TSTP Solution File: SEU159+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU159+3 : 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_uns --cores 0 -t %d %s

% Computer : n021.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 18:26:59 EDT 2022

% Result   : Theorem 0.21s 0.56s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   55 (   7 unt;   0 def)
%            Number of atoms       :  225 (  74 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  262 (  92   ~; 106   |;  48   &)
%                                         (  10 <=>;   5  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-3 aty)
%            Number of variables   :  112 (  90   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f95,plain,
    $false,
    inference(unit_resulting_resolution,[],[f72,f67,f94,f44]) ).

fof(f44,plain,
    ( ~ subset(unordered_pair(sK2,sK4),sK3)
    | ~ in(sK2,sK3)
    | ~ in(sK4,sK3) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ( ( ~ subset(unordered_pair(sK2,sK4),sK3)
      | ~ in(sK4,sK3)
      | ~ in(sK2,sK3) )
    & ( subset(unordered_pair(sK2,sK4),sK3)
      | ( in(sK4,sK3)
        & in(sK2,sK3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f25,f26]) ).

fof(f26,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ subset(unordered_pair(X0,X2),X1)
          | ~ in(X2,X1)
          | ~ in(X0,X1) )
        & ( subset(unordered_pair(X0,X2),X1)
          | ( in(X2,X1)
            & in(X0,X1) ) ) )
   => ( ( ~ subset(unordered_pair(sK2,sK4),sK3)
        | ~ in(sK4,sK3)
        | ~ in(sK2,sK3) )
      & ( subset(unordered_pair(sK2,sK4),sK3)
        | ( in(sK4,sK3)
          & in(sK2,sK3) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ? [X0,X1,X2] :
      ( ( ~ subset(unordered_pair(X0,X2),X1)
        | ~ in(X2,X1)
        | ~ in(X0,X1) )
      & ( subset(unordered_pair(X0,X2),X1)
        | ( in(X2,X1)
          & in(X0,X1) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ? [X2,X1,X0] :
      ( ( ~ subset(unordered_pair(X2,X0),X1)
        | ~ in(X0,X1)
        | ~ in(X2,X1) )
      & ( subset(unordered_pair(X2,X0),X1)
        | ( in(X0,X1)
          & in(X2,X1) ) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ? [X2,X1,X0] :
      ( ( ~ subset(unordered_pair(X2,X0),X1)
        | ~ in(X0,X1)
        | ~ in(X2,X1) )
      & ( subset(unordered_pair(X2,X0),X1)
        | ( in(X0,X1)
          & in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ? [X2,X1,X0] :
      ( ( in(X0,X1)
        & in(X2,X1) )
    <~> subset(unordered_pair(X2,X0),X1) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ~ ! [X2,X1,X0] :
        ( subset(unordered_pair(X2,X0),X1)
      <=> ( in(X0,X1)
          & in(X2,X1) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( in(X0,X2)
          & in(X1,X2) )
      <=> subset(unordered_pair(X0,X1),X2) ),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X1,X2,X0] :
      ( ( in(X0,X2)
        & in(X1,X2) )
    <=> subset(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(f94,plain,
    subset(unordered_pair(sK2,sK4),sK3),
    inference(subsumption_resolution,[],[f93,f67]) ).

fof(f93,plain,
    ( subset(unordered_pair(sK2,sK4),sK3)
    | ~ in(sK2,sK3) ),
    inference(superposition,[],[f46,f89]) ).

fof(f89,plain,
    sK2 = sK5(sK3,unordered_pair(sK2,sK4)),
    inference(subsumption_resolution,[],[f88,f72]) ).

fof(f88,plain,
    ( sK2 = sK5(sK3,unordered_pair(sK2,sK4))
    | ~ in(sK4,sK3) ),
    inference(subsumption_resolution,[],[f86,f67]) ).

fof(f86,plain,
    ( ~ in(sK2,sK3)
    | sK2 = sK5(sK3,unordered_pair(sK2,sK4))
    | ~ in(sK4,sK3) ),
    inference(resolution,[],[f85,f44]) ).

fof(f85,plain,
    ( subset(unordered_pair(sK2,sK4),sK3)
    | sK2 = sK5(sK3,unordered_pair(sK2,sK4)) ),
    inference(subsumption_resolution,[],[f83,f72]) ).

fof(f83,plain,
    ( ~ in(sK4,sK3)
    | sK2 = sK5(sK3,unordered_pair(sK2,sK4))
    | subset(unordered_pair(sK2,sK4),sK3) ),
    inference(superposition,[],[f46,f80]) ).

fof(f80,plain,
    ( sK4 = sK5(sK3,unordered_pair(sK2,sK4))
    | sK2 = sK5(sK3,unordered_pair(sK2,sK4)) ),
    inference(subsumption_resolution,[],[f76,f72]) ).

fof(f76,plain,
    ( ~ in(sK4,sK3)
    | sK4 = sK5(sK3,unordered_pair(sK2,sK4))
    | sK2 = sK5(sK3,unordered_pair(sK2,sK4)) ),
    inference(resolution,[],[f73,f54]) ).

fof(f54,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,unordered_pair(X0,X1))
      | X0 = X3
      | X1 = X3 ),
    inference(equality_resolution,[],[f53]) ).

fof(f53,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X3
      | X0 = X3
      | ~ in(X3,X2)
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X0,X1) != X2 )
      & ( unordered_pair(X0,X1) = X2
        | ( ( ~ in(sK6(X0,X1,X2),X2)
            | ( sK6(X0,X1,X2) != X1
              & sK6(X0,X1,X2) != X0 ) )
          & ( in(sK6(X0,X1,X2),X2)
            | sK6(X0,X1,X2) = X1
            | sK6(X0,X1,X2) = X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f34,f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X2)
            | ( X1 != X4
              & X0 != X4 ) )
          & ( in(X4,X2)
            | X1 = X4
            | X0 = X4 ) )
     => ( ( ~ in(sK6(X0,X1,X2),X2)
          | ( sK6(X0,X1,X2) != X1
            & sK6(X0,X1,X2) != X0 ) )
        & ( in(sK6(X0,X1,X2),X2)
          | sK6(X0,X1,X2) = X1
          | sK6(X0,X1,X2) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X0,X1) != X2 )
      & ( unordered_pair(X0,X1) = X2
        | ? [X4] :
            ( ( ~ in(X4,X2)
              | ( X1 != X4
                & X0 != X4 ) )
            & ( in(X4,X2)
              | X1 = X4
              | X0 = X4 ) ) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( in(X3,X1)
              | X2 = X3
              | X0 = X3 ) ) ) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( in(X3,X1)
              | X2 = X3
              | X0 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( ( X2 = X3
            | X0 = X3 )
        <=> in(X3,X1) )
    <=> unordered_pair(X0,X2) = X1 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X2,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( ( X0 = X3
            | X1 = X3 )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f73,plain,
    ( in(sK5(sK3,unordered_pair(sK2,sK4)),unordered_pair(sK2,sK4))
    | ~ in(sK4,sK3) ),
    inference(subsumption_resolution,[],[f63,f67]) ).

fof(f63,plain,
    ( ~ in(sK2,sK3)
    | in(sK5(sK3,unordered_pair(sK2,sK4)),unordered_pair(sK2,sK4))
    | ~ in(sK4,sK3) ),
    inference(resolution,[],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
      | in(sK5(X0,X1),X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( ~ in(sK5(X0,X1),X0)
          & in(sK5(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ in(X3,X0)
          & in(X3,X1) )
     => ( ~ in(sK5(X0,X1),X0)
        & in(sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( ~ in(X3,X0)
            & in(X3,X1) ) ) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
          | ~ in(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f4]) ).

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

fof(f46,plain,
    ! [X0,X1] :
      ( ~ in(sK5(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f67,plain,
    in(sK2,sK3),
    inference(duplicate_literal_removal,[],[f65]) ).

fof(f65,plain,
    ( in(sK2,sK3)
    | in(sK2,sK3) ),
    inference(resolution,[],[f59,f58]) ).

fof(f58,plain,
    ! [X3,X1] : in(X3,unordered_pair(X3,X1)),
    inference(equality_resolution,[],[f57]) ).

fof(f57,plain,
    ! [X2,X3,X1] :
      ( in(X3,X2)
      | unordered_pair(X3,X1) != X2 ),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | X0 != X3
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK2,sK4))
      | in(X0,sK3)
      | in(sK2,sK3) ),
    inference(resolution,[],[f42,f47]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | ~ in(X2,X1)
      | in(X2,X0) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f42,plain,
    ( subset(unordered_pair(sK2,sK4),sK3)
    | in(sK2,sK3) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f72,plain,
    in(sK4,sK3),
    inference(duplicate_literal_removal,[],[f69]) ).

fof(f69,plain,
    ( in(sK4,sK3)
    | in(sK4,sK3) ),
    inference(resolution,[],[f60,f56]) ).

fof(f56,plain,
    ! [X3,X0] : in(X3,unordered_pair(X0,X3)),
    inference(equality_resolution,[],[f55]) ).

fof(f55,plain,
    ! [X2,X3,X0] :
      ( in(X3,X2)
      | unordered_pair(X0,X3) != X2 ),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | X1 != X3
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK2,sK4))
      | in(sK4,sK3)
      | in(X0,sK3) ),
    inference(resolution,[],[f43,f47]) ).

fof(f43,plain,
    ( subset(unordered_pair(sK2,sK4),sK3)
    | in(sK4,sK3) ),
    inference(cnf_transformation,[],[f27]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU159+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n021.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 14:39:41 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.54  % (1983)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.55  % (1983)Refutation not found, incomplete strategy% (1983)------------------------------
% 0.21/0.55  % (1983)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55  % (1983)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55  % (1983)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.55  
% 0.21/0.55  % (1983)Memory used [KB]: 5884
% 0.21/0.55  % (1983)Time elapsed: 0.125 s
% 0.21/0.55  % (1983)Instructions burned: 2 (million)
% 0.21/0.55  % (1983)------------------------------
% 0.21/0.55  % (1983)------------------------------
% 0.21/0.55  % (2002)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.55  % (1986)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.56  % (2000)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.56  % (2002)First to succeed.
% 0.21/0.56  % (1991)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.56  % (2003)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.56  % (1991)Refutation not found, incomplete strategy% (1991)------------------------------
% 0.21/0.56  % (1991)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56  % (1991)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.56  % (1991)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.56  
% 0.21/0.56  % (1991)Memory used [KB]: 1535
% 0.21/0.56  % (1991)Time elapsed: 0.146 s
% 0.21/0.56  % (1991)Instructions burned: 3 (million)
% 0.21/0.56  % (1991)------------------------------
% 0.21/0.56  % (1991)------------------------------
% 0.21/0.56  % (2002)Refutation found. Thanks to Tanya!
% 0.21/0.56  % SZS status Theorem for theBenchmark
% 0.21/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.56  % (2002)------------------------------
% 0.21/0.56  % (2002)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56  % (2002)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.56  % (2002)Termination reason: Refutation
% 0.21/0.56  
% 0.21/0.56  % (2002)Memory used [KB]: 1535
% 0.21/0.56  % (2002)Time elapsed: 0.085 s
% 0.21/0.56  % (2002)Instructions burned: 4 (million)
% 0.21/0.56  % (2002)------------------------------
% 0.21/0.56  % (2002)------------------------------
% 0.21/0.56  % (1978)Success in time 0.214 s
%------------------------------------------------------------------------------