TSTP Solution File: SET968+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET968+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 : n001.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 10:57:26 EDT 2023

% Result   : Theorem 7.19s 2.92s
% Output   : CNFRefutation 7.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   29 (  19 unt;   9 typ;   0 def)
%            Number of atoms       :   21 (  20 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    9 (   8   ~;   0   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   36 (;  36   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
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_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_51,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/sandbox2/benchmark/theBenchmark.p',t120_zfmisc_1) ).

tff(f_28,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_56,axiom,
    ! [A,B,C] : ( set_union2(set_union2(A,B),C) = set_union2(A,set_union2(B,C)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_1) ).

tff(f_54,negated_conjecture,
    ~ ! [A,B,C,D] : ( cartesian_product2(set_union2(A,B),set_union2(C,D)) = set_union2(set_union2(set_union2(cartesian_product2(A,C),cartesian_product2(A,D)),cartesian_product2(B,C)),cartesian_product2(B,D)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t121_zfmisc_1) ).

tff(c_14,plain,
    ! [A_9,C_11,B_10] : ( set_union2(cartesian_product2(A_9,C_11),cartesian_product2(B_10,C_11)) = cartesian_product2(set_union2(A_9,B_10),C_11) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_2,plain,
    ! [B_2,A_1] : ( set_union2(B_2,A_1) = set_union2(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_28]) ).

tff(c_348,plain,
    ! [C_35,A_36,B_37] : ( set_union2(cartesian_product2(C_35,A_36),cartesian_product2(C_35,B_37)) = cartesian_product2(C_35,set_union2(A_36,B_37)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_20,plain,
    ! [A_12,B_13,C_14] : ( set_union2(set_union2(A_12,B_13),C_14) = set_union2(A_12,set_union2(B_13,C_14)) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_366,plain,
    ! [C_35,A_36,B_37,C_14] : ( set_union2(cartesian_product2(C_35,A_36),set_union2(cartesian_product2(C_35,B_37),C_14)) = set_union2(cartesian_product2(C_35,set_union2(A_36,B_37)),C_14) ),
    inference(superposition,[status(thm),theory(equality)],[c_348,c_20]) ).

tff(c_86,plain,
    ! [A_22,B_23,C_24] : ( set_union2(set_union2(A_22,B_23),C_24) = set_union2(A_22,set_union2(B_23,C_24)) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_98,plain,
    ! [C_24,A_22,B_23] : ( set_union2(C_24,set_union2(A_22,B_23)) = set_union2(A_22,set_union2(B_23,C_24)) ),
    inference(superposition,[status(thm),theory(equality)],[c_86,c_2]) ).

tff(c_16,plain,
    ! [C_11,A_9,B_10] : ( set_union2(cartesian_product2(C_11,A_9),cartesian_product2(C_11,B_10)) = cartesian_product2(C_11,set_union2(A_9,B_10)) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_18,plain,
    set_union2(set_union2(set_union2(cartesian_product2('#skF_3','#skF_5'),cartesian_product2('#skF_3','#skF_6')),cartesian_product2('#skF_4','#skF_5')),cartesian_product2('#skF_4','#skF_6')) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_21,plain,
    set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_4','#skF_5'),cartesian_product2('#skF_4','#skF_6')))) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_20,c_20,c_18]) ).

tff(c_22,plain,
    set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),cartesian_product2('#skF_4',set_union2('#skF_5','#skF_6')))) != cartesian_product2(set_union2('#skF_3','#skF_4'),set_union2('#skF_5','#skF_6')),
    inference(demodulation,[status(thm),theory(equality)],[c_16,c_21]) ).

tff(c_23,plain,
    set_union2(cartesian_product2('#skF_3','#skF_5'),set_union2(cartesian_product2('#skF_3','#skF_6'),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_2,c_2,c_22]) ).

tff(c_421,plain,
    set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')),cartesian_product2('#skF_3','#skF_5'))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_98,c_23]) ).

tff(c_422,plain,
    set_union2(cartesian_product2('#skF_3','#skF_6'),set_union2(cartesian_product2('#skF_3','#skF_5'),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5')))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_421]) ).

tff(c_6861,plain,
    set_union2(cartesian_product2('#skF_3',set_union2('#skF_6','#skF_5')),cartesian_product2('#skF_4',set_union2('#skF_6','#skF_5'))) != cartesian_product2(set_union2('#skF_4','#skF_3'),set_union2('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_366,c_422]) ).

tff(c_6864,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_2,c_6861]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET968+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
% 0.13/0.36  % Computer : n001.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 17:26:10 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 7.19/2.92  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.19/2.93  
% 7.19/2.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.19/2.96  
% 7.19/2.96  Inference rules
% 7.19/2.96  ----------------------
% 7.19/2.96  #Ref     : 0
% 7.19/2.96  #Sup     : 1836
% 7.19/2.96  #Fact    : 0
% 7.19/2.96  #Define  : 0
% 7.19/2.96  #Split   : 0
% 7.19/2.96  #Chain   : 0
% 7.19/2.96  #Close   : 0
% 7.19/2.96  
% 7.19/2.96  Ordering : KBO
% 7.19/2.96  
% 7.19/2.96  Simplification rules
% 7.19/2.96  ----------------------
% 7.19/2.96  #Subsume      : 462
% 7.19/2.96  #Demod        : 1341
% 7.19/2.96  #Tautology    : 396
% 7.19/2.96  #SimpNegUnit  : 0
% 7.19/2.96  #BackRed      : 2
% 7.19/2.96  
% 7.19/2.96  #Partial instantiations: 0
% 7.19/2.96  #Strategies tried      : 1
% 7.19/2.96  
% 7.19/2.96  Timing (in seconds)
% 7.19/2.96  ----------------------
% 7.19/2.96  Preprocessing        : 0.47
% 7.19/2.96  Parsing              : 0.26
% 7.19/2.96  CNF conversion       : 0.03
% 7.19/2.96  Main loop            : 1.39
% 7.19/2.96  Inferencing          : 0.33
% 7.19/2.96  Reduction            : 0.76
% 7.19/2.96  Demodulation         : 0.68
% 7.19/2.96  BG Simplification    : 0.05
% 7.19/2.96  Subsumption          : 0.18
% 7.19/2.96  Abstraction          : 0.06
% 7.19/2.96  MUC search           : 0.00
% 7.19/2.96  Cooper               : 0.00
% 7.19/2.96  Total                : 1.90
% 7.19/2.96  Index Insertion      : 0.00
% 7.19/2.96  Index Deletion       : 0.00
% 7.19/2.96  Index Matching       : 0.00
% 7.19/2.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------