TSTP Solution File: SET183+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET183+3 : 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 : n024.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 03:17:40 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : Refutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (   9 unt;   0 def)
%            Number of atoms       :   92 (  13 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  100 (  39   ~;  30   |;  22   &)
%                                         (   4 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   59 (  52   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f237,plain,
    $false,
    inference(unit_resulting_resolution,[],[f69,f77,f68,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,intersection(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) )
      & ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

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

fof(f68,plain,
    ~ member(sK4(sK1,intersection(sK1,sK2)),intersection(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f63,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK4(X0,X1),X1)
          & member(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK4(X0,X1),X1)
        & member(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,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,[],[f23]) ).

fof(f23,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,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f63,plain,
    ~ subset(sK1,intersection(sK1,sK2)),
    inference(unit_resulting_resolution,[],[f30,f32,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f32,plain,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : subset(intersection(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_is_subset) ).

fof(f30,plain,
    sK1 != intersection(sK1,sK2),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ( sK1 != intersection(sK1,sK2)
    & subset(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f10,f14]) ).

fof(f14,plain,
    ( ? [X0,X1] :
        ( intersection(X0,X1) != X0
        & subset(X0,X1) )
   => ( sK1 != intersection(sK1,sK2)
      & subset(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1] :
      ( intersection(X0,X1) != X0
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X0,X1] :
        ( subset(X0,X1)
       => intersection(X0,X1) = X0 ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X0,X1] :
      ( subset(X0,X1)
     => intersection(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_intersection) ).

fof(f77,plain,
    member(sK4(sK1,intersection(sK1,sK2)),sK2),
    inference(unit_resulting_resolution,[],[f69,f29,f43]) ).

fof(f43,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X3,X0)
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f29,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f15]) ).

fof(f69,plain,
    member(sK4(sK1,intersection(sK1,sK2)),sK1),
    inference(unit_resulting_resolution,[],[f63,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : SET183+3 : TPTP v8.2.0. Released v2.2.0.
% 0.09/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31  % Computer : n024.cluster.edu
% 0.11/0.31  % Model    : x86_64 x86_64
% 0.11/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31  % Memory   : 8042.1875MB
% 0.11/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31  % CPULimit   : 300
% 0.11/0.31  % WCLimit    : 300
% 0.11/0.31  % DateTime   : Mon May 20 12:50:37 EDT 2024
% 0.11/0.31  % CPUTime    : 
% 0.11/0.32  % (12846)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33  % (12849)WARNING: value z3 for option sas not known
% 0.11/0.33  % (12851)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)
% 0.11/0.33  % (12853)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)
% 0.11/0.33  % (12848)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33  % (12852)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)
% 0.11/0.33  % (12849)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)
% 0.11/0.33  % (12847)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33  % (12850)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33  TRYING [1]
% 0.11/0.33  TRYING [2]
% 0.11/0.34  TRYING [3]
% 0.11/0.34  TRYING [4]
% 0.11/0.34  TRYING [1]
% 0.11/0.34  TRYING [2]
% 0.11/0.34  % (12853)First to succeed.
% 0.11/0.34  % (12853)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12846"
% 0.11/0.34  % (12853)Refutation found. Thanks to Tanya!
% 0.11/0.34  % SZS status Theorem for theBenchmark
% 0.11/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.34  % (12853)------------------------------
% 0.11/0.34  % (12853)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.11/0.34  % (12853)Termination reason: Refutation
% 0.11/0.34  
% 0.11/0.34  % (12853)Memory used [KB]: 838
% 0.11/0.34  % (12853)Time elapsed: 0.007 s
% 0.11/0.34  % (12853)Instructions burned: 11 (million)
% 0.11/0.34  % (12846)Success in time 0.022 s
%------------------------------------------------------------------------------