TSTP Solution File: SET906+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET906+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 : n017.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 10:57:18 EDT 2023

% Result   : Theorem 5.52s 2.38s
% Output   : CNFRefutation 5.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   31 (   8 unt;  15 typ;   0 def)
%            Number of atoms       :   31 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   23 (   8   ~;   8   |;   0   &)
%                                         (   5 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  10   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :   31 (;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_union2 > #nlpp > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_2 > #skF_9 > #skF_8 > #skF_3 > #skF_5

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

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

tff(f_86,negated_conjecture,
    ~ ! [A,B,C] :
        ( subset(set_union2(unordered_pair(A,B),C),C)
       => in(A,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_zfmisc_1) ).

tff(f_44,axiom,
    ! [A,B,C] :
      ( ( C = unordered_pair(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

tff(f_35,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_53,axiom,
    ! [A,B,C] :
      ( ( C = set_union2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

tff(f_60,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

tff(c_62,plain,
    ~ in('#skF_8','#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_12,plain,
    ! [D_12,B_8] : in(D_12,unordered_pair(D_12,B_8)),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_6,plain,
    ! [B_6,A_5] : ( set_union2(B_6,A_5) = set_union2(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_64,plain,
    subset(set_union2(unordered_pair('#skF_8','#skF_9'),'#skF_10'),'#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_65,plain,
    subset(set_union2('#skF_10',unordered_pair('#skF_8','#skF_9')),'#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_64]) ).

tff(c_28,plain,
    ! [D_18,B_14,A_13] :
      ( ~ in(D_18,B_14)
      | in(D_18,set_union2(A_13,B_14)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_410,plain,
    ! [C_77,B_78,A_79] :
      ( in(C_77,B_78)
      | ~ in(C_77,A_79)
      | ~ subset(A_79,B_78) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_2934,plain,
    ! [D_2879,B_2880,A_2881,B_2882] :
      ( in(D_2879,B_2880)
      | ~ subset(set_union2(A_2881,B_2882),B_2880)
      | ~ in(D_2879,B_2882) ),
    inference(resolution,[status(thm)],[c_28,c_410]) ).

tff(c_2950,plain,
    ! [D_2919] :
      ( in(D_2919,'#skF_10')
      | ~ in(D_2919,unordered_pair('#skF_8','#skF_9')) ),
    inference(resolution,[status(thm)],[c_65,c_2934]) ).

tff(c_2990,plain,
    in('#skF_8','#skF_10'),
    inference(resolution,[status(thm)],[c_12,c_2950]) ).

tff(c_3001,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_62,c_2990]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET906+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/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
% 0.14/0.36  % Computer : n017.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 16:15:21 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 5.52/2.38  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.52/2.39  
% 5.52/2.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.91/2.41  
% 5.91/2.41  Inference rules
% 5.91/2.41  ----------------------
% 5.91/2.41  #Ref     : 0
% 5.91/2.41  #Sup     : 563
% 5.91/2.41  #Fact    : 6
% 5.91/2.41  #Define  : 0
% 5.91/2.41  #Split   : 6
% 5.91/2.41  #Chain   : 0
% 5.91/2.41  #Close   : 0
% 5.91/2.41  
% 5.91/2.41  Ordering : KBO
% 5.91/2.41  
% 5.91/2.41  Simplification rules
% 5.91/2.41  ----------------------
% 5.91/2.41  #Subsume      : 208
% 5.91/2.41  #Demod        : 20
% 5.91/2.41  #Tautology    : 55
% 5.91/2.41  #SimpNegUnit  : 1
% 5.91/2.41  #BackRed      : 0
% 5.91/2.41  
% 5.91/2.41  #Partial instantiations: 1800
% 5.91/2.41  #Strategies tried      : 1
% 5.91/2.41  
% 5.91/2.41  Timing (in seconds)
% 5.91/2.41  ----------------------
% 5.91/2.42  Preprocessing        : 0.51
% 5.91/2.42  Parsing              : 0.26
% 5.91/2.42  CNF conversion       : 0.04
% 5.91/2.42  Main loop            : 0.85
% 5.91/2.42  Inferencing          : 0.35
% 5.91/2.42  Reduction            : 0.25
% 5.91/2.42  Demodulation         : 0.19
% 5.91/2.42  BG Simplification    : 0.04
% 5.91/2.42  Subsumption          : 0.17
% 5.91/2.42  Abstraction          : 0.03
% 5.91/2.42  MUC search           : 0.00
% 5.91/2.42  Cooper               : 0.00
% 5.91/2.42  Total                : 1.40
% 5.91/2.42  Index Insertion      : 0.00
% 5.91/2.42  Index Deletion       : 0.00
% 5.91/2.42  Index Matching       : 0.00
% 5.91/2.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------