TSTP Solution File: SEU130+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU130+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n004.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 : Wed Aug 31 18:32:02 EDT 2022

% Result   : Theorem 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   45 (  11 unt;   0 def)
%            Number of atoms       :  178 (  29 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  215 (  82   ~;  71   |;  47   &)
%                                         (   8 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   96 (  83   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f162,plain,
    $false,
    inference(subsumption_resolution,[],[f161,f143]) ).

fof(f143,plain,
    in(sK0(set_intersection2(sK1,sK2),sK1),sK1),
    inference(resolution,[],[f141,f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | in(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( in(sK0(X0,X1),X1)
          & ~ in(sK0(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f34,f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & ~ in(X3,X0) )
     => ( in(sK0(X0,X1),X1)
        & ~ in(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X0) ) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f141,plain,
    ~ subset(sK1,set_intersection2(sK1,sK2)),
    inference(subsumption_resolution,[],[f133,f81]) ).

fof(f81,plain,
    ! [X0,X1] : subset(set_intersection2(X1,X0),X1),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] : subset(set_intersection2(X1,X0),X1),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X1,X0] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(f133,plain,
    ( ~ subset(sK1,set_intersection2(sK1,sK2))
    | ~ subset(set_intersection2(sK1,sK2),sK1) ),
    inference(extensionality_resolution,[],[f78,f59]) ).

fof(f59,plain,
    sK1 != set_intersection2(sK1,sK2),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ( subset(sK1,sK2)
    & sK1 != set_intersection2(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f37,f38]) ).

fof(f38,plain,
    ( ? [X0,X1] :
        ( subset(X0,X1)
        & set_intersection2(X0,X1) != X0 )
   => ( subset(sK1,sK2)
      & sK1 != set_intersection2(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f37,plain,
    ? [X0,X1] :
      ( subset(X0,X1)
      & set_intersection2(X0,X1) != X0 ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ? [X1,X0] :
      ( subset(X1,X0)
      & set_intersection2(X1,X0) != X1 ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ ! [X1,X0] :
        ( subset(X1,X0)
       => set_intersection2(X1,X0) = X1 ),
    inference(rectify,[],[f15]) ).

fof(f15,negated_conjecture,
    ~ ! [X1,X0] :
        ( subset(X0,X1)
       => set_intersection2(X0,X1) = X0 ),
    inference(negated_conjecture,[],[f14]) ).

fof(f14,conjecture,
    ! [X1,X0] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ~ subset(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f54]) ).

fof(f54,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f53]) ).

fof(f53,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).

fof(f161,plain,
    ~ in(sK0(set_intersection2(sK1,sK2),sK1),sK1),
    inference(resolution,[],[f160,f130]) ).

fof(f130,plain,
    ! [X16] :
      ( in(X16,sK2)
      | ~ in(X16,sK1) ),
    inference(resolution,[],[f58,f60]) ).

fof(f60,plain,
    subset(sK1,sK2),
    inference(cnf_transformation,[],[f39]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | in(X2,X0)
      | ~ in(X2,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f160,plain,
    ~ in(sK0(set_intersection2(sK1,sK2),sK1),sK2),
    inference(subsumption_resolution,[],[f153,f143]) ).

fof(f153,plain,
    ( ~ in(sK0(set_intersection2(sK1,sK2),sK1),sK1)
    | ~ in(sK0(set_intersection2(sK1,sK2),sK1),sK2) ),
    inference(resolution,[],[f84,f144]) ).

fof(f144,plain,
    ~ in(sK0(set_intersection2(sK1,sK2),sK1),set_intersection2(sK1,sK2)),
    inference(resolution,[],[f141,f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | ~ in(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f84,plain,
    ! [X2,X3,X1] :
      ( in(X3,set_intersection2(X1,X2))
      | ~ in(X3,X1)
      | ~ in(X3,X2) ),
    inference(equality_resolution,[],[f73]) ).

fof(f73,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(X3,X1)
      | ~ in(X3,X2)
      | set_intersection2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X2) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ( ( ~ in(sK5(X0,X1,X2),X0)
            | ~ in(sK5(X0,X1,X2),X1)
            | ~ in(sK5(X0,X1,X2),X2) )
          & ( in(sK5(X0,X1,X2),X0)
            | ( in(sK5(X0,X1,X2),X1)
              & in(sK5(X0,X1,X2),X2) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f50,f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ~ in(X4,X1)
            | ~ in(X4,X2) )
          & ( in(X4,X0)
            | ( in(X4,X1)
              & in(X4,X2) ) ) )
     => ( ( ~ in(sK5(X0,X1,X2),X0)
          | ~ in(sK5(X0,X1,X2),X1)
          | ~ in(sK5(X0,X1,X2),X2) )
        & ( in(sK5(X0,X1,X2),X0)
          | ( in(sK5(X0,X1,X2),X1)
            & in(sK5(X0,X1,X2),X2) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X2) )
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ~ in(X3,X1)
              | ~ in(X3,X2) ) )
        | set_intersection2(X1,X2) != X0 )
      & ( set_intersection2(X1,X2) = X0
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ~ in(X4,X1)
              | ~ in(X4,X2) )
            & ( in(X4,X0)
              | ( in(X4,X1)
                & in(X4,X2) ) ) ) ) ),
    inference(rectify,[],[f49]) ).

fof(f49,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X0) != X2 )
      & ( set_intersection2(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) ) ) ) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( ( in(X3,X1)
                & in(X3,X0) )
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) ) )
        | set_intersection2(X1,X0) != X2 )
      & ( set_intersection2(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ~ in(X3,X1)
              | ~ in(X3,X0) )
            & ( in(X3,X2)
              | ( in(X3,X1)
                & in(X3,X0) ) ) ) ) ),
    inference(nnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( ( in(X3,X1)
            & in(X3,X0) )
        <=> in(X3,X2) )
    <=> set_intersection2(X1,X0) = X2 ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0,X2] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU130+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:37:49 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.44  % (17154)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/498Mi)
% 0.20/0.44  % (17146)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.45  % (17154)First to succeed.
% 0.20/0.46  % (17154)Refutation found. Thanks to Tanya!
% 0.20/0.46  % SZS status Theorem for theBenchmark
% 0.20/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.46  % (17154)------------------------------
% 0.20/0.46  % (17154)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.46  % (17154)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.46  % (17154)Termination reason: Refutation
% 0.20/0.46  
% 0.20/0.46  % (17154)Memory used [KB]: 1023
% 0.20/0.46  % (17154)Time elapsed: 0.037 s
% 0.20/0.46  % (17154)Instructions burned: 4 (million)
% 0.20/0.46  % (17154)------------------------------
% 0.20/0.46  % (17154)------------------------------
% 0.20/0.46  % (17131)Success in time 0.106 s
%------------------------------------------------------------------------------