TSTP Solution File: SEU186+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU186+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : n004.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 10:57:56 EDT 2023

% Result   : Theorem 3.87s 1.93s
% Output   : CNFRefutation 4.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   48 (  16 unt;  17 typ;   0 def)
%            Number of atoms       :   56 (  12 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   50 (  25   ~;  19   |;   1   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  11   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :   34 (;  32   !;   2   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

tff(singleton,type,
    singleton: $i > $i ).

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

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

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

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

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

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

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

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

tff('#skF_6',type,
    '#skF_6': $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_2',type,
    '#skF_2': ( $i * $i ) > $i ).

tff(f_72,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_103,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_99,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( ! [B,C] : ~ in(ordered_pair(B,C),A)
         => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).

tff(f_53,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

tff(f_90,axiom,
    ! [A,B] :
      ( element(A,B)
     => ( empty(B)
        | in(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

tff(f_47,axiom,
    ! [A] :
      ( relation(A)
    <=> ! [B] :
          ~ ( in(B,A)
            & ! [C,D] : ( B != ordered_pair(C,D) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).

tff(c_44,plain,
    empty('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_70,plain,
    ! [A_49] :
      ( ( empty_set = A_49 )
      | ~ empty(A_49) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_80,plain,
    empty_set = '#skF_6',
    inference(resolution,[status(thm)],[c_44,c_70]) ).

tff(c_56,plain,
    empty_set != '#skF_9',
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_86,plain,
    '#skF_6' != '#skF_9',
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_56]) ).

tff(c_60,plain,
    relation('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_26,plain,
    ! [A_26] : element('#skF_4'(A_26),A_26),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_54,plain,
    ! [A_35,B_36] :
      ( in(A_35,B_36)
      | empty(B_36)
      | ~ element(A_35,B_36) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_268,plain,
    ! [A_83,B_84] :
      ( ( ordered_pair('#skF_2'(A_83,B_84),'#skF_3'(A_83,B_84)) = B_84 )
      | ~ in(B_84,A_83)
      | ~ relation(A_83) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_171,plain,
    ! [A_73,B_74] :
      ( in(A_73,B_74)
      | empty(B_74)
      | ~ element(A_73,B_74) ),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_58,plain,
    ! [B_39,C_40] : ~ in(ordered_pair(B_39,C_40),'#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_99]) ).

tff(c_191,plain,
    ! [B_39,C_40] :
      ( empty('#skF_9')
      | ~ element(ordered_pair(B_39,C_40),'#skF_9') ),
    inference(resolution,[status(thm)],[c_171,c_58]) ).

tff(c_192,plain,
    ! [B_39,C_40] : ~ element(ordered_pair(B_39,C_40),'#skF_9'),
    inference(splitLeft,[status(thm)],[c_191]) ).

tff(c_303,plain,
    ! [B_89,A_90] :
      ( ~ element(B_89,'#skF_9')
      | ~ in(B_89,A_90)
      | ~ relation(A_90) ),
    inference(superposition,[status(thm),theory(equality)],[c_268,c_192]) ).

tff(c_457,plain,
    ! [A_104,B_105] :
      ( ~ element(A_104,'#skF_9')
      | ~ relation(B_105)
      | empty(B_105)
      | ~ element(A_104,B_105) ),
    inference(resolution,[status(thm)],[c_54,c_303]) ).

tff(c_467,plain,
    ! [B_106] :
      ( ~ relation(B_106)
      | empty(B_106)
      | ~ element('#skF_4'('#skF_9'),B_106) ),
    inference(resolution,[status(thm)],[c_26,c_457]) ).

tff(c_471,plain,
    ( ~ relation('#skF_9')
    | empty('#skF_9') ),
    inference(resolution,[status(thm)],[c_26,c_467]) ).

tff(c_474,plain,
    empty('#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_471]) ).

tff(c_62,plain,
    ! [A_41] :
      ( ( empty_set = A_41 )
      | ~ empty(A_41) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_84,plain,
    ! [A_41] :
      ( ( A_41 = '#skF_6' )
      | ~ empty(A_41) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_62]) ).

tff(c_479,plain,
    '#skF_6' = '#skF_9',
    inference(resolution,[status(thm)],[c_474,c_84]) ).

tff(c_484,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_86,c_479]) ).

tff(c_485,plain,
    empty('#skF_9'),
    inference(splitRight,[status(thm)],[c_191]) ).

tff(c_490,plain,
    '#skF_6' = '#skF_9',
    inference(resolution,[status(thm)],[c_485,c_84]) ).

tff(c_495,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_86,c_490]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU186+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % 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
% 0.14/0.34  % Computer : n004.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 11:43:26 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 3.87/1.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.87/1.93  
% 3.87/1.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.17/1.96  
% 4.17/1.96  Inference rules
% 4.17/1.96  ----------------------
% 4.17/1.96  #Ref     : 1
% 4.17/1.96  #Sup     : 104
% 4.17/1.96  #Fact    : 0
% 4.17/1.96  #Define  : 0
% 4.17/1.96  #Split   : 1
% 4.17/1.96  #Chain   : 0
% 4.17/1.96  #Close   : 0
% 4.17/1.96  
% 4.17/1.96  Ordering : KBO
% 4.17/1.96  
% 4.17/1.96  Simplification rules
% 4.17/1.96  ----------------------
% 4.17/1.96  #Subsume      : 10
% 4.17/1.96  #Demod        : 26
% 4.17/1.96  #Tautology    : 57
% 4.17/1.96  #SimpNegUnit  : 2
% 4.17/1.96  #BackRed      : 6
% 4.17/1.96  
% 4.17/1.96  #Partial instantiations: 0
% 4.17/1.96  #Strategies tried      : 1
% 4.17/1.96  
% 4.17/1.96  Timing (in seconds)
% 4.17/1.96  ----------------------
% 4.17/1.97  Preprocessing        : 0.52
% 4.17/1.97  Parsing              : 0.28
% 4.17/1.97  CNF conversion       : 0.04
% 4.17/1.97  Main loop            : 0.40
% 4.17/1.97  Inferencing          : 0.16
% 4.17/1.97  Reduction            : 0.11
% 4.17/1.97  Demodulation         : 0.08
% 4.17/1.97  BG Simplification    : 0.02
% 4.17/1.97  Subsumption          : 0.08
% 4.17/1.97  Abstraction          : 0.02
% 4.17/1.97  MUC search           : 0.00
% 4.17/1.97  Cooper               : 0.00
% 4.17/1.97  Total                : 0.97
% 4.17/1.97  Index Insertion      : 0.00
% 4.17/1.97  Index Deletion       : 0.00
% 4.17/1.97  Index Matching       : 0.00
% 4.17/1.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------