TSTP Solution File: SET912+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET912+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 : 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 10:57:19 EDT 2023

% Result   : Theorem 3.25s 1.89s
% Output   : CNFRefutation 3.30s
% 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_intersection2 > #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(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $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(f_61,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( in(A,B)
          & in(C,B) )
       => ( set_intersection2(unordered_pair(A,C),B) = unordered_pair(A,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).

tff(f_54,axiom,
    ! [A,B,C] :
      ( subset(unordered_pair(A,B),C)
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

tff(f_48,axiom,
    ! [A,B] :
      ( subset(A,B)
     => ( set_intersection2(A,B) = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

tff(f_35,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(c_28,plain,
    in('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_26,plain,
    in('#skF_5','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_181,plain,
    ! [A_40,B_41,C_42] :
      ( subset(unordered_pair(A_40,B_41),C_42)
      | ~ in(B_41,C_42)
      | ~ in(A_40,C_42) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_16,plain,
    ! [A_11,B_12] :
      ( ( set_intersection2(A_11,B_12) = A_11 )
      | ~ subset(A_11,B_12) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_200,plain,
    ! [A_43,B_44,C_45] :
      ( ( set_intersection2(unordered_pair(A_43,B_44),C_45) = unordered_pair(A_43,B_44) )
      | ~ in(B_44,C_45)
      | ~ in(A_43,C_45) ),
    inference(resolution,[status(thm)],[c_181,c_16]) ).

tff(c_6,plain,
    ! [B_6,A_5] : ( set_intersection2(B_6,A_5) = set_intersection2(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_243,plain,
    ! [C_46,A_47,B_48] :
      ( ( set_intersection2(C_46,unordered_pair(A_47,B_48)) = unordered_pair(A_47,B_48) )
      | ~ in(B_48,C_46)
      | ~ in(A_47,C_46) ),
    inference(superposition,[status(thm),theory(equality)],[c_200,c_6]) ).

tff(c_24,plain,
    set_intersection2(unordered_pair('#skF_3','#skF_5'),'#skF_4') != unordered_pair('#skF_3','#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_29,plain,
    set_intersection2('#skF_4',unordered_pair('#skF_3','#skF_5')) != unordered_pair('#skF_3','#skF_5'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_24]) ).

tff(c_253,plain,
    ( ~ in('#skF_5','#skF_4')
    | ~ in('#skF_3','#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_243,c_29]) ).

tff(c_293,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_26,c_253]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET912+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 : n025.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 16:35:49 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.25/1.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.25/1.90  
% 3.25/1.90  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.30/1.92  
% 3.30/1.92  Inference rules
% 3.30/1.92  ----------------------
% 3.30/1.92  #Ref     : 0
% 3.30/1.92  #Sup     : 65
% 3.30/1.92  #Fact    : 0
% 3.30/1.92  #Define  : 0
% 3.30/1.92  #Split   : 0
% 3.30/1.92  #Chain   : 0
% 3.30/1.92  #Close   : 0
% 3.30/1.92  
% 3.30/1.92  Ordering : KBO
% 3.30/1.92  
% 3.30/1.92  Simplification rules
% 3.30/1.92  ----------------------
% 3.30/1.92  #Subsume      : 10
% 3.30/1.92  #Demod        : 12
% 3.30/1.92  #Tautology    : 30
% 3.30/1.92  #SimpNegUnit  : 0
% 3.30/1.92  #BackRed      : 0
% 3.30/1.92  
% 3.30/1.92  #Partial instantiations: 0
% 3.30/1.92  #Strategies tried      : 1
% 3.30/1.92  
% 3.30/1.92  Timing (in seconds)
% 3.30/1.92  ----------------------
% 3.30/1.93  Preprocessing        : 0.46
% 3.30/1.93  Parsing              : 0.25
% 3.30/1.93  CNF conversion       : 0.03
% 3.30/1.93  Main loop            : 0.32
% 3.30/1.93  Inferencing          : 0.12
% 3.30/1.93  Reduction            : 0.10
% 3.30/1.93  Demodulation         : 0.08
% 3.30/1.93  BG Simplification    : 0.01
% 3.30/1.93  Subsumption          : 0.07
% 3.30/1.93  Abstraction          : 0.01
% 3.30/1.93  MUC search           : 0.00
% 3.30/1.93  Cooper               : 0.00
% 3.30/1.93  Total                : 0.82
% 3.30/1.93  Index Insertion      : 0.00
% 3.30/1.93  Index Deletion       : 0.00
% 3.30/1.93  Index Matching       : 0.00
% 3.30/1.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------