TSTP Solution File: SET592+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET592+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 : n022.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 03:19:28 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   22 (   7 unt;   0 def)
%            Number of atoms       :   58 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   54 (  18   ~;  11   |;  20   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   31 (  22   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f105,plain,
    $false,
    inference(subsumption_resolution,[],[f103,f36]) ).

fof(f36,plain,
    empty_set != sK0,
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( empty_set != sK0
    & empty_set = intersection(sK1,sK2)
    & subset(sK0,sK2)
    & subset(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f14,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2] :
        ( empty_set != X0
        & empty_set = intersection(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
   => ( empty_set != sK0
      & empty_set = intersection(sK1,sK2)
      & subset(sK0,sK2)
      & subset(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & empty_set = intersection(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & empty_set = intersection(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( empty_set = intersection(X1,X2)
          & subset(X0,X2)
          & subset(X0,X1) )
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X0,X1,X2] :
      ( ( empty_set = intersection(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th51) ).

fof(f103,plain,
    empty_set = sK0,
    inference(resolution,[],[f102,f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ subset(X0,empty_set) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f102,plain,
    subset(sK0,empty_set),
    inference(subsumption_resolution,[],[f99,f33]) ).

fof(f33,plain,
    subset(sK0,sK1),
    inference(cnf_transformation,[],[f20]) ).

fof(f99,plain,
    ( subset(sK0,empty_set)
    | ~ subset(sK0,sK1) ),
    inference(resolution,[],[f96,f34]) ).

fof(f34,plain,
    subset(sK0,sK2),
    inference(cnf_transformation,[],[f20]) ).

fof(f96,plain,
    ! [X0] :
      ( ~ subset(X0,sK2)
      | subset(X0,empty_set)
      | ~ subset(X0,sK1) ),
    inference(superposition,[],[f51,f35]) ).

fof(f35,plain,
    empty_set = intersection(sK1,sK2),
    inference(cnf_transformation,[],[f20]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( subset(X0,intersection(X1,X2))
      | ~ subset(X0,X2)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1,X2] :
      ( ( subset(X0,X2)
        & subset(X0,X1) )
     => subset(X0,intersection(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_subsets) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : SET592+3 : TPTP v8.2.0. Released v2.2.0.
% 0.10/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n022.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon May 20 12:09:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  % (20553)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (20560)WARNING: value z3 for option sas not known
% 0.15/0.37  % (20561)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37  % (20559)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37  % (20562)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)
% 0.15/0.37  % (20560)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)
% 0.15/0.37  % (20565)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)
% 0.15/0.37  % (20558)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37  TRYING [1]
% 0.15/0.37  % (20563)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)
% 0.15/0.37  TRYING [2]
% 0.15/0.37  TRYING [3]
% 0.15/0.38  TRYING [4]
% 0.15/0.38  % (20560)First to succeed.
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  % (20560)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20553"
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  % (20563)Also succeeded, but the first one will report.
% 0.15/0.38  % (20560)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (20560)------------------------------
% 0.15/0.38  % (20560)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (20560)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (20560)Memory used [KB]: 834
% 0.15/0.38  % (20560)Time elapsed: 0.006 s
% 0.15/0.38  % (20560)Instructions burned: 5 (million)
% 0.15/0.38  % (20553)Success in time 0.023 s
%------------------------------------------------------------------------------