TSTP Solution File: SET025-8 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET025-8 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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 10:55:37 EDT 2023

% Result   : Unsatisfiable 5.55s 2.30s
% Output   : CNFRefutation 6.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   77
% Syntax   : Number of formulae    :   84 (   8 unt;  73 typ;   0 def)
%            Number of atoms       :   14 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   5   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  122 (  66   >;  56   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-5 aty)
%            Number of functors    :   60 (  60 usr;   7 con; 0-5 aty)
%            Number of variables   :    7 (;   7   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ homomorphism > maps > subset > proper_subset > member > disjoint > closed > single_valued_set > relation > ordered_pair_predicate > one_to_one_function > little_set > function > f33 > f32 > f31 > f30 > f29 > f28 > f22 > apply_to_two_arguments > union > restrict > ordered_pair > non_ordered_pair > intersection > image > f9 > f8 > f7 > f6 > f5 > f4 > f27 > f23 > f17 > f16 > f14 > f13 > f12 > f11 > f10 > f1 > cross_product > compose > apply > #nlpp > successor > singleton_set > sigma > second > rotate_right > range_of > powerset > flip_range_of > first > f3 > f26 > f24 > f21 > f20 > f2 > f19 > f18 > domain_of > converse > complement > universal_set > infinity > identity_relation > f25 > estin > empty_set > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(f3,type,
    f3: $i > $i ).

tff(f11,type,
    f11: ( $i * $i ) > $i ).

tff(f5,type,
    f5: ( $i * $i ) > $i ).

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

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

tff(f18,type,
    f18: $i > $i ).

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

tff(f12,type,
    f12: ( $i * $i ) > $i ).

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

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

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

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

tff(f13,type,
    f13: ( $i * $i ) > $i ).

tff(f9,type,
    f9: ( $i * $i ) > $i ).

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

tff(f14,type,
    f14: ( $i * $i ) > $i ).

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

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

tff(f25,type,
    f25: $i ).

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

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

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

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

tff(f30,type,
    f30: ( $i * $i * $i ) > $i ).

tff(f20,type,
    f20: $i > $i ).

tff(f32,type,
    f32: ( $i * $i * $i * $i * $i ) > $i ).

tff(f17,type,
    f17: ( $i * $i ) > $i ).

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

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

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

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

tff(f24,type,
    f24: $i > $i ).

tff(f7,type,
    f7: ( $i * $i ) > $i ).

tff(f26,type,
    f26: $i > $i ).

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

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

tff(f22,type,
    f22: ( $i * $i * $i ) > $i ).

tff(f2,type,
    f2: $i > $i ).

tff(f31,type,
    f31: ( $i * $i * $i ) > $i ).

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

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

tff(f28,type,
    f28: ( $i * $i * $i ) > $i ).

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

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

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

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

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

tff(f33,type,
    f33: ( $i * $i * $i * $i * $i ) > $i ).

tff(f8,type,
    f8: ( $i * $i ) > $i ).

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

tff(f21,type,
    f21: $i > $i ).

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

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

tff(f4,type,
    f4: ( $i * $i ) > $i ).

tff(f23,type,
    f23: ( $i * $i ) > $i ).

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

tff(f29,type,
    f29: ( $i * $i * $i ) > $i ).

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

tff(f16,type,
    f16: ( $i * $i ) > $i ).

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

tff(f10,type,
    f10: ( $i * $i ) > $i ).

tff(f27,type,
    f27: ( $i * $i ) > $i ).

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

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

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

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

tff(f19,type,
    f19: $i > $i ).

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

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

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

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

tff(f1,type,
    f1: ( $i * $i ) > $i ).

tff(f6,type,
    f6: ( $i * $i ) > $i ).

tff(f_1080,axiom,
    ~ little_set(a),
    file(unknown,unknown) ).

tff(f_1078,axiom,
    ordered_pair_predicate(a),
    file(unknown,unknown) ).

tff(f_121,axiom,
    ! [X] :
      ( ~ ordered_pair_predicate(X)
      | ( X = ordered_pair(f2(X),f3(X)) ) ),
    file(unknown,unknown) ).

tff(f_1077,axiom,
    ! [X,Y] : little_set(ordered_pair(X,Y)),
    file(unknown,unknown) ).

tff(c_306,plain,
    ~ little_set(a),
    inference(cnfTransformation,[status(thm)],[f_1080]) ).

tff(c_304,plain,
    ordered_pair_predicate(a),
    inference(cnfTransformation,[status(thm)],[f_1078]) ).

tff(c_629,plain,
    ! [X_432] :
      ( ( ordered_pair(f2(X_432),f3(X_432)) = X_432 )
      | ~ ordered_pair_predicate(X_432) ),
    inference(cnfTransformation,[status(thm)],[f_121]) ).

tff(c_302,plain,
    ! [X_341,Y_342] : little_set(ordered_pair(X_341,Y_342)),
    inference(cnfTransformation,[status(thm)],[f_1077]) ).

tff(c_640,plain,
    ! [X_433] :
      ( little_set(X_433)
      | ~ ordered_pair_predicate(X_433) ),
    inference(superposition,[status(thm),theory(equality)],[c_629,c_302]) ).

tff(c_649,plain,
    little_set(a),
    inference(resolution,[status(thm)],[c_304,c_640]) ).

tff(c_655,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_306,c_649]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET025-8 : TPTP v8.1.2. Released v1.0.0.
% 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 : n004.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 16:52:26 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.55/2.30  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.55/2.31  
% 5.55/2.31  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.03/2.36  
% 6.03/2.36  Inference rules
% 6.03/2.36  ----------------------
% 6.03/2.36  #Ref     : 0
% 6.03/2.36  #Sup     : 64
% 6.03/2.36  #Fact    : 0
% 6.03/2.36  #Define  : 0
% 6.03/2.36  #Split   : 4
% 6.03/2.36  #Chain   : 0
% 6.03/2.36  #Close   : 0
% 6.03/2.36  
% 6.03/2.36  Ordering : KBO
% 6.03/2.36  
% 6.03/2.36  Simplification rules
% 6.03/2.36  ----------------------
% 6.03/2.36  #Subsume      : 9
% 6.03/2.36  #Demod        : 8
% 6.03/2.36  #Tautology    : 19
% 6.03/2.36  #SimpNegUnit  : 1
% 6.03/2.36  #BackRed      : 2
% 6.03/2.36  
% 6.03/2.36  #Partial instantiations: 0
% 6.03/2.36  #Strategies tried      : 1
% 6.03/2.36  
% 6.03/2.36  Timing (in seconds)
% 6.03/2.36  ----------------------
% 6.03/2.37  Preprocessing        : 0.79
% 6.03/2.37  Parsing              : 0.41
% 6.03/2.37  CNF conversion       : 0.06
% 6.03/2.37  Main loop            : 0.49
% 6.03/2.37  Inferencing          : 0.16
% 6.03/2.37  Reduction            : 0.15
% 6.03/2.37  Demodulation         : 0.10
% 6.03/2.37  BG Simplification    : 0.05
% 6.03/2.37  Subsumption          : 0.10
% 6.03/2.37  Abstraction          : 0.02
% 6.03/2.37  MUC search           : 0.00
% 6.03/2.37  Cooper               : 0.00
% 6.03/2.37  Total                : 1.36
% 6.03/2.37  Index Insertion      : 0.00
% 6.03/2.37  Index Deletion       : 0.00
% 6.03/2.37  Index Matching       : 0.00
% 6.03/2.37  BG Taut test         : 0.00
%------------------------------------------------------------------------------