TSTP Solution File: SET024-4 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET024-4 : 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 : n013.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 10:55:35 EDT 2023

% Result   : Unsatisfiable 5.32s 2.18s
% Output   : CNFRefutation 5.32s
% 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       :   15 (   3 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   7   ~;   4   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   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   :    8 (;   8   !;   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_996,axiom,
    little_set(a),
    file(unknown,unknown) ).

tff(f_101,axiom,
    ! [X] : ( singleton_set(X) = non_ordered_pair(X,X) ),
    file(unknown,unknown) ).

tff(f_88,axiom,
    ! [U,X,Y] :
      ( member(U,non_ordered_pair(X,Y))
      | ~ little_set(U)
      | ( U != X ) ),
    file(unknown,unknown) ).

tff(f_998,axiom,
    ~ member(a,singleton_set(a)),
    file(unknown,unknown) ).

tff(c_284,plain,
    little_set(a),
    inference(cnfTransformation,[status(thm)],[f_996]) ).

tff(c_18,plain,
    ! [X_20] : ( non_ordered_pair(X_20,X_20) = singleton_set(X_20) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_428,plain,
    ! [X_366,Y_367] :
      ( ~ little_set(X_366)
      | member(X_366,non_ordered_pair(X_366,Y_367)) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_446,plain,
    ! [X_369] :
      ( ~ little_set(X_369)
      | member(X_369,singleton_set(X_369)) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_428]) ).

tff(c_286,plain,
    ~ member(a,singleton_set(a)),
    inference(cnfTransformation,[status(thm)],[f_998]) ).

tff(c_455,plain,
    ~ little_set(a),
    inference(resolution,[status(thm)],[c_446,c_286]) ).

tff(c_461,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_284,c_455]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET024-4 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14  % 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
% 0.15/0.36  % Computer : n013.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 16:04:17 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 5.32/2.18  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.32/2.19  
% 5.32/2.19  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.32/2.22  
% 5.32/2.22  Inference rules
% 5.32/2.22  ----------------------
% 5.32/2.22  #Ref     : 0
% 5.32/2.22  #Sup     : 33
% 5.32/2.22  #Fact    : 0
% 5.32/2.22  #Define  : 0
% 5.32/2.22  #Split   : 4
% 5.32/2.22  #Chain   : 0
% 5.32/2.22  #Close   : 0
% 5.32/2.22  
% 5.32/2.22  Ordering : KBO
% 5.32/2.22  
% 5.32/2.22  Simplification rules
% 5.32/2.22  ----------------------
% 5.32/2.22  #Subsume      : 2
% 5.32/2.22  #Demod        : 3
% 5.32/2.22  #Tautology    : 14
% 5.32/2.22  #SimpNegUnit  : 0
% 5.32/2.22  #BackRed      : 2
% 5.32/2.22  
% 5.32/2.22  #Partial instantiations: 0
% 5.32/2.22  #Strategies tried      : 1
% 5.32/2.22  
% 5.32/2.22  Timing (in seconds)
% 5.32/2.22  ----------------------
% 5.32/2.22  Preprocessing        : 0.78
% 5.32/2.22  Parsing              : 0.40
% 5.32/2.22  CNF conversion       : 0.06
% 5.32/2.22  Main loop            : 0.38
% 5.32/2.22  Inferencing          : 0.10
% 5.32/2.22  Reduction            : 0.13
% 5.32/2.22  Demodulation         : 0.08
% 5.32/2.22  BG Simplification    : 0.05
% 5.32/2.22  Subsumption          : 0.08
% 5.32/2.22  Abstraction          : 0.02
% 5.32/2.22  MUC search           : 0.00
% 5.32/2.22  Cooper               : 0.00
% 5.32/2.22  Total                : 1.20
% 5.32/2.22  Index Insertion      : 0.00
% 5.32/2.22  Index Deletion       : 0.00
% 5.32/2.22  Index Matching       : 0.00
% 5.32/2.22  BG Taut test         : 0.00
%------------------------------------------------------------------------------