TSTP Solution File: SET767+4 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 : Sun May  5 09:18:54 EDT 2024

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   24 (   3 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   76 (  27   ~;  21   |;  18   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-3 aty)
%            Number of variables   :   69 (  60   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2980,plain,
    $false,
    inference(resolution,[],[f2976,f66]) ).

fof(f66,plain,
    ~ subset(equivalence_class(sK2,sK0,sK1),sK0),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ~ subset(equivalence_class(sK2,sK0,sK1),sK0)
    & equivalence(sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(equivalence_class(X2,X0,X1),X0)
        & equivalence(X1,X0) )
   => ( ~ subset(equivalence_class(sK2,sK0,sK1),sK0)
      & equivalence(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0,X1,X2] :
      ( ~ subset(equivalence_class(X2,X0,X1),X0)
      & equivalence(X1,X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2] :
        ( equivalence(X1,X0)
       => subset(equivalence_class(X2,X0,X1),X0) ),
    inference(rectify,[],[f18]) ).

fof(f18,negated_conjecture,
    ~ ! [X3,X6,X0] :
        ( equivalence(X6,X3)
       => subset(equivalence_class(X0,X3,X6),X3) ),
    inference(negated_conjecture,[],[f17]) ).

fof(f17,conjecture,
    ! [X3,X6,X0] :
      ( equivalence(X6,X3)
     => subset(equivalence_class(X0,X3,X6),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).

fof(f2976,plain,
    ! [X2,X0,X1] : subset(equivalence_class(X0,X1,X2),X1),
    inference(duplicate_literal_removal,[],[f2928]) ).

fof(f2928,plain,
    ! [X2,X0,X1] :
      ( subset(equivalence_class(X0,X1,X2),X1)
      | subset(equivalence_class(X0,X1,X2),X1) ),
    inference(resolution,[],[f195,f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK3(X0,X1),X1)
          & member(sK3(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f42,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK3(X0,X1),X1)
        & member(sK3(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,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,[],[f41]) ).

fof(f41,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,[],[f35]) ).

fof(f35,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(f195,plain,
    ! [X2,X3,X0,X1] :
      ( member(sK3(equivalence_class(X0,X1,X2),X3),X1)
      | subset(equivalence_class(X0,X1,X2),X3) ),
    inference(resolution,[],[f96,f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f96,plain,
    ! [X2,X3,X0,X1] :
      ( ~ member(X3,equivalence_class(X2,X1,X0))
      | member(X3,X1) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2,X3] :
      ( ( member(X3,equivalence_class(X2,X1,X0))
        | ~ apply(X0,X2,X3)
        | ~ member(X3,X1) )
      & ( ( apply(X0,X2,X3)
          & member(X3,X1) )
        | ~ member(X3,equivalence_class(X2,X1,X0)) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3] :
      ( member(X3,equivalence_class(X2,X1,X0))
    <=> ( apply(X0,X2,X3)
        & member(X3,X1) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X6,X3,X0,X2] :
      ( member(X2,equivalence_class(X0,X3,X6))
    <=> ( apply(X6,X0,X2)
        & member(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_class) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35  % Computer : n012.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 16:20:38 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (2342)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (2346)WARNING: value z3 for option sas not known
% 0.13/0.37  % (2347)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (2345)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37  % (2344)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  % (2348)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)
% 0.13/0.37  % (2349)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)
% 0.13/0.37  % (2346)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)
% 0.13/0.37  % (2350)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)
% 0.13/0.37  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.38  TRYING [3]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [4]
% 0.13/0.38  TRYING [2]
% 0.21/0.39  TRYING [5]
% 0.21/0.40  TRYING [3]
% 0.21/0.42  TRYING [1]
% 0.21/0.42  TRYING [2]
% 0.21/0.42  TRYING [6]
% 0.21/0.42  TRYING [3]
% 0.21/0.43  TRYING [4]
% 0.21/0.43  TRYING [4]
% 0.21/0.44  TRYING [5]
% 0.21/0.45  % (2346)First to succeed.
% 0.21/0.45  % (2346)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2342"
% 0.21/0.45  % (2348)Also succeeded, but the first one will report.
% 0.21/0.45  % (2346)Refutation found. Thanks to Tanya!
% 0.21/0.45  % SZS status Theorem for theBenchmark
% 0.21/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.45  % (2346)------------------------------
% 0.21/0.45  % (2346)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45  % (2346)Termination reason: Refutation
% 0.21/0.45  
% 0.21/0.45  % (2346)Memory used [KB]: 2203
% 0.21/0.45  % (2346)Time elapsed: 0.079 s
% 0.21/0.45  % (2346)Instructions burned: 129 (million)
% 0.21/0.45  % (2342)Success in time 0.096 s
%------------------------------------------------------------------------------