TSTP Solution File: SEU128+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU128+2 : TPTP v8.2.0. Released v3.3.0.
% 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 03:53:06 EDT 2024

% Result   : Theorem 1.62s 0.61s
% Output   : Refutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   44 (  14 unt;   0 def)
%            Number of atoms       :  150 (   7 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  165 (  59   ~;  52   |;  40   &)
%                                         (   8 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  104 (  89   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f13311,plain,
    $false,
    inference(subsumption_resolution,[],[f13204,f9163]) ).

fof(f9163,plain,
    sP0(sK5,sK10(sK4,set_intersection2(sK5,sK6)),sK6),
    inference(unit_resulting_resolution,[],[f2693,f2697,f150]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X0)
      | sP0(X0,X1,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ~ in(X1,X0)
        | ~ in(X1,X2) )
      & ( ( in(X1,X0)
          & in(X1,X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f89]) ).

fof(f89,plain,
    ! [X1,X3,X0] :
      ( ( sP0(X1,X3,X0)
        | ~ in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( in(X3,X1)
          & in(X3,X0) )
        | ~ sP0(X1,X3,X0) ) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X1,X3,X0] :
      ( ( sP0(X1,X3,X0)
        | ~ in(X3,X1)
        | ~ in(X3,X0) )
      & ( ( in(X3,X1)
          & in(X3,X0) )
        | ~ sP0(X1,X3,X0) ) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X1,X3,X0] :
      ( sP0(X1,X3,X0)
    <=> ( in(X3,X1)
        & in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f2697,plain,
    in(sK10(sK4,set_intersection2(sK5,sK6)),sK6),
    inference(unit_resulting_resolution,[],[f527,f105,f139]) ).

fof(f139,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ in(X3,X0)
      | in(X3,X1) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK10(X0,X1),X1)
          & in(sK10(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f81,f82]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK10(X0,X1),X1)
        & in(sK10(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f105,plain,
    subset(sK4,sK6),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ( ~ subset(sK4,set_intersection2(sK5,sK6))
    & subset(sK4,sK6)
    & subset(sK4,sK5) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f44,f67]) ).

fof(f67,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(X0,set_intersection2(X1,X2))
        & subset(X0,X2)
        & subset(X0,X1) )
   => ( ~ subset(sK4,set_intersection2(sK5,sK6))
      & subset(sK4,sK6)
      & subset(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,set_intersection2(X1,X2))
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(flattening,[],[f43]) ).

fof(f43,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,set_intersection2(X1,X2))
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( subset(X0,X2)
          & subset(X0,X1) )
       => subset(X0,set_intersection2(X1,X2)) ),
    inference(negated_conjecture,[],[f24]) ).

fof(f24,conjecture,
    ! [X0,X1,X2] :
      ( ( subset(X0,X2)
        & subset(X0,X1) )
     => subset(X0,set_intersection2(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).

fof(f527,plain,
    in(sK10(sK4,set_intersection2(sK5,sK6)),sK4),
    inference(unit_resulting_resolution,[],[f106,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK10(X0,X1),X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f106,plain,
    ~ subset(sK4,set_intersection2(sK5,sK6)),
    inference(cnf_transformation,[],[f68]) ).

fof(f2693,plain,
    in(sK10(sK4,set_intersection2(sK5,sK6)),sK5),
    inference(unit_resulting_resolution,[],[f527,f104,f139]) ).

fof(f104,plain,
    subset(sK4,sK5),
    inference(cnf_transformation,[],[f68]) ).

fof(f13204,plain,
    ~ sP0(sK5,sK10(sK4,set_intersection2(sK5,sK6)),sK6),
    inference(unit_resulting_resolution,[],[f1235,f289,f145]) ).

fof(f145,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ sP0(X1,X4,X0)
      | in(X4,X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ sP0(X1,sK11(X0,X1,X2),X0)
            | ~ in(sK11(X0,X1,X2),X2) )
          & ( sP0(X1,sK11(X0,X1,X2),X0)
            | in(sK11(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP0(X1,X4,X0) )
            & ( sP0(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f85,f86]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP0(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP0(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP0(X1,sK11(X0,X1,X2),X0)
          | ~ in(sK11(X0,X1,X2),X2) )
        & ( sP0(X1,sK11(X0,X1,X2),X0)
          | in(sK11(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f85,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP0(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP0(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ~ sP0(X1,X4,X0) )
            & ( sP0(X1,X4,X0)
              | ~ in(X4,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(rectify,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ? [X3] :
            ( ( ~ sP0(X1,X3,X0)
              | ~ in(X3,X2) )
            & ( sP0(X1,X3,X0)
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ~ sP0(X1,X3,X0) )
            & ( sP0(X1,X3,X0)
              | ~ in(X3,X2) ) )
        | ~ sP1(X0,X1,X2) ) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( sP1(X0,X1,X2)
    <=> ! [X3] :
          ( in(X3,X2)
        <=> sP0(X1,X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f289,plain,
    ! [X0,X1] : sP1(X0,X1,set_intersection2(X1,X0)),
    inference(superposition,[],[f167,f129]) ).

fof(f129,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f167,plain,
    ! [X0,X1] : sP1(X0,X1,set_intersection2(X0,X1)),
    inference(equality_resolution,[],[f151]) ).

fof(f151,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | set_intersection2(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1,X2] :
      ( ( set_intersection2(X0,X1) = X2
        | ~ sP1(X0,X1,X2) )
      & ( sP1(X0,X1,X2)
        | set_intersection2(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> sP1(X0,X1,X2) ),
    inference(definition_folding,[],[f8,f62,f61]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

fof(f1235,plain,
    ~ in(sK10(sK4,set_intersection2(sK5,sK6)),set_intersection2(sK5,sK6)),
    inference(unit_resulting_resolution,[],[f106,f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ~ in(sK10(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11  % Problem    : SEU128+2 : TPTP v8.2.0. Released v3.3.0.
% 0.02/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Sun May 19 17:14:37 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (5917)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (5920)WARNING: value z3 for option sas not known
% 0.13/0.36  % (5920)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)
% 0.13/0.36  % (5921)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (5922)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)
% 0.13/0.36  % (5923)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)
% 0.13/0.36  % (5924)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)
% 0.13/0.36  % (5918)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (5919)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.19/0.37  TRYING [3]
% 0.19/0.37  TRYING [4]
% 0.19/0.38  TRYING [1]
% 0.19/0.38  TRYING [2]
% 0.19/0.40  TRYING [5]
% 0.19/0.40  TRYING [3]
% 0.19/0.46  TRYING [6]
% 0.19/0.48  TRYING [4]
% 1.62/0.59  TRYING [7]
% 1.62/0.60  % (5924)First to succeed.
% 1.62/0.60  % (5924)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-5917"
% 1.62/0.61  % (5924)Refutation found. Thanks to Tanya!
% 1.62/0.61  % SZS status Theorem for theBenchmark
% 1.62/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.62/0.61  % (5924)------------------------------
% 1.62/0.61  % (5924)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.62/0.61  % (5924)Termination reason: Refutation
% 1.62/0.61  
% 1.62/0.61  % (5924)Memory used [KB]: 3184
% 1.62/0.61  % (5924)Time elapsed: 0.245 s
% 1.62/0.61  % (5924)Instructions burned: 400 (million)
% 1.62/0.61  % (5917)Success in time 0.247 s
%------------------------------------------------------------------------------