TSTP Solution File: SET602+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET602+4 : TPTP v8.2.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 03:19:37 EDT 2024

% Result   : Theorem 0.18s 0.38s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   36 (  13 unt;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   97 (  43   ~;  29   |;  16   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   69 (  64   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1212,plain,
    $false,
    inference(resolution,[],[f1211,f110]) ).

fof(f110,plain,
    ~ subset(difference(sK0,sK0),empty_set),
    inference(subsumption_resolution,[],[f109,f87]) ).

fof(f87,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f57,f55]) ).

fof(f55,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f57,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK1(X0,X1),X1)
          & member(sK1(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f33,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f109,plain,
    ( ~ subset(empty_set,difference(sK0,sK0))
    | ~ subset(difference(sK0,sK0),empty_set) ),
    inference(resolution,[],[f59,f54]) ).

fof(f54,plain,
    ~ equal_set(difference(sK0,sK0),empty_set),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ equal_set(difference(sK0,sK0),empty_set),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f25,f30]) ).

fof(f30,plain,
    ( ? [X0] : ~ equal_set(difference(X0,X0),empty_set)
   => ~ equal_set(difference(sK0,sK0),empty_set) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0] : ~ equal_set(difference(X0,X0),empty_set),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0] : equal_set(difference(X0,X0),empty_set),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X3] : equal_set(difference(X3,X3),empty_set),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X3] : equal_set(difference(X3,X3),empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI29) ).

fof(f59,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( equal_set(X0,X1)
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

fof(f1211,plain,
    ! [X0,X1] : subset(difference(X0,X0),X1),
    inference(duplicate_literal_removal,[],[f1176]) ).

fof(f1176,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X0),X1)
      | subset(difference(X0,X0),X1) ),
    inference(resolution,[],[f98,f97]) ).

fof(f97,plain,
    ! [X2,X0,X1] :
      ( member(sK1(difference(X0,X1),X2),X0)
      | subset(difference(X0,X1),X2) ),
    inference(resolution,[],[f79,f57]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | member(X0,X2) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( member(X0,difference(X2,X1))
        | member(X0,X1)
        | ~ member(X0,X2) )
      & ( ( ~ member(X0,X1)
          & member(X0,X2) )
        | ~ member(X0,difference(X2,X1)) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( member(X0,difference(X2,X1))
    <=> ( ~ member(X0,X1)
        & member(X0,X2) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0,X3] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f98,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK1(difference(X0,X1),X2),X1)
      | subset(difference(X0,X1),X2) ),
    inference(resolution,[],[f80,f57]) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( ~ member(X0,difference(X2,X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[],[f53]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : SET602+4 : TPTP v8.2.0. Released v2.2.0.
% 0.02/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33  % Computer : n027.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Mon May 20 11:20:38 EDT 2024
% 0.11/0.33  % CPUTime    : 
% 0.11/0.33  % (28123)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.35  % (28126)WARNING: value z3 for option sas not known
% 0.18/0.35  % (28126)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)
% 0.18/0.35  % (28128)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)
% 0.18/0.35  % (28130)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)
% 0.18/0.35  % (28124)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.35  % (28127)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.35  % (28125)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35  TRYING [1]
% 0.18/0.35  % (28129)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)
% 0.18/0.35  TRYING [2]
% 0.18/0.35  TRYING [3]
% 0.18/0.36  TRYING [1]
% 0.18/0.36  TRYING [4]
% 0.18/0.36  TRYING [2]
% 0.18/0.37  TRYING [5]
% 0.18/0.37  TRYING [3]
% 0.18/0.37  TRYING [1]
% 0.18/0.37  TRYING [2]
% 0.18/0.37  TRYING [3]
% 0.18/0.38  % (28126)First to succeed.
% 0.18/0.38  % (28126)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-28123"
% 0.18/0.38  % (28126)Refutation found. Thanks to Tanya!
% 0.18/0.38  % SZS status Theorem for theBenchmark
% 0.18/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.38  % (28126)------------------------------
% 0.18/0.38  % (28126)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.38  % (28126)Termination reason: Refutation
% 0.18/0.38  
% 0.18/0.38  % (28126)Memory used [KB]: 1354
% 0.18/0.38  % (28126)Time elapsed: 0.029 s
% 0.18/0.38  % (28126)Instructions burned: 48 (million)
% 0.18/0.38  % (28123)Success in time 0.044 s
%------------------------------------------------------------------------------