TSTP Solution File: SET872+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET872+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 : n027.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 18:25:58 EDT 2022

% Result   : Theorem 1.55s 0.58s
% Output   : Refutation 1.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   43 (  14 unt;   0 def)
%            Number of atoms       :  184 (  91 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  223 (  82   ~;  83   |;  43   &)
%                                         (  10 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  101 (  85   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f123,plain,
    $false,
    inference(subsumption_resolution,[],[f122,f68]) ).

fof(f68,plain,
    ~ subset(sF7,sF8),
    inference(definition_folding,[],[f57,f67,f66]) ).

fof(f66,plain,
    singleton(sK6) = sF7,
    introduced(function_definition,[]) ).

fof(f67,plain,
    sF8 = unordered_pair(sK6,sK5),
    introduced(function_definition,[]) ).

fof(f57,plain,
    ~ subset(singleton(sK6),unordered_pair(sK6,sK5)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ subset(singleton(sK6),unordered_pair(sK6,sK5)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f36,f37]) ).

fof(f37,plain,
    ( ? [X0,X1] : ~ subset(singleton(X1),unordered_pair(X1,X0))
   => ~ subset(singleton(sK6),unordered_pair(sK6,sK5)) ),
    introduced(choice_axiom,[]) ).

fof(f36,plain,
    ? [X0,X1] : ~ subset(singleton(X1),unordered_pair(X1,X0)),
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ? [X1,X0] : ~ subset(singleton(X0),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X0] : subset(singleton(X0),unordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X0] : subset(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_zfmisc_1) ).

fof(f122,plain,
    subset(sF7,sF8),
    inference(subsumption_resolution,[],[f121,f71]) ).

fof(f71,plain,
    in(sK6,sF8),
    inference(superposition,[],[f62,f67]) ).

fof(f62,plain,
    ! [X3,X1] : in(X3,unordered_pair(X3,X1)),
    inference(equality_resolution,[],[f61]) ).

fof(f61,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | unordered_pair(X3,X1) != X0 ),
    inference(equality_resolution,[],[f50]) ).

fof(f50,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | X2 != X3
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ( ( ( sK2(X0,X1,X2) != X2
              & sK2(X0,X1,X2) != X1 )
            | ~ in(sK2(X0,X1,X2),X0) )
          & ( sK2(X0,X1,X2) = X2
            | sK2(X0,X1,X2) = X1
            | in(sK2(X0,X1,X2),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( X2 != X4
              & X1 != X4 )
            | ~ in(X4,X0) )
          & ( X2 = X4
            | X1 = X4
            | in(X4,X0) ) )
     => ( ( ( sK2(X0,X1,X2) != X2
            & sK2(X0,X1,X2) != X1 )
          | ~ in(sK2(X0,X1,X2),X0) )
        & ( sK2(X0,X1,X2) = X2
          | sK2(X0,X1,X2) = X1
          | in(sK2(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ? [X4] :
            ( ( ( X2 != X4
                & X1 != X4 )
              | ~ in(X4,X0) )
            & ( X2 = X4
              | X1 = X4
              | in(X4,X0) ) ) ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ( X1 != X3
                & X0 != X3 )
              | ~ in(X3,X2) )
            & ( X1 = X3
              | X0 = X3
              | in(X3,X2) ) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) )
    <=> unordered_pair(X1,X0) = X2 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f121,plain,
    ( ~ in(sK6,sF8)
    | subset(sF7,sF8) ),
    inference(superposition,[],[f53,f117]) ).

fof(f117,plain,
    sK6 = sK4(sF8,sF7),
    inference(resolution,[],[f103,f68]) ).

fof(f103,plain,
    ! [X0] :
      ( subset(sF7,X0)
      | sK6 = sK4(X0,sF7) ),
    inference(resolution,[],[f98,f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( in(sK4(X0,X1),X1)
          & ~ in(sK4(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f33,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & ~ in(X3,X0) )
     => ( in(sK4(X0,X1),X1)
        & ~ in(sK4(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f33,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,[],[f32]) ).

fof(f32,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,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f98,plain,
    ! [X0] :
      ( ~ in(X0,sF7)
      | sK6 = X0 ),
    inference(superposition,[],[f60,f66]) ).

fof(f60,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f42]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ in(X2,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( sK1(X0,X1) != X0
            | ~ in(sK1(X0,X1),X1) )
          & ( sK1(X0,X1) = X0
            | in(sK1(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X0 != X3
            | ~ in(X3,X1) )
          & ( X0 = X3
            | in(X3,X1) ) )
     => ( ( sK1(X0,X1) != X0
          | ~ in(sK1(X0,X1),X1) )
        & ( sK1(X0,X1) = X0
          | in(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( X0 != X3
              | ~ in(X3,X1) )
            & ( X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X2] :
            ( ( X1 != X2
              | ~ in(X2,X0) )
            & ( X1 = X2
              | in(X2,X0) ) ) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> X1 = X2 )
    <=> singleton(X1) = X0 ),
    inference(rectify,[],[f3]) ).

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

fof(f53,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f35]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET872+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % 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 : n027.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 14:42:46 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.55  % (6640)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56  % (6641)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56  % (6632)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.20/0.56  % (6633)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.20/0.56  % (6649)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/177Mi)
% 0.20/0.56  % (6640)First to succeed.
% 0.20/0.56  % (6626)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.57  % (6648)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)
% 1.55/0.57  % (6649)Also succeeded, but the first one will report.
% 1.55/0.58  % (6640)Refutation found. Thanks to Tanya!
% 1.55/0.58  % SZS status Theorem for theBenchmark
% 1.55/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 1.55/0.58  % (6640)------------------------------
% 1.55/0.58  % (6640)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.55/0.58  % (6640)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.55/0.58  % (6640)Termination reason: Refutation
% 1.55/0.58  
% 1.55/0.58  % (6640)Memory used [KB]: 5500
% 1.55/0.58  % (6640)Time elapsed: 0.146 s
% 1.55/0.58  % (6640)Instructions burned: 4 (million)
% 1.55/0.58  % (6640)------------------------------
% 1.55/0.58  % (6640)------------------------------
% 1.55/0.58  % (6621)Success in time 0.225 s
%------------------------------------------------------------------------------