TSTP Solution File: SEU361+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU361+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 : n020.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 10:58:32 EDT 2023

% Result   : Theorem 4.36s 1.99s
% Output   : CNFRefutation 4.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   67 (  16 unt;  28 typ;   0 def)
%            Number of atoms       :  108 (   9 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  113 (  44   ~;  39   |;  14   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  19   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   16 (  14 usr;   1 prp; 0-3 aty)
%            Number of functors    :   14 (  14 usr;   9 con; 0-3 aty)
%            Number of variables   :   32 (;  31   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ relstr_set_smaller > relstr_element_smaller > related > in > ex_sup_of_relstr_set > ex_inf_of_relstr_set > element > rel_str > one_sorted_str > lower_bounded_relstr > finite > empty_carrier > empty > antisymmetric_relstr > join_on_relstr > #nlpp > the_carrier > bottom_of_relstr > empty_set > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_2 > #skF_1 > #skF_9 > #skF_4 > #skF_3 > #skF_8

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_9',type,
    '#skF_9': $i ).

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

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

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

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

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

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

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

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

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

tff(f_155,negated_conjecture,
    ~ ! [A] :
        ( ( ~ empty_carrier(A)
          & antisymmetric_relstr(A)
          & lower_bounded_relstr(A)
          & rel_str(A) )
       => ! [B] :
            ( element(B,the_carrier(A))
           => related(A,bottom_of_relstr(A),B) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t44_yellow_0) ).

tff(f_75,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_159,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

tff(f_168,axiom,
    ! [A] :
      ( rel_str(A)
     => ! [B] :
          ( element(B,the_carrier(A))
         => ( relstr_set_smaller(A,empty_set,B)
            & relstr_element_smaller(A,empty_set,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).

tff(f_140,axiom,
    ! [A] :
      ( ( ~ empty_carrier(A)
        & antisymmetric_relstr(A)
        & lower_bounded_relstr(A)
        & rel_str(A) )
     => ( ex_sup_of_relstr_set(A,empty_set)
        & ex_inf_of_relstr_set(A,the_carrier(A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t42_yellow_0) ).

tff(f_39,axiom,
    ! [A] :
      ( rel_str(A)
     => ( bottom_of_relstr(A) = join_on_relstr(A,empty_set) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11_yellow_0) ).

tff(f_44,axiom,
    ! [A,B] :
      ( rel_str(A)
     => element(join_on_relstr(A,B),the_carrier(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_yellow_0) ).

tff(f_127,axiom,
    ! [A] :
      ( ( antisymmetric_relstr(A)
        & rel_str(A) )
     => ! [B] :
          ( element(B,the_carrier(A))
         => ! [C] :
              ( ( ( ( B = join_on_relstr(A,C) )
                  & ex_sup_of_relstr_set(A,C) )
               => ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( element(D,the_carrier(A))
                     => ( relstr_set_smaller(A,C,D)
                       => related(A,B,D) ) ) ) )
              & ( ( relstr_set_smaller(A,C,B)
                  & ! [D] :
                      ( element(D,the_carrier(A))
                     => ( relstr_set_smaller(A,C,D)
                       => related(A,B,D) ) ) )
               => ( ( B = join_on_relstr(A,C) )
                  & ex_sup_of_relstr_set(A,C) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_yellow_0) ).

tff(c_70,plain,
    element('#skF_10',the_carrier('#skF_9')),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_72,plain,
    rel_str('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_36,plain,
    empty('#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_98,plain,
    ! [A_49] :
      ( ( empty_set = A_49 )
      | ~ empty(A_49) ),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_105,plain,
    empty_set = '#skF_5',
    inference(resolution,[status(thm)],[c_36,c_98]) ).

tff(c_84,plain,
    ! [A_41,B_43] :
      ( relstr_set_smaller(A_41,empty_set,B_43)
      | ~ element(B_43,the_carrier(A_41))
      | ~ rel_str(A_41) ),
    inference(cnfTransformation,[status(thm)],[f_168]) ).

tff(c_179,plain,
    ! [A_70,B_71] :
      ( relstr_set_smaller(A_70,'#skF_5',B_71)
      | ~ element(B_71,the_carrier(A_70))
      | ~ rel_str(A_70) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_84]) ).

tff(c_198,plain,
    ( relstr_set_smaller('#skF_9','#skF_5','#skF_10')
    | ~ rel_str('#skF_9') ),
    inference(resolution,[status(thm)],[c_70,c_179]) ).

tff(c_210,plain,
    relstr_set_smaller('#skF_9','#skF_5','#skF_10'),
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_198]) ).

tff(c_78,plain,
    ~ empty_carrier('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_76,plain,
    antisymmetric_relstr('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_74,plain,
    lower_bounded_relstr('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_66,plain,
    ! [A_38] :
      ( ex_sup_of_relstr_set(A_38,empty_set)
      | ~ rel_str(A_38)
      | ~ lower_bounded_relstr(A_38)
      | ~ antisymmetric_relstr(A_38)
      | empty_carrier(A_38) ),
    inference(cnfTransformation,[status(thm)],[f_140]) ).

tff(c_257,plain,
    ! [A_38] :
      ( ex_sup_of_relstr_set(A_38,'#skF_5')
      | ~ rel_str(A_38)
      | ~ lower_bounded_relstr(A_38)
      | ~ antisymmetric_relstr(A_38)
      | empty_carrier(A_38) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_66]) ).

tff(c_6,plain,
    ! [A_4] :
      ( ( join_on_relstr(A_4,empty_set) = bottom_of_relstr(A_4) )
      | ~ rel_str(A_4) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_132,plain,
    ! [A_62] :
      ( ( join_on_relstr(A_62,'#skF_5') = bottom_of_relstr(A_62) )
      | ~ rel_str(A_62) ),
    inference(demodulation,[status(thm),theory(equality)],[c_105,c_6]) ).

tff(c_140,plain,
    join_on_relstr('#skF_9','#skF_5') = bottom_of_relstr('#skF_9'),
    inference(resolution,[status(thm)],[c_72,c_132]) ).

tff(c_150,plain,
    ! [A_64,B_65] :
      ( element(join_on_relstr(A_64,B_65),the_carrier(A_64))
      | ~ rel_str(A_64) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_156,plain,
    ( element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9'))
    | ~ rel_str('#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_140,c_150]) ).

tff(c_160,plain,
    element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_156]) ).

tff(c_363,plain,
    ! [A_124,C_125,D_126] :
      ( related(A_124,join_on_relstr(A_124,C_125),D_126)
      | ~ relstr_set_smaller(A_124,C_125,D_126)
      | ~ element(D_126,the_carrier(A_124))
      | ~ ex_sup_of_relstr_set(A_124,C_125)
      | ~ element(join_on_relstr(A_124,C_125),the_carrier(A_124))
      | ~ rel_str(A_124)
      | ~ antisymmetric_relstr(A_124) ),
    inference(cnfTransformation,[status(thm)],[f_127]) ).

tff(c_369,plain,
    ! [D_126] :
      ( related('#skF_9',join_on_relstr('#skF_9','#skF_5'),D_126)
      | ~ relstr_set_smaller('#skF_9','#skF_5',D_126)
      | ~ element(D_126,the_carrier('#skF_9'))
      | ~ ex_sup_of_relstr_set('#skF_9','#skF_5')
      | ~ element(bottom_of_relstr('#skF_9'),the_carrier('#skF_9'))
      | ~ rel_str('#skF_9')
      | ~ antisymmetric_relstr('#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_140,c_363]) ).

tff(c_374,plain,
    ! [D_126] :
      ( related('#skF_9',bottom_of_relstr('#skF_9'),D_126)
      | ~ relstr_set_smaller('#skF_9','#skF_5',D_126)
      | ~ element(D_126,the_carrier('#skF_9'))
      | ~ ex_sup_of_relstr_set('#skF_9','#skF_5') ),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_72,c_160,c_140,c_369]) ).

tff(c_375,plain,
    ~ ex_sup_of_relstr_set('#skF_9','#skF_5'),
    inference(splitLeft,[status(thm)],[c_374]) ).

tff(c_378,plain,
    ( ~ rel_str('#skF_9')
    | ~ lower_bounded_relstr('#skF_9')
    | ~ antisymmetric_relstr('#skF_9')
    | empty_carrier('#skF_9') ),
    inference(resolution,[status(thm)],[c_257,c_375]) ).

tff(c_381,plain,
    empty_carrier('#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_74,c_72,c_378]) ).

tff(c_383,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_78,c_381]) ).

tff(c_386,plain,
    ! [D_127] :
      ( related('#skF_9',bottom_of_relstr('#skF_9'),D_127)
      | ~ relstr_set_smaller('#skF_9','#skF_5',D_127)
      | ~ element(D_127,the_carrier('#skF_9')) ),
    inference(splitRight,[status(thm)],[c_374]) ).

tff(c_68,plain,
    ~ related('#skF_9',bottom_of_relstr('#skF_9'),'#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_397,plain,
    ( ~ relstr_set_smaller('#skF_9','#skF_5','#skF_10')
    | ~ element('#skF_10',the_carrier('#skF_9')) ),
    inference(resolution,[status(thm)],[c_386,c_68]) ).

tff(c_407,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_70,c_210,c_397]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15  % 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
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 11:55:22 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 4.36/1.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.36/1.99  
% 4.36/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.36/2.02  
% 4.36/2.02  Inference rules
% 4.36/2.02  ----------------------
% 4.36/2.02  #Ref     : 0
% 4.36/2.02  #Sup     : 62
% 4.36/2.02  #Fact    : 0
% 4.36/2.02  #Define  : 0
% 4.36/2.02  #Split   : 4
% 4.36/2.02  #Chain   : 0
% 4.36/2.02  #Close   : 0
% 4.36/2.02  
% 4.36/2.02  Ordering : KBO
% 4.36/2.02  
% 4.36/2.02  Simplification rules
% 4.36/2.02  ----------------------
% 4.36/2.02  #Subsume      : 4
% 4.36/2.02  #Demod        : 59
% 4.36/2.02  #Tautology    : 23
% 4.36/2.02  #SimpNegUnit  : 1
% 4.36/2.02  #BackRed      : 2
% 4.36/2.02  
% 4.36/2.02  #Partial instantiations: 0
% 4.36/2.02  #Strategies tried      : 1
% 4.36/2.02  
% 4.36/2.02  Timing (in seconds)
% 4.36/2.02  ----------------------
% 4.36/2.03  Preprocessing        : 0.57
% 4.36/2.03  Parsing              : 0.28
% 4.36/2.03  CNF conversion       : 0.04
% 4.36/2.03  Main loop            : 0.40
% 4.36/2.03  Inferencing          : 0.15
% 4.36/2.03  Reduction            : 0.11
% 4.36/2.03  Demodulation         : 0.08
% 4.36/2.03  BG Simplification    : 0.02
% 4.36/2.03  Subsumption          : 0.09
% 4.36/2.03  Abstraction          : 0.02
% 4.36/2.03  MUC search           : 0.00
% 4.36/2.03  Cooper               : 0.00
% 4.36/2.03  Total                : 1.02
% 4.36/2.03  Index Insertion      : 0.00
% 4.36/2.03  Index Deletion       : 0.00
% 4.36/2.03  Index Matching       : 0.00
% 4.36/2.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------