TSTP Solution File: SEU149+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU149+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_sat --cores 0 -t %d %s

% Computer : n013.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 18:32:10 EDT 2022

% Result   : Theorem 0.16s 0.51s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (  16 unt;   0 def)
%            Number of atoms       :  162 ( 111 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  192 (  70   ~;  71   |;  40   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 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   :   94 (  78   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f70,plain,
    $false,
    inference(subsumption_resolution,[],[f69,f68]) ).

fof(f68,plain,
    sK1 != sK2,
    inference(backward_demodulation,[],[f36,f64]) ).

fof(f64,plain,
    sK1 = sK3,
    inference(resolution,[],[f57,f55]) ).

fof(f55,plain,
    ! [X2,X1] :
      ( ~ in(X2,singleton(X1))
      | X1 = X2 ),
    inference(equality_resolution,[],[f45]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ in(X2,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X0)
              | X1 != X2 )
            & ( X1 = X2
              | ~ in(X2,X0) ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ( ( sK5(X0,X1) != X1
            | ~ in(sK5(X0,X1),X0) )
          & ( sK5(X0,X1) = X1
            | in(sK5(X0,X1),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X1 != X3
            | ~ in(X3,X0) )
          & ( X1 = X3
            | in(X3,X0) ) )
     => ( ( sK5(X0,X1) != X1
          | ~ in(sK5(X0,X1),X0) )
        & ( sK5(X0,X1) = X1
          | in(sK5(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

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

fof(f26,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

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

fof(f57,plain,
    in(sK1,singleton(sK3)),
    inference(superposition,[],[f50,f56]) ).

fof(f56,plain,
    singleton(sK3) = unordered_pair(sK1,sK2),
    inference(forward_demodulation,[],[f35,f32]) ).

fof(f32,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f35,plain,
    singleton(sK3) = unordered_pair(sK2,sK1),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ( sK3 != sK2
    & singleton(sK3) = unordered_pair(sK2,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f18,f19]) ).

fof(f19,plain,
    ( ? [X0,X1,X2] :
        ( X1 != X2
        & unordered_pair(X1,X0) = singleton(X2) )
   => ( sK3 != sK2
      & singleton(sK3) = unordered_pair(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ? [X0,X1,X2] :
      ( X1 != X2
      & unordered_pair(X1,X0) = singleton(X2) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ? [X2,X1,X0] :
      ( X0 != X1
      & singleton(X0) = unordered_pair(X1,X2) ),
    inference(ennf_transformation,[],[f8]) ).

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

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

fof(f50,plain,
    ! [X3,X0] : in(X3,unordered_pair(X3,X0)),
    inference(equality_resolution,[],[f49]) ).

fof(f49,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | unordered_pair(X3,X0) != X1 ),
    inference(equality_resolution,[],[f41]) ).

fof(f41,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | X2 != X3
      | unordered_pair(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X2,X0) != X1 )
      & ( unordered_pair(X2,X0) = X1
        | ( ( ~ in(sK4(X0,X1,X2),X1)
            | ( sK4(X0,X1,X2) != X2
              & sK4(X0,X1,X2) != X0 ) )
          & ( in(sK4(X0,X1,X2),X1)
            | sK4(X0,X1,X2) = X2
            | sK4(X0,X1,X2) = X0 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f23,f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X1)
            | ( X2 != X4
              & X0 != X4 ) )
          & ( in(X4,X1)
            | X2 = X4
            | X0 = X4 ) )
     => ( ( ~ in(sK4(X0,X1,X2),X1)
          | ( sK4(X0,X1,X2) != X2
            & sK4(X0,X1,X2) != X0 ) )
        & ( in(sK4(X0,X1,X2),X1)
          | sK4(X0,X1,X2) = X2
          | sK4(X0,X1,X2) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X2,X0) != X1 )
      & ( unordered_pair(X2,X0) = X1
        | ? [X4] :
            ( ( ~ in(X4,X1)
              | ( X2 != X4
                & X0 != X4 ) )
            & ( in(X4,X1)
              | X2 = X4
              | X0 = X4 ) ) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X2 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) )
            & ( in(X3,X1)
              | X0 = X3
              | X2 = X3 ) ) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X2,X1,X0] :
      ( ( ! [X3] :
            ( ( X0 = X3
              | X2 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) ) )
        | unordered_pair(X0,X2) != X1 )
      & ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ( X0 != X3
                & X2 != X3 ) )
            & ( in(X3,X1)
              | X0 = X3
              | X2 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f10]) ).

fof(f10,plain,
    ! [X2,X1,X0] :
      ( ! [X3] :
          ( ( X0 = X3
            | X2 = X3 )
        <=> in(X3,X1) )
    <=> unordered_pair(X0,X2) = X1 ),
    inference(rectify,[],[f4]) ).

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

fof(f36,plain,
    sK3 != sK2,
    inference(cnf_transformation,[],[f20]) ).

fof(f69,plain,
    sK1 = sK2,
    inference(resolution,[],[f65,f55]) ).

fof(f65,plain,
    in(sK2,singleton(sK1)),
    inference(backward_demodulation,[],[f58,f64]) ).

fof(f58,plain,
    in(sK2,singleton(sK3)),
    inference(superposition,[],[f52,f56]) ).

fof(f52,plain,
    ! [X2,X3] : in(X3,unordered_pair(X2,X3)),
    inference(equality_resolution,[],[f51]) ).

fof(f51,plain,
    ! [X2,X3,X1] :
      ( in(X3,X1)
      | unordered_pair(X2,X3) != X1 ),
    inference(equality_resolution,[],[f40]) ).

fof(f40,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | unordered_pair(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SEU149+3 : 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
% 0.11/0.32  % Computer : n013.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 14:50:01 EDT 2022
% 0.11/0.33  % CPUTime    : 
% 0.16/0.49  % (30083)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.16/0.50  % (30082)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)
% 0.16/0.50  % (30075)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.16/0.50  % (30066)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.16/0.50  TRYING [1]
% 0.16/0.50  TRYING [2]
% 0.16/0.50  TRYING [3]
% 0.16/0.50  TRYING [4]
% 0.16/0.50  % (30083)First to succeed.
% 0.16/0.51  TRYING [5]
% 0.16/0.51  % (30083)Refutation found. Thanks to Tanya!
% 0.16/0.51  % SZS status Theorem for theBenchmark
% 0.16/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.51  % (30083)------------------------------
% 0.16/0.51  % (30083)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.51  % (30083)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.51  % (30083)Termination reason: Refutation
% 0.16/0.51  
% 0.16/0.51  % (30083)Memory used [KB]: 5373
% 0.16/0.51  % (30083)Time elapsed: 0.067 s
% 0.16/0.51  % (30083)Instructions burned: 3 (million)
% 0.16/0.51  % (30083)------------------------------
% 0.16/0.51  % (30083)------------------------------
% 0.16/0.51  % (30059)Success in time 0.178 s
%------------------------------------------------------------------------------