TSTP Solution File: SET908+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET908+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 : n026.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 2.81s 1.86s
% Output   : CNFRefutation 2.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   25 (   6 unt;  14 typ;   0 def)
%            Number of atoms       :   19 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   15 (   7   ~;   3   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (   9   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   5 con; 0-3 aty)
%            Number of variables   :   18 (;  18   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(empty_set,type,
    empty_set: $i ).

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

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

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

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

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

tff(f_40,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_46,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_79,negated_conjecture,
    ~ ! [A,B] : ( set_union2(singleton(A),B) != empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t49_zfmisc_1) ).

tff(f_55,axiom,
    ! [A,B,C] :
      ( ( C = set_union2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

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

tff(c_18,plain,
    ! [B_13] : ~ in(B_13,empty_set),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_52,plain,
    set_union2(singleton('#skF_8'),'#skF_9') = empty_set,
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_230,plain,
    ! [D_46,A_47,B_48] :
      ( ~ in(D_46,A_47)
      | in(D_46,set_union2(A_47,B_48)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_248,plain,
    ! [D_46] :
      ( ~ in(D_46,singleton('#skF_8'))
      | in(D_46,empty_set) ),
    inference(superposition,[status(thm),theory(equality)],[c_52,c_230]) ).

tff(c_308,plain,
    ! [D_50] : ~ in(D_50,singleton('#skF_8')),
    inference(negUnitSimplification,[status(thm)],[c_18,c_248]) ).

tff(c_313,plain,
    $false,
    inference(resolution,[status(thm)],[c_8,c_308]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET908+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
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:59:47 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 2.81/1.86  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.81/1.86  
% 2.81/1.86  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.81/1.89  
% 2.81/1.89  Inference rules
% 2.81/1.89  ----------------------
% 2.81/1.89  #Ref     : 0
% 2.81/1.89  #Sup     : 65
% 2.81/1.89  #Fact    : 0
% 2.81/1.89  #Define  : 0
% 2.81/1.89  #Split   : 0
% 2.81/1.89  #Chain   : 0
% 2.81/1.89  #Close   : 0
% 2.81/1.89  
% 2.81/1.89  Ordering : KBO
% 2.81/1.89  
% 2.81/1.89  Simplification rules
% 2.81/1.89  ----------------------
% 2.81/1.89  #Subsume      : 10
% 2.81/1.89  #Demod        : 22
% 2.81/1.89  #Tautology    : 35
% 2.81/1.89  #SimpNegUnit  : 6
% 2.81/1.89  #BackRed      : 7
% 2.81/1.89  
% 2.81/1.89  #Partial instantiations: 0
% 2.81/1.89  #Strategies tried      : 1
% 2.81/1.89  
% 2.81/1.89  Timing (in seconds)
% 2.81/1.89  ----------------------
% 2.81/1.89  Preprocessing        : 0.49
% 2.81/1.89  Parsing              : 0.25
% 2.81/1.89  CNF conversion       : 0.04
% 2.81/1.89  Main loop            : 0.32
% 2.81/1.89  Inferencing          : 0.11
% 2.81/1.89  Reduction            : 0.10
% 2.81/1.89  Demodulation         : 0.08
% 2.81/1.89  BG Simplification    : 0.02
% 2.81/1.89  Subsumption          : 0.07
% 2.81/1.89  Abstraction          : 0.01
% 2.81/1.89  MUC search           : 0.00
% 2.81/1.89  Cooper               : 0.00
% 2.81/1.90  Total                : 0.86
% 2.81/1.90  Index Insertion      : 0.00
% 2.81/1.90  Index Deletion       : 0.00
% 2.81/1.90  Index Matching       : 0.00
% 2.81/1.90  BG Taut test         : 0.00
%------------------------------------------------------------------------------