_219,B_220,C_221] :
      ( in(D_218,'#skF_9')
      | ~ in(D_218,'#skF_6')
      | ~ in(D_218,A_219)
      | ~ subset(A_219,cartesian_product2(B_220,C_221))
      | ~ in(D_218,A_219)
      | ~ subset(A_219,cartesian_product2(B_220,C_221)) ),
    inference(superposition,[status(thm),theory(equality)],[c_22,c_429]) ).

tff(c_3034,plain,
    ! [B_240,A_241,B_242,C_243] :
      ( in('#skF_1'('#skF_6',B_240),'#skF_9')
      | ~ in('#skF_1'('#skF_6',B_240),A_241)
      | ~ subset(A_241,cartesian_product2(B_242,C_243))
      | subset('#skF_6',B_240) ),
    inference(resolution,[status(thm)],[c_10,c_2768]) ).

tff(c_3048,plain,
    ! [B_6,B_242,C_243] :
      ( in('#skF_1'('#skF_6',B_6),'#skF_9')
      | ~ subset('#skF_6',cartesian_product2(B_242,C_243))
      | subset('#skF_6',B_6) ),
    inference(resolution,[status(thm)],[c_10,c_3034]) ).

tff(c_3053,plain,
    ! [B_242,C_243] : ~ subset('#skF_6',cartesian_product2(B_242,C_243)),
    inference(splitLeft,[status(thm)],[c_3048]) ).

tff(c_32,plain,
    subset('#skF_6',cartesian_product2('#skF_7','#skF_8')),
    inference(cnfTransformation,[status(thm)],[f_77]) ).

tff(c_3055,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3053,c_32]) ).

tff(c_3057,plain,
    ! [B_248] :
      ( in('#skF_1'('#skF_6',B_248),'#skF_9')
      | subset('#skF_6',B_248) ),
    inference(splitRight,[status(thm)],[c_3048]) ).

tff(c_8,plain,
    ! [A_5,B_6] :
      ( ~ in('#skF_1'(A_5,B_6),B_6)
      | subset(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_3065,plain,
    subset('#skF_6','#skF_9'),
    inference(resolution,[status(thm)],[c_3057,c_8]) ).

tff(c_3073,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_28,c_28,c_3065]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET956+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % 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
% 0.17/0.35  % Computer : n008.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Thu Aug  3 16:54:19 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 6.15/2.63  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.49/2.64  
% 6.49/2.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.49/2.67  
% 6.49/2.67  Inference rules
% 6.49/2.67  ----------------------
% 6.49/2.67  #Ref     : 0
% 6.49/2.67  #Sup     : 781
% 6.49/2.67  #Fact    : 0
% 6.49/2.67  #Define  : 0
% 6.49/2.67  #Split   : 9
% 6.49/2.67  #Chain   : 0
% 6.49/2.67  #Close   : 0
% 6.49/2.67  
% 6.49/2.67  Ordering : KBO
% 6.49/2.67  
% 6.49/2.67  Simplification rules
% 6.49/2.67  ----------------------
% 6.49/2.67  #Subsume      : 96
% 6.49/2.67  #Demod        : 579
% 6.49/2.67  #Tautology    : 167
% 6.49/2.67  #SimpNegUnit  : 2
% 6.49/2.67  #BackRed      : 1
% 6.49/2.67  
% 6.49/2.67  #Partial instantiations: 0
% 6.49/2.67  #Strategies tried      : 1
% 6.49/2.67  
% 6.49/2.67  Timing (in seconds)
% 6.49/2.67  ----------------------
% 6.49/2.67  Preprocessing        : 0.48
% 6.49/2.67  Parsing              : 0.27
% 6.49/2.67  CNF conversion       : 0.03
% 6.49/2.67  Main loop            : 1.07
% 6.49/2.67  Inferencing          : 0.34
% 6.49/2.67  Reduction            : 0.44
% 6.49/2.67  Demodulation         : 0.36
% 6.49/2.67  BG Simplification    : 0.04
% 6.49/2.67  Subsumption          : 0.19
% 6.49/2.67  Abstraction          : 0.05
% 6.49/2.67  MUC search           : 0.00
% 6.49/2.67  Cooper               : 0.00
% 6.49/2.67  Total                : 1.60
% 6.49/2.67  Index Insertion      : 0.00
% 6.49/2.67  Index Deletion       : 0.00
% 6.49/2.67  Index Matching       : 0.00
% 6.49/2.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------