TSTP Solution File: SET908+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 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 : n018.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 18:26:04 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   34 (  10 unt;   0 def)
%            Number of atoms       :  159 (  54 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  199 (  74   ~;  76   |;  38   &)
%                                         (   7 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-3 aty)
%            Number of variables   :   88 (  72   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f113,plain,
    $false,
    inference(resolution,[],[f106,f71]) ).

fof(f71,plain,
    ! [X2] : in(X2,singleton(X2)),
    inference(equality_resolution,[],[f70]) ).

fof(f70,plain,
    ! [X2,X0] :
      ( in(X2,X0)
      | singleton(X2) != X0 ),
    inference(equality_resolution,[],[f56]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( in(X2,X0)
      | X1 != X2
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ( ( ~ in(sK3(X0,X1),X0)
            | sK3(X0,X1) != X1 )
          & ( in(sK3(X0,X1),X0)
            | sK3(X0,X1) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | X1 != X3 )
          & ( in(X3,X0)
            | X1 = X3 ) )
     => ( ( ~ in(sK3(X0,X1),X0)
          | sK3(X0,X1) != X1 )
        & ( in(sK3(X0,X1),X0)
          | sK3(X0,X1) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | X1 != X3 )
            & ( in(X3,X0)
              | X1 = X3 ) ) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

fof(f106,plain,
    ! [X8] : ~ in(X8,singleton(sK1)),
    inference(subsumption_resolution,[],[f104,f68]) ).

fof(f68,plain,
    ! [X1] : ~ in(X1,empty_set),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | in(sK2(X0),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f28,f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ? [X2] : in(X2,X0)
     => in(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f28,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X2] : in(X2,X0) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X0] :
      ( ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 )
      & ( empty_set = X0
        | ? [X1] : in(X1,X0) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( ! [X1] : ~ in(X1,X0)
    <=> empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f104,plain,
    ! [X8] :
      ( ~ in(X8,singleton(sK1))
      | in(X8,empty_set) ),
    inference(superposition,[],[f73,f48]) ).

fof(f48,plain,
    empty_set = set_union2(singleton(sK1),sK0),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    empty_set = set_union2(singleton(sK1),sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f24,f25]) ).

fof(f25,plain,
    ( ? [X0,X1] : empty_set = set_union2(singleton(X1),X0)
   => empty_set = set_union2(singleton(sK1),sK0) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ? [X0,X1] : empty_set = set_union2(singleton(X1),X0),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ? [X1,X0] : empty_set = set_union2(singleton(X0),X1),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X1,X0] : empty_set != set_union2(singleton(X0),X1),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X1,X0] : empty_set != set_union2(singleton(X0),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t49_zfmisc_1) ).

fof(f73,plain,
    ! [X2,X1,X4] :
      ( in(X4,set_union2(X1,X2))
      | ~ in(X4,X1) ),
    inference(equality_resolution,[],[f62]) ).

fof(f62,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | ~ in(X4,X1)
      | set_union2(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ( ( ~ in(sK6(X0,X1,X2),X0)
            | ( ~ in(sK6(X0,X1,X2),X1)
              & ~ in(sK6(X0,X1,X2),X2) ) )
          & ( in(sK6(X0,X1,X2),X0)
            | in(sK6(X0,X1,X2),X1)
            | in(sK6(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | in(X4,X2)
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | ( ~ in(X3,X1)
              & ~ in(X3,X2) ) )
          & ( in(X3,X0)
            | in(X3,X1)
            | in(X3,X2) ) )
     => ( ( ~ in(sK6(X0,X1,X2),X0)
          | ( ~ in(sK6(X0,X1,X2),X1)
            & ~ in(sK6(X0,X1,X2),X2) ) )
        & ( in(sK6(X0,X1,X2),X0)
          | in(sK6(X0,X1,X2),X1)
          | in(sK6(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | in(X4,X2)
              | ~ in(X4,X0) )
            & ( in(X4,X0)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | set_union2(X1,X2) != X0 ) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X0,X2,X1] :
      ( ( set_union2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X2)
                & ~ in(X3,X1) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X2)
                & ~ in(X3,X1) ) ) )
        | set_union2(X2,X1) != X0 ) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X0,X2,X1] :
      ( ( set_union2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X2)
                & ~ in(X3,X1) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | in(X3,X1)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X2)
                & ~ in(X3,X1) ) ) )
        | set_union2(X2,X1) != X0 ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X2,X1] :
      ( set_union2(X2,X1) = X0
    <=> ! [X3] :
          ( ( in(X3,X2)
            | in(X3,X1) )
        <=> in(X3,X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X1,X0] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X0) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET908+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n018.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   : Tue Aug 30 14:33:10 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.51  % (24201)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.52  % (24192)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52  % (24189)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (24185)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.52  % (24201)First to succeed.
% 0.20/0.52  % (24188)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52  % (24190)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53  % (24213)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.53  % (24201)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (24201)------------------------------
% 0.20/0.53  % (24201)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (24201)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (24201)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (24201)Memory used [KB]: 5500
% 0.20/0.53  % (24201)Time elapsed: 0.116 s
% 0.20/0.53  % (24201)Instructions burned: 4 (million)
% 0.20/0.53  % (24201)------------------------------
% 0.20/0.53  % (24201)------------------------------
% 0.20/0.53  % (24184)Success in time 0.184 s
%------------------------------------------------------------------------------