TSTP Solution File: SET025-3 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n023.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 May 21 03:15:27 EDT 2024

% Result   : Unsatisfiable 0.24s 0.41s
% Output   : Refutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   40 (  22 unt;   0 def)
%            Number of atoms       :   62 (   4 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   41 (  19   ~;  12   |;   0   &)
%                                         (  10 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  11 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   23 (  23   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f246,plain,
    $false,
    inference(avatar_sat_refutation,[],[f204,f209,f214,f218,f223,f227,f231,f235,f239,f243,f245]) ).

fof(f245,plain,
    ( spl0_1
    | ~ spl0_7 ),
    inference(avatar_contradiction_clause,[],[f244]) ).

fof(f244,plain,
    ( $false
    | spl0_1
    | ~ spl0_7 ),
    inference(resolution,[],[f230,f203]) ).

fof(f203,plain,
    ( ~ little_set(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)))
    | spl0_1 ),
    inference(avatar_component_clause,[],[f201]) ).

fof(f201,plain,
    ( spl0_1
  <=> little_set(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f230,plain,
    ( ! [X0,X1] : little_set(non_ordered_pair(X0,X1))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f229,plain,
    ( spl0_7
  <=> ! [X0,X1] : little_set(non_ordered_pair(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f243,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f111,f241]) ).

fof(f241,plain,
    ( spl0_10
  <=> ! [X7] :
        ( ~ one_to_one_function(X7)
        | function(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f111,axiom,
    ! [X7] :
      ( ~ one_to_one_function(X7)
      | function(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one_function1) ).

fof(f239,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f87,f237]) ).

fof(f237,plain,
    ( spl0_9
  <=> ! [X7] :
        ( ~ function(X7)
        | single_valued_set(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f87,axiom,
    ! [X7] :
      ( ~ function(X7)
      | single_valued_set(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).

fof(f235,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f86,f233]) ).

fof(f233,plain,
    ( spl0_8
  <=> ! [X7] :
        ( ~ function(X7)
        | relation(X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f86,axiom,
    ! [X7] :
      ( ~ function(X7)
      | relation(X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).

fof(f231,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f8,f229]) ).

fof(f8,axiom,
    ! [X0,X1] : little_set(non_ordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',non_ordered_pair4) ).

fof(f227,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f186,f225]) ).

fof(f225,plain,
    ( spl0_6
  <=> ! [X1] : ~ proper_subset(X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f186,plain,
    ! [X1] : ~ proper_subset(X1,X1),
    inference(equality_resolution,[],[f71]) ).

fof(f71,axiom,
    ! [X0,X1] :
      ( X0 != X1
      | ~ proper_subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',proper_subset2) ).

fof(f223,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f61,f220]) ).

fof(f220,plain,
    ( spl0_5
  <=> member(empty_set,infinity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f61,axiom,
    member(empty_set,infinity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity2) ).

fof(f218,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f58,f216]) ).

fof(f216,plain,
    ( spl0_4
  <=> ! [X3] : ~ member(X3,empty_set) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f58,axiom,
    ! [X3] : ~ member(X3,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f214,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f100,f211]) ).

fof(f211,plain,
    ( spl0_3
  <=> function(f25) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f100,axiom,
    function(f25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).

fof(f209,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f60,f206]) ).

fof(f206,plain,
    ( spl0_2
  <=> little_set(infinity) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f60,axiom,
    little_set(infinity),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity1) ).

fof(f204,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f155,f201]) ).

fof(f155,plain,
    ~ little_set(non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
    inference(definition_unfolding,[],[f151,f153]) ).

fof(f153,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(non_ordered_pair(X0,X0),non_ordered_pair(X0,X1)),
    inference(definition_unfolding,[],[f10,f9]) ).

fof(f9,axiom,
    ! [X0] : singleton_set(X0) = non_ordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).

fof(f10,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = non_ordered_pair(singleton_set(X0),non_ordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).

fof(f151,axiom,
    ~ little_set(ordered_pair(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ordered_pairs_are_small) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET025-3 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n023.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Mon May 20 12:20:08 EDT 2024
% 0.15/0.38  % CPUTime    : 
% 0.15/0.38  % (9249)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40  % (9256)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.24/0.40  % (9254)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.24/0.40  % (9255)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.24/0.41  % (9252)WARNING: value z3 for option sas not known
% 0.24/0.41  % (9254)First to succeed.
% 0.24/0.41  % (9254)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9249"
% 0.24/0.41  % (9252)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.24/0.41  % (9251)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.24/0.41  % (9254)Refutation found. Thanks to Tanya!
% 0.24/0.41  % SZS status Unsatisfiable for theBenchmark
% 0.24/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.41  % (9254)------------------------------
% 0.24/0.41  % (9254)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.24/0.41  % (9254)Termination reason: Refutation
% 0.24/0.41  
% 0.24/0.41  % (9254)Memory used [KB]: 988
% 0.24/0.41  % (9254)Time elapsed: 0.009 s
% 0.24/0.41  % (9254)Instructions burned: 9 (million)
% 0.24/0.41  % (9249)Success in time 0.02 s
%------------------------------------------------------------------------------