TSTP Solution File: SEU368+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU368+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 : n016.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 10:58:33 EDT 2023

% Result   : Theorem 6.78s 2.55s
% Output   : CNFRefutation 6.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   50
% Syntax   : Number of formulae    :   83 (  14 unt;  42 typ;   0 def)
%            Number of atoms       :   90 (  45 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   88 (  39   ~;  34   |;  10   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  32   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-3 aty)
%            Number of functors    :   24 (  24 usr;  10 con; 0-2 aty)
%            Number of variables   :   69 (;  69   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ v1_partfun1 > relation_of2_as_subset > relation_of2 > subset > in > element > transitive_relstr > transitive > strict_rel_str > relation > rel_str > reflexive_relstr > reflexive > one_sorted_str > empty_carrier > empty > antisymmetric_relstr > antisymmetric > rel_str_of > cartesian_product2 > #nlpp > the_carrier > the_InternalRel > powerset > inclusion_relation > inclusion_order > incl_POSet > empty_set > #skF_9 > #skF_5 > #skF_2 > #skF_4 > #skF_11 > #skF_15 > #skF_7 > #skF_10 > #skF_12 > #skF_14 > #skF_6 > #skF_13 > #skF_3 > #skF_1 > #skF_8

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(relation_of2,type,
    relation_of2: ( $i * $i * $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(relation_of2_as_subset,type,
    relation_of2_as_subset: ( $i * $i * $i ) > $o ).

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

tff(f_279,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_291,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_214,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_275,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_225,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_293,axiom,
    ! [A] : ( incl_POSet(A) = rel_str_of(A,inclusion_order(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).

tff(f_208,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_298,negated_conjecture,
    ~ ! [A] :
        ( ( the_carrier(incl_POSet(A)) = A )
        & ( the_InternalRel(incl_POSet(A)) = inclusion_order(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_yellow_1) ).

tff(c_158,plain,
    ! [A_68] : rel_str(incl_POSet(A_68)),
    inference(cnfTransformation,[status(thm)],[f_279]) ).

tff(c_164,plain,
    ! [A_70] : strict_rel_str(incl_POSet(A_70)),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_106,plain,
    ! [A_51] :
      ( ( rel_str_of(the_carrier(A_51),the_InternalRel(A_51)) = A_51 )
      | ~ strict_rel_str(A_51)
      | ~ rel_str(A_51) ),
    inference(cnfTransformation,[status(thm)],[f_214]) ).

tff(c_154,plain,
    ! [A_67] : relation_of2_as_subset(inclusion_order(A_67),A_67,A_67),
    inference(cnfTransformation,[status(thm)],[f_275]) ).

tff(c_1540,plain,
    ! [C_349,A_350,B_351] :
      ( relation_of2(C_349,A_350,B_351)
      | ~ relation_of2_as_subset(C_349,A_350,B_351) ),
    inference(cnfTransformation,[status(thm)],[f_225]) ).

tff(c_1552,plain,
    ! [A_67] : relation_of2(inclusion_order(A_67),A_67,A_67),
    inference(resolution,[status(thm)],[c_154,c_1540]) ).

tff(c_172,plain,
    ! [A_71] : ( rel_str_of(A_71,inclusion_order(A_71)) = incl_POSet(A_71) ),
    inference(cnfTransformation,[status(thm)],[f_293]) ).

tff(c_2061,plain,
    ! [C_454,A_455,D_456,B_457] :
      ( ( C_454 = A_455 )
      | ( rel_str_of(C_454,D_456) != rel_str_of(A_455,B_457) )
      | ~ relation_of2(B_457,A_455,A_455) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_2073,plain,
    ! [C_454,A_71,D_456] :
      ( ( C_454 = A_71 )
      | ( rel_str_of(C_454,D_456) != incl_POSet(A_71) )
      | ~ relation_of2(inclusion_order(A_71),A_71,A_71) ),
    inference(superposition,[status(thm),theory(equality)],[c_172,c_2061]) ).

tff(c_2078,plain,
    ! [C_458,A_459,D_460] :
      ( ( C_458 = A_459 )
      | ( rel_str_of(C_458,D_460) != incl_POSet(A_459) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1552,c_2073]) ).

tff(c_2084,plain,
    ! [A_51,A_459] :
      ( ( the_carrier(A_51) = A_459 )
      | ( incl_POSet(A_459) != A_51 )
      | ~ strict_rel_str(A_51)
      | ~ rel_str(A_51) ),
    inference(superposition,[status(thm),theory(equality)],[c_106,c_2078]) ).

tff(c_2419,plain,
    ! [A_459] :
      ( ( the_carrier(incl_POSet(A_459)) = A_459 )
      | ~ strict_rel_str(incl_POSet(A_459))
      | ~ rel_str(incl_POSet(A_459)) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_2084]) ).

tff(c_2421,plain,
    ! [A_459] : ( the_carrier(incl_POSet(A_459)) = A_459 ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_164,c_2419]) ).

tff(c_360,plain,
    ! [C_136,A_137,B_138] :
      ( relation_of2(C_136,A_137,B_138)
      | ~ relation_of2_as_subset(C_136,A_137,B_138) ),
    inference(cnfTransformation,[status(thm)],[f_225]) ).

tff(c_372,plain,
    ! [A_67] : relation_of2(inclusion_order(A_67),A_67,A_67),
    inference(resolution,[status(thm)],[c_154,c_360]) ).

tff(c_871,plain,
    ! [C_243,A_244,D_245,B_246] :
      ( ( C_243 = A_244 )
      | ( rel_str_of(C_243,D_245) != rel_str_of(A_244,B_246) )
      | ~ relation_of2(B_246,A_244,A_244) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_879,plain,
    ! [C_243,A_71,D_245] :
      ( ( C_243 = A_71 )
      | ( rel_str_of(C_243,D_245) != incl_POSet(A_71) )
      | ~ relation_of2(inclusion_order(A_71),A_71,A_71) ),
    inference(superposition,[status(thm),theory(equality)],[c_172,c_871]) ).

tff(c_882,plain,
    ! [C_247,A_248,D_249] :
      ( ( C_247 = A_248 )
      | ( rel_str_of(C_247,D_249) != incl_POSet(A_248) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_372,c_879]) ).

tff(c_885,plain,
    ! [A_51,A_248] :
      ( ( the_carrier(A_51) = A_248 )
      | ( incl_POSet(A_248) != A_51 )
      | ~ strict_rel_str(A_51)
      | ~ rel_str(A_51) ),
    inference(superposition,[status(thm),theory(equality)],[c_106,c_882]) ).

tff(c_993,plain,
    ! [A_248] :
      ( ( the_carrier(incl_POSet(A_248)) = A_248 )
      | ~ strict_rel_str(incl_POSet(A_248))
      | ~ rel_str(incl_POSet(A_248)) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_885]) ).

tff(c_997,plain,
    ! [A_269] : ( the_carrier(incl_POSet(A_269)) = A_269 ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_164,c_993]) ).

tff(c_1030,plain,
    ! [A_269] :
      ( ( rel_str_of(A_269,the_InternalRel(incl_POSet(A_269))) = incl_POSet(A_269) )
      | ~ strict_rel_str(incl_POSet(A_269))
      | ~ rel_str(incl_POSet(A_269)) ),
    inference(superposition,[status(thm),theory(equality)],[c_997,c_106]) ).

tff(c_1156,plain,
    ! [A_282] : ( rel_str_of(A_282,the_InternalRel(incl_POSet(A_282))) = incl_POSet(A_282) ),
    inference(demodulation,[status(thm),theory(equality)],[c_158,c_164,c_1030]) ).

tff(c_771,plain,
    ! [D_232,B_233,C_234,A_235] :
      ( ( D_232 = B_233 )
      | ( rel_str_of(C_234,D_232) != rel_str_of(A_235,B_233) )
      | ~ relation_of2(B_233,A_235,A_235) ),
    inference(cnfTransformation,[status(thm)],[f_208]) ).

tff(c_779,plain,
    ! [A_71,D_232,C_234] :
      ( ( inclusion_order(A_71) = D_232 )
      | ( rel_str_of(C_234,D_232) != incl_POSet(A_71) )
      | ~ relation_of2(inclusion_order(A_71),A_71,A_71) ),
    inference(superposition,[status(thm),theory(equality)],[c_172,c_771]) ).

tff(c_781,plain,
    ! [A_71,D_232,C_234] :
      ( ( inclusion_order(A_71) = D_232 )
      | ( rel_str_of(C_234,D_232) != incl_POSet(A_71) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_372,c_779]) ).

tff(c_1223,plain,
    ! [A_289,A_290] :
      ( ( the_InternalRel(incl_POSet(A_289)) = inclusion_order(A_290) )
      | ( incl_POSet(A_290) != incl_POSet(A_289) ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1156,c_781]) ).

tff(c_174,plain,
    ( ( the_carrier(incl_POSet('#skF_15')) != '#skF_15' )
    | ( the_InternalRel(incl_POSet('#skF_14')) != inclusion_order('#skF_14') ) ),
    inference(cnfTransformation,[status(thm)],[f_298]) ).

tff(c_181,plain,
    the_InternalRel(incl_POSet('#skF_14')) != inclusion_order('#skF_14'),
    inference(splitLeft,[status(thm)],[c_174]) ).

tff(c_1321,plain,
    ! [A_290] :
      ( ( inclusion_order(A_290) != inclusion_order('#skF_14') )
      | ( incl_POSet(A_290) != incl_POSet('#skF_14') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1223,c_181]) ).

tff(c_1373,plain,
    $false,
    inference(reflexivity,[status(thm),theory(equality)],[c_1321]) ).

tff(c_1374,plain,
    the_carrier(incl_POSet('#skF_15')) != '#skF_15',
    inference(splitRight,[status(thm)],[c_174]) ).

tff(c_2426,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2421,c_1374]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU368+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
% 0.16/0.35  % Computer : n016.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Thu Aug  3 12:23:22 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 6.78/2.55  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.78/2.56  
% 6.78/2.56  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.96/2.59  
% 6.96/2.59  Inference rules
% 6.96/2.59  ----------------------
% 6.96/2.59  #Ref     : 11
% 6.96/2.59  #Sup     : 504
% 6.96/2.59  #Fact    : 0
% 6.96/2.59  #Define  : 0
% 6.96/2.59  #Split   : 4
% 6.96/2.59  #Chain   : 0
% 6.96/2.59  #Close   : 0
% 6.96/2.59  
% 6.96/2.59  Ordering : KBO
% 6.96/2.59  
% 6.96/2.59  Simplification rules
% 6.96/2.59  ----------------------
% 6.96/2.59  #Subsume      : 64
% 6.96/2.59  #Demod        : 313
% 6.96/2.59  #Tautology    : 189
% 6.96/2.59  #SimpNegUnit  : 21
% 6.96/2.59  #BackRed      : 18
% 6.96/2.59  
% 6.96/2.59  #Partial instantiations: 0
% 6.96/2.59  #Strategies tried      : 1
% 6.96/2.59  
% 6.96/2.59  Timing (in seconds)
% 6.96/2.59  ----------------------
% 6.96/2.59  Preprocessing        : 0.66
% 6.96/2.59  Parsing              : 0.34
% 6.96/2.59  CNF conversion       : 0.05
% 6.96/2.59  Main loop            : 0.85
% 6.96/2.59  Inferencing          : 0.32
% 6.96/2.59  Reduction            : 0.26
% 6.96/2.59  Demodulation         : 0.18
% 6.96/2.59  BG Simplification    : 0.04
% 6.96/2.59  Subsumption          : 0.16
% 6.96/2.59  Abstraction          : 0.03
% 6.96/2.59  MUC search           : 0.00
% 6.96/2.59  Cooper               : 0.00
% 6.96/2.59  Total                : 1.56
% 6.96/2.59  Index Insertion      : 0.00
% 6.96/2.59  Index Deletion       : 0.00
% 6.96/2.59  Index Matching       : 0.00
% 6.96/2.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------