TSTP Solution File: SEU133+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 09:27:18 EDT 2024

% Result   : Theorem 0.15s 0.39s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   34 (  10 unt;   0 def)
%            Number of atoms       :  123 (   5 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  146 (  57   ~;  49   |;  28   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   89 (  79   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f174,plain,
    $false,
    inference(unit_resulting_resolution,[],[f91,f87,f68,f57]) ).

fof(f57,plain,
    ! [X2,X0,X1,X4] :
      ( ~ sP1(X0,X1,X2)
      | ~ in(X4,X2)
      | sP0(X1,X4,X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( sP1(X0,X1,X2)
        | ( ( ~ sP0(X1,sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( sP0(X1,sK5(X0,X1,X2),X0)
            | in(sK5(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,[sK5])],[f34,f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ sP0(X1,X3,X0)
            | ~ in(X3,X2) )
          & ( sP0(X1,X3,X0)
            | in(X3,X2) ) )
     => ( ( ~ sP0(X1,sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( sP0(X1,sK5(X0,X1,X2),X0)
          | in(sK5(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,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,[],[f33]) ).

fof(f33,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,[],[f25]) ).

fof(f25,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(f68,plain,
    ! [X0,X1] : sP1(X0,X1,set_difference(X0,X1)),
    inference(equality_resolution,[],[f64]) ).

fof(f64,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X1,X2)
      | set_difference(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(X0,X1) = X2
        | ~ sP1(X0,X1,X2) )
      & ( sP1(X0,X1,X2)
        | set_difference(X0,X1) != X2 ) ),
    inference(nnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> sP1(X0,X1,X2) ),
    inference(definition_folding,[],[f3,f25,f24]) ).

fof(f24,plain,
    ! [X1,X3,X0] :
      ( sP0(X1,X3,X0)
    <=> ( ~ in(X3,X1)
        & in(X3,X0) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f3,axiom,
    ! [X0,X1,X2] :
      ( set_difference(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).

fof(f87,plain,
    in(sK4(set_difference(sK2,sK3),sK2),set_difference(sK2,sK3)),
    inference(unit_resulting_resolution,[],[f45,f53]) ).

fof(f53,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ in(sK4(X0,X1),X1)
          & in(sK4(X0,X1),X0) ) )
      & ( ! [X3] :
            ( in(X3,X1)
            | ~ in(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X1)
          & in(X2,X0) )
     => ( ~ in(sK4(X0,X1),X1)
        & in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,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,[],[f29]) ).

fof(f29,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,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f45,plain,
    ~ subset(set_difference(sK2,sK3),sK2),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ~ subset(set_difference(sK2,sK3),sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f18,f27]) ).

fof(f27,plain,
    ( ? [X0,X1] : ~ subset(set_difference(X0,X1),X0)
   => ~ subset(set_difference(sK2,sK3),sK2) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1] : ~ subset(set_difference(X0,X1),X0),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).

fof(f91,plain,
    ! [X0] : ~ sP0(X0,sK4(set_difference(sK2,sK3),sK2),sK2),
    inference(unit_resulting_resolution,[],[f90,f61]) ).

fof(f61,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X0,X1,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,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,[],[f38]) ).

fof(f38,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,[],[f37]) ).

fof(f37,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,[],[f24]) ).

fof(f90,plain,
    ~ in(sK4(set_difference(sK2,sK3),sK2),sK2),
    inference(unit_resulting_resolution,[],[f45,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SEU133+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 11:14:16 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (7270)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (7273)WARNING: value z3 for option sas not known
% 0.15/0.38  % (7274)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (7271)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (7275)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)
% 0.15/0.38  % (7273)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)
% 0.15/0.38  % (7276)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)
% 0.15/0.38  % (7277)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)
% 0.15/0.38  % (7272)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  TRYING [1]
% 0.15/0.38  TRYING [2]
% 0.15/0.38  TRYING [3]
% 0.15/0.38  % (7277)First to succeed.
% 0.15/0.39  % (7273)Also succeeded, but the first one will report.
% 0.15/0.39  % (7277)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-7270"
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [4]
% 0.15/0.39  % (7277)Refutation found. Thanks to Tanya!
% 0.15/0.39  % SZS status Theorem for theBenchmark
% 0.15/0.39  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39  % (7277)------------------------------
% 0.15/0.39  % (7277)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (7277)Termination reason: Refutation
% 0.15/0.39  
% 0.15/0.39  % (7277)Memory used [KB]: 833
% 0.15/0.39  % (7277)Time elapsed: 0.007 s
% 0.15/0.39  % (7277)Instructions burned: 7 (million)
% 0.15/0.39  % (7270)Success in time 0.023 s
%------------------------------------------------------------------------------