TSTP Solution File: SET979+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET979+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 : n010.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 10:57:27 EDT 2023

% Result   : Theorem 2.38s 1.55s
% Output   : CNFRefutation 2.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   24 (   7 unt;  13 typ;   0 def)
%            Number of atoms       :   15 (  14 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   11 (   7   ~;   2   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ empty > unordered_pair > set_union2 > cartesian_product2 > #nlpp > singleton > #skF_7 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_1 > #skF_8 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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_8',type,
    '#skF_8': $i ).

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

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

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

tff(f_60,axiom,
    ! [A,B] : ( unordered_pair(A,B) = set_union2(singleton(A),singleton(B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).

tff(f_53,axiom,
    ! [A,B,C] :
      ( ( cartesian_product2(set_union2(A,B),C) = set_union2(cartesian_product2(A,C),cartesian_product2(B,C)) )
      & ( cartesian_product2(C,set_union2(A,B)) = set_union2(cartesian_product2(C,A),cartesian_product2(C,B)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).

tff(f_58,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( cartesian_product2(unordered_pair(A,B),C) = set_union2(cartesian_product2(singleton(A),C),cartesian_product2(singleton(B),C)) )
        & ( cartesian_product2(C,unordered_pair(A,B)) = set_union2(cartesian_product2(C,singleton(A)),cartesian_product2(C,singleton(B))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).

tff(c_22,plain,
    ! [A_14,B_15] : ( set_union2(singleton(A_14),singleton(B_15)) = unordered_pair(A_14,B_15) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_16,plain,
    ! [A_11,C_13,B_12] : ( set_union2(cartesian_product2(A_11,C_13),cartesian_product2(B_12,C_13)) = cartesian_product2(set_union2(A_11,B_12),C_13) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_18,plain,
    ! [C_13,A_11,B_12] : ( set_union2(cartesian_product2(C_13,A_11),cartesian_product2(C_13,B_12)) = cartesian_product2(C_13,set_union2(A_11,B_12)) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_20,plain,
    ( ( set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8') )
    | ( set_union2(cartesian_product2('#skF_5',singleton('#skF_3')),cartesian_product2('#skF_5',singleton('#skF_4'))) != cartesian_product2('#skF_5',unordered_pair('#skF_3','#skF_4')) ) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_23,plain,
    ( ( set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8') )
    | ( cartesian_product2('#skF_5',set_union2(singleton('#skF_3'),singleton('#skF_4'))) != cartesian_product2('#skF_5',unordered_pair('#skF_3','#skF_4')) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_20]) ).

tff(c_25,plain,
    set_union2(cartesian_product2(singleton('#skF_6'),'#skF_8'),cartesian_product2(singleton('#skF_7'),'#skF_8')) != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_23]) ).

tff(c_26,plain,
    cartesian_product2(set_union2(singleton('#skF_6'),singleton('#skF_7')),'#skF_8') != cartesian_product2(unordered_pair('#skF_6','#skF_7'),'#skF_8'),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_25]) ).

tff(c_28,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET979+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
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 16:03:58 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 2.38/1.55  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.38/1.55  
% 2.38/1.55  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.38/1.58  
% 2.38/1.58  Inference rules
% 2.38/1.58  ----------------------
% 2.38/1.58  #Ref     : 0
% 2.38/1.58  #Sup     : 0
% 2.38/1.58  #Fact    : 0
% 2.38/1.58  #Define  : 0
% 2.38/1.58  #Split   : 0
% 2.38/1.58  #Chain   : 0
% 2.38/1.58  #Close   : 0
% 2.38/1.58  
% 2.38/1.58  Ordering : KBO
% 2.38/1.58  
% 2.38/1.58  Simplification rules
% 2.38/1.58  ----------------------
% 2.38/1.58  #Subsume      : 10
% 2.38/1.58  #Demod        : 4
% 2.38/1.58  #Tautology    : 0
% 2.38/1.58  #SimpNegUnit  : 0
% 2.38/1.58  #BackRed      : 0
% 2.38/1.58  
% 2.38/1.58  #Partial instantiations: 0
% 2.38/1.58  #Strategies tried      : 1
% 2.38/1.58  
% 2.38/1.58  Timing (in seconds)
% 2.38/1.58  ----------------------
% 2.38/1.58  Preprocessing        : 0.45
% 2.38/1.58  Parsing              : 0.25
% 2.38/1.59  CNF conversion       : 0.03
% 2.38/1.59  Main loop            : 0.06
% 2.38/1.59  Inferencing          : 0.00
% 2.38/1.59  Reduction            : 0.03
% 2.38/1.59  Demodulation         : 0.02
% 2.38/1.59  BG Simplification    : 0.01
% 2.38/1.59  Subsumption          : 0.03
% 2.38/1.59  Abstraction          : 0.01
% 2.38/1.59  MUC search           : 0.00
% 2.38/1.59  Cooper               : 0.00
% 2.38/1.59  Total                : 0.57
% 2.38/1.59  Index Insertion      : 0.00
% 2.38/1.59  Index Deletion       : 0.00
% 2.38/1.59  Index Matching       : 0.00
% 2.38/1.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------