TSTP Solution File: SEU003+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU003+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 : n027.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 10:57:29 EDT 2023

% Result   : Theorem 49.62s 35.99s
% Output   : CNFRefutation 49.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   34
% Syntax   : Number of formulae    :   56 (  10 unt;  29 typ;   0 def)
%            Number of atoms       :   88 (   5 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  104 (  43   ~;  43   |;   7   &)
%                                         (   4 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  20   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;   9 con; 0-3 aty)
%            Number of variables   :   40 (;  39   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > relation_composition > apply > #nlpp > relation_rng > relation_dom > powerset > empty_set > #skF_9 > #skF_11 > #skF_15 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_13 > #skF_5 > #skF_8 > #skF_2 > #skF_12 > #skF_1 > #skF_6 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i ).

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

tff('#skF_15',type,
    '#skF_15': $i ).

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': $i ).

tff('#skF_16',type,
    '#skF_16': $i ).

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

tff('#skF_14',type,
    '#skF_14': $i ).

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

tff('#skF_13',type,
    '#skF_13': $i ).

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

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

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

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

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

tff('#skF_8',type,
    '#skF_8': $i ).

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

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

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

tff('#skF_12',type,
    '#skF_12': $i > $i ).

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

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

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

tff(f_209,negated_conjecture,
    ~ ! [A] :
        ( ( relation(A)
          & function(A) )
       => ! [B] :
            ( ( relation(B)
              & function(B) )
           => ( ( relation_dom(relation_composition(B,A)) = relation_dom(B) )
             => subset(relation_rng(B),relation_dom(A)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).

tff(f_46,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_176,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_61,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B] :
          ( ( B = relation_rng(A) )
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] :
                  ( in(D,relation_dom(A))
                  & ( C = apply(A,D) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).

tff(f_195,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_dom(relation_composition(C,B)))
          <=> ( in(A,relation_dom(C))
              & in(apply(C,A),relation_dom(B)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

tff(c_112,plain,
    ~ subset(relation_rng('#skF_16'),relation_dom('#skF_15')),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_12,plain,
    ! [A_5,B_6] :
      ( in('#skF_1'(A_5,B_6),A_5)
      | subset(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_118,plain,
    relation('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_116,plain,
    function('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_102,plain,
    ! [A_69] : subset(A_69,A_69),
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_1933,plain,
    ! [A_227,C_228] :
      ( in('#skF_5'(A_227,relation_rng(A_227),C_228),relation_dom(A_227))
      | ~ in(C_228,relation_rng(A_227))
      | ~ function(A_227)
      | ~ relation(A_227) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_8,plain,
    ! [C_9,B_6,A_5] :
      ( in(C_9,B_6)
      | ~ in(C_9,A_5)
      | ~ subset(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_1971,plain,
    ! [A_227,C_228,B_6] :
      ( in('#skF_5'(A_227,relation_rng(A_227),C_228),B_6)
      | ~ subset(relation_dom(A_227),B_6)
      | ~ in(C_228,relation_rng(A_227))
      | ~ function(A_227)
      | ~ relation(A_227) ),
    inference(resolution,[status(thm)],[c_1933,c_8]) ).

tff(c_122,plain,
    relation('#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_120,plain,
    function('#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_114,plain,
    relation_dom(relation_composition('#skF_16','#skF_15')) = relation_dom('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_209]) ).

tff(c_16,plain,
    ! [A_10,C_46] :
      ( ( apply(A_10,'#skF_5'(A_10,relation_rng(A_10),C_46)) = C_46 )
      | ~ in(C_46,relation_rng(A_10))
      | ~ function(A_10)
      | ~ relation(A_10) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_4698,plain,
    ! [C_296,A_297,B_298] :
      ( in(apply(C_296,A_297),relation_dom(B_298))
      | ~ in(A_297,relation_dom(relation_composition(C_296,B_298)))
      | ~ function(C_296)
      | ~ relation(C_296)
      | ~ function(B_298)
      | ~ relation(B_298) ),
    inference(cnfTransformation,[status(thm)],[f_195]) ).

tff(c_44041,plain,
    ! [C_848,B_849,A_850] :
      ( in(C_848,relation_dom(B_849))
      | ~ in('#skF_5'(A_850,relation_rng(A_850),C_848),relation_dom(relation_composition(A_850,B_849)))
      | ~ function(A_850)
      | ~ relation(A_850)
      | ~ function(B_849)
      | ~ relation(B_849)
      | ~ in(C_848,relation_rng(A_850))
      | ~ function(A_850)
      | ~ relation(A_850) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_4698]) ).

tff(c_44395,plain,
    ! [C_848] :
      ( in(C_848,relation_dom('#skF_15'))
      | ~ in('#skF_5'('#skF_16',relation_rng('#skF_16'),C_848),relation_dom('#skF_16'))
      | ~ function('#skF_16')
      | ~ relation('#skF_16')
      | ~ function('#skF_15')
      | ~ relation('#skF_15')
      | ~ in(C_848,relation_rng('#skF_16'))
      | ~ function('#skF_16')
      | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_114,c_44041]) ).

tff(c_235746,plain,
    ! [C_1504] :
      ( in(C_1504,relation_dom('#skF_15'))
      | ~ in('#skF_5'('#skF_16',relation_rng('#skF_16'),C_1504),relation_dom('#skF_16'))
      | ~ in(C_1504,relation_rng('#skF_16')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_118,c_116,c_122,c_120,c_118,c_116,c_44395]) ).

tff(c_235753,plain,
    ! [C_228] :
      ( in(C_228,relation_dom('#skF_15'))
      | ~ subset(relation_dom('#skF_16'),relation_dom('#skF_16'))
      | ~ in(C_228,relation_rng('#skF_16'))
      | ~ function('#skF_16')
      | ~ relation('#skF_16') ),
    inference(resolution,[status(thm)],[c_1971,c_235746]) ).

tff(c_235771,plain,
    ! [C_1505] :
      ( in(C_1505,relation_dom('#skF_15'))
      | ~ in(C_1505,relation_rng('#skF_16')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_118,c_116,c_102,c_235753]) ).

tff(c_247052,plain,
    ! [B_1564] :
      ( in('#skF_1'(relation_rng('#skF_16'),B_1564),relation_dom('#skF_15'))
      | subset(relation_rng('#skF_16'),B_1564) ),
    inference(resolution,[status(thm)],[c_12,c_235771]) ).

tff(c_10,plain,
    ! [A_5,B_6] :
      ( ~ in('#skF_1'(A_5,B_6),B_6)
      | subset(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_247070,plain,
    subset(relation_rng('#skF_16'),relation_dom('#skF_15')),
    inference(resolution,[status(thm)],[c_247052,c_10]) ).

tff(c_247090,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_112,c_112,c_247070]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU003+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.34  % Computer : n027.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 11:52:08 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 49.62/35.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.62/36.00  
% 49.62/36.00  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 49.62/36.02  
% 49.62/36.02  Inference rules
% 49.62/36.02  ----------------------
% 49.62/36.02  #Ref     : 2
% 49.62/36.02  #Sup     : 65687
% 49.62/36.02  #Fact    : 0
% 49.62/36.02  #Define  : 0
% 49.62/36.02  #Split   : 37
% 49.62/36.02  #Chain   : 0
% 49.62/36.02  #Close   : 0
% 49.62/36.02  
% 49.62/36.02  Ordering : KBO
% 49.62/36.02  
% 49.62/36.02  Simplification rules
% 49.62/36.02  ----------------------
% 49.62/36.02  #Subsume      : 18077
% 49.62/36.02  #Demod        : 53977
% 49.62/36.02  #Tautology    : 16264
% 49.62/36.02  #SimpNegUnit  : 1675
% 49.62/36.02  #BackRed      : 53
% 49.62/36.02  
% 49.62/36.02  #Partial instantiations: 0
% 49.62/36.02  #Strategies tried      : 1
% 49.62/36.02  
% 49.62/36.02  Timing (in seconds)
% 49.62/36.02  ----------------------
% 49.62/36.03  Preprocessing        : 0.66
% 49.62/36.03  Parsing              : 0.29
% 49.62/36.03  CNF conversion       : 0.08
% 49.62/36.03  Main loop            : 34.26
% 49.62/36.03  Inferencing          : 3.72
% 49.62/36.03  Reduction            : 9.42
% 49.62/36.03  Demodulation         : 6.90
% 49.62/36.03  BG Simplification    : 0.33
% 49.62/36.03  Subsumption          : 18.95
% 49.62/36.03  Abstraction          : 0.50
% 49.62/36.03  MUC search           : 0.00
% 49.62/36.03  Cooper               : 0.00
% 49.62/36.03  Total                : 34.97
% 49.62/36.03  Index Insertion      : 0.00
% 49.62/36.03  Index Deletion       : 0.00
% 49.62/36.03  Index Matching       : 0.00
% 49.62/36.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------