TSTP Solution File: SEU382+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU382+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 : n028.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 10:58:35 EDT 2023

% Result   : Theorem 10.36s 3.41s
% Output   : CNFRefutation 10.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   73
% Syntax   : Number of formulae    :   90 (  13 unt;  64 typ;   0 def)
%            Number of atoms       :   53 (  22 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   42 (  15   ~;  13   |;   9   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   62 (  49   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  32 usr;   1 prp; 0-3 aty)
%            Number of functors    :   32 (  32 usr;  15 con; 0-2 aty)
%            Number of variables   :   39 (;  39   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_partfun1 > relation_of2_as_subset > relation_of2 > subset > in > element > with_suprema_relstr > with_infima_relstr > v1_yellow_3 > upper_bounded_relstr > up_complete_relstr > transitive_relstr > transitive > strict_rel_str > relation > rel_str > reflexive_relstr > reflexive > one_sorted_str > lower_bounded_relstr > join_complete_relstr > heyting_relstr > finite > empty_carrier > empty > distributive_relstr > complete_relstr > complemented_relstr > bounded_relstr > boolean_relstr > antisymmetric_relstr > antisymmetric > rel_str_of > cartesian_product2 > #nlpp > the_carrier > the_InternalRel > powerset > inclusion_relation > inclusion_order > incl_POSet > boole_POSet > empty_set > #skF_9 > #skF_16 > #skF_4 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_19 > #skF_7 > #skF_3 > #skF_10 > #skF_14 > #skF_6 > #skF_2 > #skF_1 > #skF_21 > #skF_8 > #skF_13 > #skF_22 > #skF_5 > #skF_12 > #skF_20

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_17',type,
    '#skF_17': $i ).

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

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

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

tff(v1_partfun1,type,
    v1_partfun1: ( $i * $i * $i ) > $o ).

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

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

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

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

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

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

tff('#skF_19',type,
    '#skF_19': $i ).

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

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

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

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

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

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

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

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

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

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

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

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

tff(v1_yellow_3,type,
    v1_yellow_3: $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(transitive_relstr,type,
    transitive_relstr: $i > $o ).

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

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

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

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

tff(relation_of2,type,
    relation_of2: ( $i * $i * $i ) > $o ).

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

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

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

tff('#skF_22',type,
    '#skF_22': $i ).

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

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

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

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

tff(relation_of2_as_subset,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

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

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

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

tff('#skF_20',type,
    '#skF_20': $i > $i ).

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

tff(f_919,axiom,
    ! [A] : ( boole_POSet(A) = incl_POSet(powerset(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow_1) ).

tff(f_477,axiom,
    ! [A] :
      ( strict_rel_str(incl_POSet(A))
      & rel_str(incl_POSet(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).

tff(f_580,axiom,
    ! [A] :
      ( strict_rel_str(incl_POSet(A))
      & reflexive_relstr(incl_POSet(A))
      & transitive_relstr(incl_POSet(A))
      & antisymmetric_relstr(incl_POSet(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).

tff(f_32,axiom,
    ! [A] :
      ( rel_str(A)
     => ( strict_rel_str(A)
       => ( A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstractness_v1_orders_2) ).

tff(f_473,axiom,
    ! [A] :
      ( reflexive(inclusion_order(A))
      & antisymmetric(inclusion_order(A))
      & transitive(inclusion_order(A))
      & v1_partfun1(inclusion_order(A),A,A)
      & relation_of2_as_subset(inclusion_order(A),A,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).

tff(f_892,axiom,
    ! [A,B,C] :
      ( relation_of2_as_subset(C,A,B)
    <=> relation_of2(C,A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).

tff(f_454,axiom,
    ! [A] : ( incl_POSet(A) = rel_str_of(A,inclusion_order(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).

tff(f_668,axiom,
    ! [A,B] :
      ( relation_of2(B,A,A)
     => ! [C,D] :
          ( ( rel_str_of(A,B) = rel_str_of(C,D) )
         => ( ( A = C )
            & ( B = D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',free_g1_orders_2) ).

tff(f_917,negated_conjecture,
    ~ ! [A] : ( the_carrier(boole_POSet(A)) = powerset(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_waybel_7) ).

tff(c_592,plain,
    ! [A_94] : ( incl_POSet(powerset(A_94)) = boole_POSet(A_94) ),
    inference(cnfTransformation,[status(thm)],[f_919]) ).

tff(c_230,plain,
    ! [A_35] : rel_str(incl_POSet(A_35)),
    inference(cnfTransformation,[status(thm)],[f_477]) ).

tff(c_304,plain,
    ! [A_58] : strict_rel_str(incl_POSet(A_58)),
    inference(cnfTransformation,[status(thm)],[f_580]) ).

tff(c_2,plain,
    ! [A_1] :
      ( ( rel_str_of(the_carrier(A_1),the_InternalRel(A_1)) = A_1 )
      | ~ strict_rel_str(A_1)
      | ~ rel_str(A_1) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_224,plain,
    ! [A_34] : relation_of2_as_subset(inclusion_order(A_34),A_34,A_34),
    inference(cnfTransformation,[status(thm)],[f_473]) ).

tff(c_2937,plain,
    ! [C_350,A_351,B_352] :
      ( relation_of2(C_350,A_351,B_352)
      | ~ relation_of2_as_subset(C_350,A_351,B_352) ),
    inference(cnfTransformation,[status(thm)],[f_892]) ).

tff(c_2949,plain,
    ! [A_34] : relation_of2(inclusion_order(A_34),A_34,A_34),
    inference(resolution,[status(thm)],[c_224,c_2937]) ).

tff(c_206,plain,
    ! [A_30] : ( rel_str_of(A_30,inclusion_order(A_30)) = incl_POSet(A_30) ),
    inference(cnfTransformation,[status(thm)],[f_454]) ).

tff(c_4002,plain,
    ! [C_421,A_422,D_423,B_424] :
      ( ( C_421 = A_422 )
      | ( rel_str_of(C_421,D_423) != rel_str_of(A_422,B_424) )
      | ~ relation_of2(B_424,A_422,A_422) ),
    inference(cnfTransformation,[status(thm)],[f_668]) ).

tff(c_4010,plain,
    ! [C_421,A_30,D_423] :
      ( ( C_421 = A_30 )
      | ( rel_str_of(C_421,D_423) != incl_POSet(A_30) )
      | ~ relation_of2(inclusion_order(A_30),A_30,A_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_206,c_4002]) ).

tff(c_4013,plain,
    ! [C_425,A_426,D_427] :
      ( ( C_425 = A_426 )
      | ( rel_str_of(C_425,D_427) != incl_POSet(A_426) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2949,c_4010]) ).

tff(c_4016,plain,
    ! [A_1,A_426] :
      ( ( the_carrier(A_1) = A_426 )
      | ( incl_POSet(A_426) != A_1 )
      | ~ strict_rel_str(A_1)
      | ~ rel_str(A_1) ),
    inference(superposition,[status(thm),theory(equality)],[c_2,c_4013]) ).

tff(c_5117,plain,
    ! [A_426] :
      ( ( the_carrier(incl_POSet(A_426)) = A_426 )
      | ~ strict_rel_str(incl_POSet(A_426))
      | ~ rel_str(incl_POSet(A_426)) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_4016]) ).

tff(c_5123,plain,
    ! [A_501] : ( the_carrier(incl_POSet(A_501)) = A_501 ),
    inference(demodulation,[status(thm),theory(equality)],[c_230,c_304,c_5117]) ).

tff(c_5168,plain,
    ! [A_94] : ( the_carrier(boole_POSet(A_94)) = powerset(A_94) ),
    inference(superposition,[status(thm),theory(equality)],[c_592,c_5123]) ).

tff(c_590,plain,
    the_carrier(boole_POSet('#skF_22')) != powerset('#skF_22'),
    inference(cnfTransformation,[status(thm)],[f_917]) ).

tff(c_5206,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5168,c_590]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU382+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % 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
% 0.15/0.36  % Computer : n028.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 11:44:09 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 10.36/3.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.36/3.41  
% 10.36/3.41  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.36/3.44  
% 10.36/3.44  Inference rules
% 10.36/3.44  ----------------------
% 10.36/3.44  #Ref     : 4
% 10.36/3.44  #Sup     : 886
% 10.36/3.44  #Fact    : 0
% 10.36/3.44  #Define  : 0
% 10.36/3.44  #Split   : 62
% 10.36/3.44  #Chain   : 0
% 10.36/3.44  #Close   : 0
% 10.36/3.44  
% 10.36/3.44  Ordering : KBO
% 10.36/3.44  
% 10.36/3.44  Simplification rules
% 10.36/3.44  ----------------------
% 10.36/3.44  #Subsume      : 223
% 10.36/3.44  #Demod        : 720
% 10.36/3.44  #Tautology    : 358
% 10.36/3.44  #SimpNegUnit  : 322
% 10.36/3.44  #BackRed      : 17
% 10.36/3.44  
% 10.36/3.44  #Partial instantiations: 0
% 10.36/3.44  #Strategies tried      : 1
% 10.36/3.44  
% 10.36/3.44  Timing (in seconds)
% 10.36/3.44  ----------------------
% 10.36/3.45  Preprocessing        : 0.78
% 10.36/3.45  Parsing              : 0.39
% 10.36/3.45  CNF conversion       : 0.07
% 10.36/3.45  Main loop            : 1.60
% 10.36/3.45  Inferencing          : 0.55
% 10.36/3.45  Reduction            : 0.59
% 10.36/3.45  Demodulation         : 0.42
% 10.36/3.45  BG Simplification    : 0.07
% 10.36/3.45  Subsumption          : 0.27
% 10.36/3.45  Abstraction          : 0.05
% 10.36/3.45  MUC search           : 0.00
% 10.36/3.45  Cooper               : 0.00
% 10.36/3.45  Total                : 2.43
% 10.36/3.45  Index Insertion      : 0.00
% 10.36/3.45  Index Deletion       : 0.00
% 10.36/3.45  Index Matching       : 0.00
% 10.36/3.45  BG Taut test         : 0.00
%------------------------------------------------------------------------------