TSTP Solution File: SEU189+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU189+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/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 : n029.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 10:57:57 EDT 2023

% Result   : Theorem 3.93s 1.95s
% Output   : CNFRefutation 4.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   69 (  34 unt;  13 typ;   0 def)
%            Number of atoms       :   87 (  51 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   60 (  29   ~;  20   |;   4   &)
%                                         (   1 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   7   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-1 aty)
%            Number of variables   :   17 (;  15   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > relation > empty > #nlpp > relation_rng > relation_dom > empty_set > #skF_1 > #skF_5 > #skF_6 > #skF_2 > #skF_3 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

tff(f_88,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_112,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_49,axiom,
    ? [A] :
      ( empty(A)
      & relation(A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).

tff(f_122,axiom,
    ( ( relation_dom(empty_set) = empty_set )
    & ( relation_rng(empty_set) = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_relat_1) ).

tff(f_119,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( ( relation_dom(A) = empty_set )
        <=> ( relation_rng(A) = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t65_relat_1) ).

tff(f_130,axiom,
    ! [A] :
      ( relation(A)
     => ( ( ( relation_dom(A) = empty_set )
          | ( relation_rng(A) = empty_set ) )
       => ( A = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t64_relat_1) ).

tff(f_66,axiom,
    ! [A] :
      ( ( ~ empty(A)
        & relation(A) )
     => ~ empty(relation_dom(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_relat_1) ).

tff(f_86,axiom,
    ! [A] :
      ( empty(A)
     => ( empty(relation_rng(A))
        & relation(relation_rng(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_relat_1) ).

tff(c_34,plain,
    empty('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_407,plain,
    ! [A_45] :
      ( ( empty_set = A_45 )
      | ~ empty(A_45) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_418,plain,
    empty_set = '#skF_4',
    inference(resolution,[status(thm)],[c_34,c_407]) ).

tff(c_14,plain,
    empty('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_417,plain,
    empty_set = '#skF_2',
    inference(resolution,[status(thm)],[c_14,c_407]) ).

tff(c_434,plain,
    '#skF_2' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_418,c_417]) ).

tff(c_83,plain,
    ! [A_20] :
      ( ( empty_set = A_20 )
      | ~ empty(A_20) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_94,plain,
    empty_set = '#skF_4',
    inference(resolution,[status(thm)],[c_34,c_83]) ).

tff(c_93,plain,
    empty_set = '#skF_2',
    inference(resolution,[status(thm)],[c_14,c_83]) ).

tff(c_110,plain,
    '#skF_2' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_93]) ).

tff(c_68,plain,
    relation_dom(empty_set) = empty_set,
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_99,plain,
    relation_dom('#skF_2') = '#skF_2',
    inference(demodulation,[status(thm),theory(equality)],[c_93,c_93,c_68]) ).

tff(c_129,plain,
    relation_dom('#skF_4') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_110,c_99]) ).

tff(c_64,plain,
    ( ( relation_dom('#skF_6') = empty_set )
    | ( relation_rng('#skF_6') = empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_122,plain,
    ( ( relation_dom('#skF_6') = '#skF_4' )
    | ( relation_rng('#skF_6') = '#skF_4' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_94,c_64]) ).

tff(c_123,plain,
    relation_rng('#skF_6') = '#skF_4',
    inference(splitLeft,[status(thm)],[c_122]) ).

tff(c_56,plain,
    relation('#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_70,plain,
    ! [A_19] :
      ( ( relation_rng(A_19) != empty_set )
      | ( empty_set = A_19 )
      | ~ relation(A_19) ),
    inference(cnfTransformation,[status(thm)],[f_130]) ).

tff(c_327,plain,
    ! [A_41] :
      ( ( relation_rng(A_41) != '#skF_4' )
      | ( A_41 = '#skF_4' )
      | ~ relation(A_41) ),
    inference(demodulation,[status(thm),theory(equality)],[c_94,c_94,c_70]) ).

tff(c_345,plain,
    ( ( relation_rng('#skF_6') != '#skF_4' )
    | ( '#skF_6' = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_56,c_327]) ).

tff(c_356,plain,
    '#skF_6' = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_123,c_345]) ).

tff(c_58,plain,
    ( ( relation_rng('#skF_6') != empty_set )
    | ( relation_dom('#skF_6') != empty_set ) ),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_74,plain,
    relation_dom('#skF_6') != empty_set,
    inference(splitLeft,[status(thm)],[c_58]) ).

tff(c_98,plain,
    relation_dom('#skF_6') != '#skF_2',
    inference(demodulation,[status(thm),theory(equality)],[c_93,c_74]) ).

tff(c_138,plain,
    relation_dom('#skF_6') != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_98]) ).

tff(c_357,plain,
    relation_dom('#skF_4') != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_356,c_138]) ).

tff(c_362,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_129,c_357]) ).

tff(c_363,plain,
    relation_dom('#skF_6') = '#skF_4',
    inference(splitRight,[status(thm)],[c_122]) ).

tff(c_381,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_363,c_110,c_98]) ).

tff(c_382,plain,
    relation_rng('#skF_6') != empty_set,
    inference(splitRight,[status(thm)],[c_58]) ).

tff(c_392,plain,
    relation_rng('#skF_6') = empty_set,
    inference(splitLeft,[status(thm)],[c_64]) ).

tff(c_397,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_382,c_392]) ).

tff(c_399,plain,
    relation_rng('#skF_6') != empty_set,
    inference(splitRight,[status(thm)],[c_64]) ).

tff(c_422,plain,
    relation_rng('#skF_6') != '#skF_2',
    inference(demodulation,[status(thm),theory(equality)],[c_417,c_399]) ).

tff(c_462,plain,
    relation_rng('#skF_6') != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_422]) ).

tff(c_383,plain,
    relation_dom('#skF_6') = empty_set,
    inference(splitRight,[status(thm)],[c_58]) ).

tff(c_423,plain,
    relation_dom('#skF_6') = '#skF_2',
    inference(demodulation,[status(thm),theory(equality)],[c_417,c_383]) ).

tff(c_446,plain,
    relation_dom('#skF_6') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_423]) ).

tff(c_550,plain,
    ! [A_61] :
      ( ~ empty(relation_dom(A_61))
      | ~ relation(A_61)
      | empty(A_61) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_559,plain,
    ( ~ empty('#skF_4')
    | ~ relation('#skF_6')
    | empty('#skF_6') ),
    inference(superposition,[status(thm),theory(equality)],[c_446,c_550]) ).

tff(c_564,plain,
    empty('#skF_6'),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_34,c_559]) ).

tff(c_500,plain,
    ! [A_52] :
      ( empty(relation_rng(A_52))
      | ~ empty(A_52) ),
    inference(cnfTransformation,[status(thm)],[f_86]) ).

tff(c_54,plain,
    ! [A_18] :
      ( ( empty_set = A_18 )
      | ~ empty(A_18) ),
    inference(cnfTransformation,[status(thm)],[f_112]) ).

tff(c_421,plain,
    ! [A_18] :
      ( ( A_18 = '#skF_2' )
      | ~ empty(A_18) ),
    inference(demodulation,[status(thm),theory(equality)],[c_417,c_54]) ).

tff(c_473,plain,
    ! [A_18] :
      ( ( A_18 = '#skF_4' )
      | ~ empty(A_18) ),
    inference(demodulation,[status(thm),theory(equality)],[c_434,c_421]) ).

tff(c_507,plain,
    ! [A_52] :
      ( ( relation_rng(A_52) = '#skF_4' )
      | ~ empty(A_52) ),
    inference(resolution,[status(thm)],[c_500,c_473]) ).

tff(c_569,plain,
    relation_rng('#skF_6') = '#skF_4',
    inference(resolution,[status(thm)],[c_564,c_507]) ).

tff(c_580,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_462,c_569]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU189+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/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
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 12:26:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 3.93/1.95  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.93/1.96  
% 3.93/1.96  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.17/1.99  
% 4.17/1.99  Inference rules
% 4.17/1.99  ----------------------
% 4.17/1.99  #Ref     : 0
% 4.17/1.99  #Sup     : 120
% 4.17/1.99  #Fact    : 0
% 4.17/1.99  #Define  : 0
% 4.17/1.99  #Split   : 3
% 4.17/1.99  #Chain   : 0
% 4.17/1.99  #Close   : 0
% 4.17/1.99  
% 4.17/1.99  Ordering : KBO
% 4.17/1.99  
% 4.17/1.99  Simplification rules
% 4.17/1.99  ----------------------
% 4.17/1.99  #Subsume      : 6
% 4.17/1.99  #Demod        : 109
% 4.17/1.99  #Tautology    : 102
% 4.17/1.99  #SimpNegUnit  : 2
% 4.17/1.99  #BackRed      : 22
% 4.17/1.99  
% 4.17/1.99  #Partial instantiations: 0
% 4.17/1.99  #Strategies tried      : 1
% 4.17/1.99  
% 4.17/1.99  Timing (in seconds)
% 4.17/1.99  ----------------------
% 4.17/1.99  Preprocessing        : 0.50
% 4.17/1.99  Parsing              : 0.28
% 4.17/1.99  CNF conversion       : 0.04
% 4.17/1.99  Main loop            : 0.43
% 4.17/1.99  Inferencing          : 0.17
% 4.17/1.99  Reduction            : 0.11
% 4.17/1.99  Demodulation         : 0.08
% 4.17/1.99  BG Simplification    : 0.02
% 4.17/1.99  Subsumption          : 0.08
% 4.17/1.99  Abstraction          : 0.01
% 4.17/1.99  MUC search           : 0.00
% 4.17/1.99  Cooper               : 0.00
% 4.17/1.99  Total                : 0.99
% 4.17/1.99  Index Insertion      : 0.00
% 4.17/1.99  Index Deletion       : 0.00
% 4.17/1.99  Index Matching       : 0.00
% 4.17/1.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------