TSTP Solution File: SET578+3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET578+3 : 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 : n015.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 Apr 30 15:08:36 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   42 (  11 unt;   0 def)
%            Number of atoms       :  153 (  16 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  175 (  64   ~;  62   |;  36   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   81 (  66   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f366,plain,
    $false,
    inference(subsumption_resolution,[],[f351,f350]) ).

fof(f350,plain,
    member(sK4(intersection(sK2,sK3),sK1),intersection(sK2,sK3)),
    inference(forward_demodulation,[],[f346,f35]) ).

fof(f35,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f346,plain,
    member(sK4(intersection(sK2,sK3),sK1),intersection(sK3,sK2)),
    inference(unit_resulting_resolution,[],[f335,f336,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | member(X2,intersection(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,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,[],[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(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(f336,plain,
    member(sK4(intersection(sK2,sK3),sK1),sK2),
    inference(subsumption_resolution,[],[f332,f30]) ).

fof(f30,plain,
    ! [X3] :
      ( ~ member(X3,sK1)
      | member(X3,sK2) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( sK1 != intersection(sK2,sK3)
    & ! [X3] :
        ( ( member(X3,sK1)
          | ~ member(X3,sK3)
          | ~ member(X3,sK2) )
        & ( ( member(X3,sK3)
            & member(X3,sK2) )
          | ~ member(X3,sK1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f14,f15]) ).

fof(f15,plain,
    ( ? [X0,X1,X2] :
        ( intersection(X1,X2) != X0
        & ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X2)
              | ~ member(X3,X1) )
            & ( ( member(X3,X2)
                & member(X3,X1) )
              | ~ member(X3,X0) ) ) )
   => ( sK1 != intersection(sK2,sK3)
      & ! [X3] :
          ( ( member(X3,sK1)
            | ~ member(X3,sK3)
            | ~ member(X3,sK2) )
          & ( ( member(X3,sK3)
              & member(X3,sK2) )
            | ~ member(X3,sK1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X2) != X0
      & ! [X3] :
          ( ( member(X3,X0)
            | ~ member(X3,X2)
            | ~ member(X3,X1) )
          & ( ( member(X3,X2)
              & member(X3,X1) )
            | ~ member(X3,X0) ) ) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X2) != X0
      & ! [X3] :
          ( ( member(X3,X0)
            | ~ member(X3,X2)
            | ~ member(X3,X1) )
          & ( ( member(X3,X2)
              & member(X3,X1) )
            | ~ member(X3,X0) ) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ? [X0,X1,X2] :
      ( intersection(X1,X2) != X0
      & ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X2)
            & member(X3,X1) ) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ! [X3] :
            ( member(X3,X0)
          <=> ( member(X3,X2)
              & member(X3,X1) ) )
       => intersection(X1,X2) = X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X2)
            & member(X3,X1) ) )
     => intersection(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th19) ).

fof(f332,plain,
    ( member(sK4(intersection(sK2,sK3),sK1),sK1)
    | member(sK4(intersection(sK2,sK3),sK1),sK2) ),
    inference(resolution,[],[f66,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f66,plain,
    ( member(sK4(intersection(sK2,sK3),sK1),intersection(sK2,sK3))
    | member(sK4(intersection(sK2,sK3),sK1),sK1) ),
    inference(resolution,[],[f41,f54]) ).

fof(f54,plain,
    ~ sP0(intersection(sK2,sK3),sK1),
    inference(unit_resulting_resolution,[],[f33,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ sP0(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ sP0(X1,X0) )
      & ( sP0(X1,X0)
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( X0 = X1
    <=> sP0(X1,X0) ),
    inference(definition_folding,[],[f6,f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( sP0(X1,X0)
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f33,plain,
    sK1 != intersection(sK2,sK3),
    inference(cnf_transformation,[],[f16]) ).

fof(f41,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | member(sK4(X0,X1),X0)
      | member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ( ( ~ member(sK4(X0,X1),X0)
            | ~ member(sK4(X0,X1),X1) )
          & ( member(sK4(X0,X1),X0)
            | member(sK4(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f20,f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK4(X0,X1),X0)
          | ~ member(sK4(X0,X1),X1) )
        & ( member(sK4(X0,X1),X0)
          | member(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( sP0(X0,X1)
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( ( sP0(X1,X0)
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f335,plain,
    member(sK4(intersection(sK2,sK3),sK1),sK3),
    inference(subsumption_resolution,[],[f331,f31]) ).

fof(f31,plain,
    ! [X3] :
      ( ~ member(X3,sK1)
      | member(X3,sK3) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f331,plain,
    ( member(sK4(intersection(sK2,sK3),sK1),sK1)
    | member(sK4(intersection(sK2,sK3),sK1),sK3) ),
    inference(resolution,[],[f66,f49]) ).

fof(f49,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f29]) ).

fof(f351,plain,
    ~ member(sK4(intersection(sK2,sK3),sK1),intersection(sK2,sK3)),
    inference(unit_resulting_resolution,[],[f54,f342,f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ~ member(sK4(X0,X1),X0)
      | sP0(X0,X1)
      | ~ member(sK4(X0,X1),X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f342,plain,
    member(sK4(intersection(sK2,sK3),sK1),sK1),
    inference(subsumption_resolution,[],[f339,f336]) ).

fof(f339,plain,
    ( member(sK4(intersection(sK2,sK3),sK1),sK1)
    | ~ member(sK4(intersection(sK2,sK3),sK1),sK2) ),
    inference(resolution,[],[f335,f32]) ).

fof(f32,plain,
    ! [X3] :
      ( ~ member(X3,sK3)
      | member(X3,sK1)
      | ~ member(X3,sK2) ),
    inference(cnf_transformation,[],[f16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET578+3 : 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 : n015.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   : Tue Apr 30 01:37:47 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (7852)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (7855)WARNING: value z3 for option sas not known
% 0.13/0.37  % (7857)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  % (7859)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  % (7858)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  % (7855)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  % (7856)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37  % (7854)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  TRYING [1]
% 0.13/0.37  TRYING [2]
% 0.13/0.37  % (7853)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37  TRYING [3]
% 0.13/0.37  TRYING [4]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.13/0.38  % (7859)First to succeed.
% 0.13/0.38  TRYING [5]
% 0.13/0.38  TRYING [3]
% 0.13/0.38  % (7859)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (7859)------------------------------
% 0.13/0.38  % (7859)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (7859)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (7859)Memory used [KB]: 915
% 0.13/0.38  % (7859)Time elapsed: 0.012 s
% 0.13/0.38  % (7859)Instructions burned: 21 (million)
% 0.13/0.38  % (7859)------------------------------
% 0.13/0.38  % (7859)------------------------------
% 0.13/0.38  % (7852)Success in time 0.027 s
%------------------------------------------------------------------------------