TSTP Solution File: SET605+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 10:56:41 EDT 2023

% Result   : Theorem 3.23s 1.80s
% Output   : CNFRefutation 3.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   25 (  11 unt;  12 typ;   0 def)
%            Number of atoms       :   15 (   9 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    6 (   4   ~;   1   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   3 con; 0-2 aty)
%            Number of variables   :   20 (;  20   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > empty > union > difference > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

tff(f_63,axiom,
    ! [B,C] : ( union(B,C) = union(C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).

tff(f_29,axiom,
    ! [B,C] : subset(B,union(B,C)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_union) ).

tff(f_34,axiom,
    ! [B,C] :
      ( ( difference(B,C) = empty_set )
    <=> subset(B,C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_empty_set) ).

tff(f_93,negated_conjecture,
    ~ ! [B,C] : ( difference(B,union(B,C)) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th76) ).

tff(c_62,plain,
    ! [C_37,B_38] : ( union(C_37,B_38) = union(B_38,C_37) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_2,plain,
    ! [B_1,C_2] : subset(B_1,union(B_1,C_2)),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_77,plain,
    ! [B_38,C_37] : subset(B_38,union(C_37,B_38)),
    inference(superposition,[status(thm),theory(equality)],[c_62,c_2]) ).

tff(c_122,plain,
    ! [B_44,C_45] :
      ( ( difference(B_44,C_45) = empty_set )
      | ~ subset(B_44,C_45) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_136,plain,
    ! [B_38,C_37] : ( difference(B_38,union(C_37,B_38)) = empty_set ),
    inference(resolution,[status(thm)],[c_77,c_122]) ).

tff(c_28,plain,
    ! [C_15,B_14] : ( union(C_15,B_14) = union(B_14,C_15) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_54,plain,
    difference('#skF_5',union('#skF_5','#skF_6')) != empty_set,
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_55,plain,
    difference('#skF_5',union('#skF_6','#skF_5')) != empty_set,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_54]) ).

tff(c_161,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_136,c_55]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET605+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n022.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 16:50:33 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 3.23/1.80  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.23/1.81  
% 3.23/1.81  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.23/1.83  
% 3.23/1.83  Inference rules
% 3.23/1.83  ----------------------
% 3.23/1.83  #Ref     : 0
% 3.23/1.83  #Sup     : 24
% 3.23/1.83  #Fact    : 0
% 3.23/1.83  #Define  : 0
% 3.23/1.83  #Split   : 0
% 3.23/1.83  #Chain   : 0
% 3.23/1.83  #Close   : 0
% 3.23/1.83  
% 3.23/1.83  Ordering : KBO
% 3.23/1.83  
% 3.23/1.83  Simplification rules
% 3.23/1.83  ----------------------
% 3.23/1.83  #Subsume      : 0
% 3.23/1.83  #Demod        : 7
% 3.23/1.83  #Tautology    : 21
% 3.23/1.83  #SimpNegUnit  : 0
% 3.23/1.83  #BackRed      : 1
% 3.23/1.83  
% 3.23/1.83  #Partial instantiations: 0
% 3.23/1.83  #Strategies tried      : 1
% 3.23/1.83  
% 3.23/1.83  Timing (in seconds)
% 3.23/1.83  ----------------------
% 3.23/1.83  Preprocessing        : 0.50
% 3.23/1.83  Parsing              : 0.27
% 3.23/1.83  CNF conversion       : 0.04
% 3.23/1.83  Main loop            : 0.21
% 3.23/1.83  Inferencing          : 0.06
% 3.23/1.83  Reduction            : 0.07
% 3.23/1.83  Demodulation         : 0.06
% 3.23/1.83  BG Simplification    : 0.02
% 3.23/1.83  Subsumption          : 0.05
% 3.23/1.83  Abstraction          : 0.01
% 3.23/1.83  MUC search           : 0.00
% 3.23/1.83  Cooper               : 0.00
% 3.23/1.83  Total                : 0.76
% 3.23/1.83  Index Insertion      : 0.00
% 3.23/1.83  Index Deletion       : 0.00
% 3.23/1.84  Index Matching       : 0.00
% 3.23/1.84  BG Taut test         : 0.00
%------------------------------------------------------------------------------