TSTP Solution File: SEU149+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU149+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 : n001.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 18:32:09 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   29 (   6 unt;   0 def)
%            Number of atoms       :  149 ( 103 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  187 (  67   ~;  68   |;  40   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   80 (  64   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f67,plain,
    $false,
    inference(subsumption_resolution,[],[f66,f29]) ).

fof(f29,plain,
    sK2 != sK0,
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( sK2 != sK0
    & singleton(sK2) = unordered_pair(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).

fof(f16,plain,
    ( ? [X0,X1,X2] :
        ( X0 != X2
        & unordered_pair(X0,X1) = singleton(X2) )
   => ( sK2 != sK0
      & singleton(sK2) = unordered_pair(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( X0 != X2
      & unordered_pair(X0,X1) = singleton(X2) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ? [X2,X1,X0] :
      ( X0 != X2
      & singleton(X0) = unordered_pair(X2,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X0,X2,X1] :
        ( singleton(X0) = unordered_pair(X2,X1)
       => X0 = X2 ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( singleton(X0) = unordered_pair(X1,X2)
       => X0 = X1 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X2,X1] :
      ( singleton(X0) = unordered_pair(X1,X2)
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).

fof(f66,plain,
    sK2 = sK0,
    inference(resolution,[],[f51,f42]) ).

fof(f42,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f31]) ).

fof(f31,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( ~ in(sK3(X0,X1),X1)
            | sK3(X0,X1) != X0 )
          & ( in(sK3(X0,X1),X1)
            | sK3(X0,X1) = X0 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | X0 != X2 )
          & ( in(X2,X1)
            | X0 = X2 ) )
     => ( ( ~ in(sK3(X0,X1),X1)
          | sK3(X0,X1) != X0 )
        & ( in(sK3(X0,X1),X1)
          | sK3(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) )
      & ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( singleton(X0) = X1
    <=> ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f51,plain,
    in(sK0,singleton(sK2)),
    inference(superposition,[],[f48,f28]) ).

fof(f28,plain,
    singleton(sK2) = unordered_pair(sK0,sK1),
    inference(cnf_transformation,[],[f17]) ).

fof(f48,plain,
    ! [X3,X1] : in(X3,unordered_pair(X3,X1)),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X2,X3,X1] :
      ( in(X3,X2)
      | unordered_pair(X3,X1) != X2 ),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X2)
      | X0 != X3
      | unordered_pair(X0,X1) != X2 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 )
      & ( unordered_pair(X0,X1) = X2
        | ( ( ( sK4(X0,X1,X2) != X1
              & sK4(X0,X1,X2) != X0 )
            | ~ in(sK4(X0,X1,X2),X2) )
          & ( sK4(X0,X1,X2) = X1
            | sK4(X0,X1,X2) = X0
            | in(sK4(X0,X1,X2),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f26]) ).

fof(f26,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ( X1 != X4
              & X0 != X4 )
            | ~ in(X4,X2) )
          & ( X1 = X4
            | X0 = X4
            | in(X4,X2) ) )
     => ( ( ( sK4(X0,X1,X2) != X1
            & sK4(X0,X1,X2) != X0 )
          | ~ in(sK4(X0,X1,X2),X2) )
        & ( sK4(X0,X1,X2) = X1
          | sK4(X0,X1,X2) = X0
          | in(sK4(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X0,X1) != X2 )
      & ( unordered_pair(X0,X1) = X2
        | ? [X4] :
            ( ( ( X1 != X4
                & X0 != X4 )
              | ~ in(X4,X2) )
            & ( X1 = X4
              | X0 = X4
              | in(X4,X2) ) ) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X2,X1] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( in(X3,X1)
        <=> ( X2 = X3
            | X0 = X3 ) )
    <=> unordered_pair(X0,X2) = X1 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X2,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( ( X0 = X3
            | X1 = X3 )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SEU149+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n001.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 15:07:17 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.48  % (7105)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/37Mi)
% 0.19/0.48  % (7105)First to succeed.
% 0.19/0.49  % (7120)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 0.19/0.49  % (7105)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (7105)------------------------------
% 0.19/0.49  % (7105)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (7105)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (7105)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (7105)Memory used [KB]: 895
% 0.19/0.49  % (7105)Time elapsed: 0.098 s
% 0.19/0.49  % (7105)Instructions burned: 2 (million)
% 0.19/0.49  % (7105)------------------------------
% 0.19/0.49  % (7105)------------------------------
% 0.19/0.49  % (7102)Success in time 0.143 s
%------------------------------------------------------------------------------