TSTP Solution File: SET090+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET090+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 03:16:01 EDT 2024

% Result   : Theorem 0.21s 0.44s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (  10 unt;   0 def)
%            Number of atoms       :   87 (  48 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   82 (  29   ~;  24   |;  21   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   44 (  38   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1777,plain,
    $false,
    inference(trivial_inequality_removal,[],[f1774]) ).

fof(f1774,plain,
    sK1 != sK1,
    inference(superposition,[],[f147,f1617]) ).

fof(f1617,plain,
    sK1 = member_of(sK0),
    inference(resolution,[],[f1546,f145]) ).

fof(f145,plain,
    member(sK1,universal_class),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ( sK1 != member_of(sK0)
    & sK0 = singleton(sK1)
    & member(sK1,universal_class) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f79,f95]) ).

fof(f95,plain,
    ( ? [X0,X1] :
        ( member_of(X0) != X1
        & singleton(X1) = X0
        & member(X1,universal_class) )
   => ( sK1 != member_of(sK0)
      & sK0 = singleton(sK1)
      & member(sK1,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ? [X0,X1] :
      ( member_of(X0) != X1
      & singleton(X1) = X0
      & member(X1,universal_class) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ? [X0,X1] :
      ( member_of(X0) != X1
      & singleton(X1) = X0
      & member(X1,universal_class) ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ~ ! [X0,X1] :
        ( ( singleton(X1) = X0
          & member(X1,universal_class) )
       => member_of(X0) = X1 ),
    inference(rectify,[],[f49]) ).

fof(f49,negated_conjecture,
    ~ ! [X0,X2] :
        ( ( singleton(X2) = X0
          & member(X2,universal_class) )
       => member_of(X0) = X2 ),
    inference(negated_conjecture,[],[f48]) ).

fof(f48,conjecture,
    ! [X0,X2] :
      ( ( singleton(X2) = X0
        & member(X2,universal_class) )
     => member_of(X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton) ).

fof(f1546,plain,
    ( ~ member(sK1,universal_class)
    | sK1 = member_of(sK0) ),
    inference(resolution,[],[f1534,f294]) ).

fof(f294,plain,
    ( member(sK1,sK0)
    | ~ member(sK1,universal_class) ),
    inference(superposition,[],[f292,f146]) ).

fof(f146,plain,
    sK0 = singleton(sK1),
    inference(cnf_transformation,[],[f96]) ).

fof(f292,plain,
    ! [X0] :
      ( member(X0,singleton(X0))
      | ~ member(X0,universal_class) ),
    inference(superposition,[],[f243,f153]) ).

fof(f153,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f243,plain,
    ! [X2,X1] :
      ( member(X2,unordered_pair(X1,X2))
      | ~ member(X2,universal_class) ),
    inference(equality_resolution,[],[f221]) ).

fof(f221,plain,
    ! [X2,X0,X1] :
      ( member(X0,unordered_pair(X1,X2))
      | X0 != X2
      | ~ member(X0,universal_class) ),
    inference(cnf_transformation,[],[f132]) ).

fof(f132,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(flattening,[],[f131]) ).

fof(f131,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,unordered_pair(X1,X2))
        | ( X0 != X2
          & X0 != X1 )
        | ~ member(X0,universal_class) )
      & ( ( ( X0 = X2
            | X0 = X1 )
          & member(X0,universal_class) )
        | ~ member(X0,unordered_pair(X1,X2)) ) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
    <=> ( ( X0 = X2
          | X0 = X1 )
        & member(X0,universal_class) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( member(X2,unordered_pair(X0,X1))
    <=> ( ( X1 = X2
          | X0 = X2 )
        & member(X2,universal_class) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).

fof(f1534,plain,
    ! [X0] :
      ( ~ member(X0,sK0)
      | member_of(sK0) = X0 ),
    inference(superposition,[],[f1516,f580]) ).

fof(f580,plain,
    sK0 = singleton(member_of(sK0)),
    inference(forward_demodulation,[],[f571,f146]) ).

fof(f571,plain,
    singleton(sK1) = singleton(member_of(singleton(sK1))),
    inference(resolution,[],[f166,f145]) ).

fof(f166,plain,
    ! [X0] :
      ( ~ member(X0,universal_class)
      | singleton(X0) = singleton(member_of(singleton(X0))) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( singleton(X0) = singleton(member_of(singleton(X0)))
      | ~ member(X0,universal_class) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( member(X0,universal_class)
     => singleton(X0) = singleton(member_of(singleton(X0))) ),
    inference(rectify,[],[f45]) ).

fof(f45,axiom,
    ! [X1] :
      ( member(X1,universal_class)
     => singleton(X1) = singleton(member_of(singleton(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_singleton) ).

fof(f1516,plain,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1 ),
    inference(duplicate_literal_removal,[],[f1508]) ).

fof(f1508,plain,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1
      | X0 = X1 ),
    inference(superposition,[],[f219,f153]) ).

fof(f219,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[],[f132]) ).

fof(f147,plain,
    sK1 != member_of(sK0),
    inference(cnf_transformation,[],[f96]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12  % Problem    : SET090+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.12/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon May 20 11:26:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (20017)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (20021)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (20020)WARNING: value z3 for option sas not known
% 0.14/0.37  % (20018)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (20020)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)
% 0.14/0.37  % (20019)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (20022)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)
% 0.14/0.37  % (20023)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)
% 0.14/0.37  % (20024)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)
% 0.14/0.39  TRYING [1]
% 0.14/0.39  TRYING [2]
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [1]
% 0.14/0.40  TRYING [2]
% 0.14/0.40  TRYING [2]
% 0.14/0.41  TRYING [3]
% 0.14/0.41  TRYING [3]
% 0.21/0.44  % (20023)First to succeed.
% 0.21/0.44  % (20023)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20017"
% 0.21/0.44  % (20023)Refutation found. Thanks to Tanya!
% 0.21/0.44  % SZS status Theorem for theBenchmark
% 0.21/0.44  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.44  % (20023)------------------------------
% 0.21/0.44  % (20023)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.44  % (20023)Termination reason: Refutation
% 0.21/0.44  
% 0.21/0.44  % (20023)Memory used [KB]: 1684
% 0.21/0.44  % (20023)Time elapsed: 0.070 s
% 0.21/0.44  % (20023)Instructions burned: 111 (million)
% 0.21/0.44  % (20017)Success in time 0.088 s
%------------------------------------------------------------------------------