TSTP Solution File: SET907+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET907+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 : n016.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 3.35s 1.93s
% Output   : CNFRefutation 3.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   25 (   7 unt;  10 typ;   0 def)
%            Number of atoms       :   28 (   9 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   25 (  12   ~;   8   |;   2   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   23 (;  23   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > set_union2 > #nlpp > #skF_5 > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

tff(f_73,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( in(A,B)
          & in(C,B) )
       => ( set_union2(unordered_pair(A,C),B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_zfmisc_1) ).

tff(f_66,axiom,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),C)
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).

tff(f_60,axiom,
    ! [A,B] :
      ( subset(A,B)
     => ( set_union2(A,B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

tff(f_35,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(c_32,plain,
    in('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_30,plain,
    in('#skF_5','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_205,plain,
    ! [A_48,B_49,C_50] :
      ( subset(unordered_pair(A_48,B_49),C_50)
      | ~ in(B_49,C_50)
      | ~ in(A_48,C_50) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_20,plain,
    ! [A_15,B_16] :
      ( ( set_union2(A_15,B_16) = B_16 )
      | ~ subset(A_15,B_16) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_224,plain,
    ! [A_51,B_52,C_53] :
      ( ( set_union2(unordered_pair(A_51,B_52),C_53) = C_53 )
      | ~ in(B_52,C_53)
      | ~ in(A_51,C_53) ),
    inference(resolution,[status(thm)],[c_205,c_20]) ).

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_273,plain,
    ! [C_54,A_55,B_56] :
      ( ( set_union2(C_54,unordered_pair(A_55,B_56)) = C_54 )
      | ~ in(B_56,C_54)
      | ~ in(A_55,C_54) ),
    inference(superposition,[status(thm),theory(equality)],[c_224,c_6]) ).

tff(c_28,plain,
    set_union2(unordered_pair('#skF_3','#skF_5'),'#skF_4') != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_33,plain,
    set_union2('#skF_4',unordered_pair('#skF_3','#skF_5')) != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_28]) ).

tff(c_292,plain,
    ( ~ in('#skF_5','#skF_4')
    | ~ in('#skF_3','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_273,c_33]) ).

tff(c_329,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_30,c_292]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.15  % Problem  : SET907+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.16  % 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
% 0.14/0.37  % Computer : n016.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit : 300
% 0.14/0.37  % WCLimit  : 300
% 0.14/0.37  % DateTime : Thu Aug  3 16:42:38 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 3.35/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.38/1.93  
% 3.38/1.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.38/1.95  
% 3.38/1.95  Inference rules
% 3.38/1.95  ----------------------
% 3.38/1.95  #Ref     : 0
% 3.38/1.95  #Sup     : 75
% 3.38/1.95  #Fact    : 0
% 3.38/1.95  #Define  : 0
% 3.38/1.95  #Split   : 0
% 3.38/1.95  #Chain   : 0
% 3.38/1.95  #Close   : 0
% 3.38/1.95  
% 3.38/1.95  Ordering : KBO
% 3.38/1.95  
% 3.38/1.95  Simplification rules
% 3.38/1.95  ----------------------
% 3.38/1.95  #Subsume      : 18
% 3.38/1.95  #Demod        : 12
% 3.38/1.95  #Tautology    : 34
% 3.38/1.95  #SimpNegUnit  : 0
% 3.38/1.95  #BackRed      : 0
% 3.38/1.95  
% 3.38/1.95  #Partial instantiations: 0
% 3.38/1.95  #Strategies tried      : 1
% 3.38/1.95  
% 3.38/1.95  Timing (in seconds)
% 3.38/1.95  ----------------------
% 3.38/1.96  Preprocessing        : 0.45
% 3.38/1.96  Parsing              : 0.26
% 3.38/1.96  CNF conversion       : 0.03
% 3.38/1.96  Main loop            : 0.32
% 3.38/1.96  Inferencing          : 0.12
% 3.38/1.96  Reduction            : 0.10
% 3.38/1.96  Demodulation         : 0.08
% 3.38/1.96  BG Simplification    : 0.01
% 3.38/1.96  Subsumption          : 0.07
% 3.38/1.96  Abstraction          : 0.01
% 3.38/1.96  MUC search           : 0.00
% 3.38/1.96  Cooper               : 0.00
% 3.38/1.96  Total                : 0.82
% 3.38/1.96  Index Insertion      : 0.00
% 3.38/1.96  Index Deletion       : 0.00
% 3.38/1.96  Index Matching       : 0.00
% 3.38/1.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------