TSTP Solution File: SET108+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 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 : n011.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 18:23:45 EDT 2022

% Result   : Theorem 1.80s 0.59s
% Output   : Refutation 1.80s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   30 (  12 unt;   0 def)
%            Number of atoms       :  103 (  55 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  121 (  48   ~;  37   |;  34   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   60 (  38   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f299,plain,
    $false,
    inference(subsumption_resolution,[],[f298,f293]) ).

fof(f293,plain,
    member(sK4,universal_class),
    inference(equality_resolution,[],[f292]) ).

fof(f292,plain,
    ! [X1] :
      ( member(sK4,universal_class)
      | sK3 != X1 ),
    inference(equality_resolution,[],[f221]) ).

fof(f221,plain,
    ! [X2,X1] :
      ( member(sK4,universal_class)
      | sK3 != X2
      | sK3 != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ! [X1,X2] :
      ( ( ( sK3 = ordered_pair(sK5,sK4)
          & member(sK5,universal_class)
          & member(sK4,universal_class) )
        | sK3 != X2
        | sK3 != X1 )
      & ( sK3 != ordered_pair(X1,X2)
        | ~ member(X1,universal_class)
        | ~ member(X2,universal_class) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f82,f137,f136]) ).

fof(f136,plain,
    ( ? [X0] :
      ! [X1,X2] :
        ( ( ? [X3,X4] :
              ( ordered_pair(X4,X3) = X0
              & member(X4,universal_class)
              & member(X3,universal_class) )
          | X0 != X2
          | X0 != X1 )
        & ( ordered_pair(X1,X2) != X0
          | ~ member(X1,universal_class)
          | ~ member(X2,universal_class) ) )
   => ! [X2,X1] :
        ( ( ? [X4,X3] :
              ( sK3 = ordered_pair(X4,X3)
              & member(X4,universal_class)
              & member(X3,universal_class) )
          | sK3 != X2
          | sK3 != X1 )
        & ( sK3 != ordered_pair(X1,X2)
          | ~ member(X1,universal_class)
          | ~ member(X2,universal_class) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f137,plain,
    ( ? [X4,X3] :
        ( sK3 = ordered_pair(X4,X3)
        & member(X4,universal_class)
        & member(X3,universal_class) )
   => ( sK3 = ordered_pair(sK5,sK4)
      & member(sK5,universal_class)
      & member(sK4,universal_class) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ? [X0] :
    ! [X1,X2] :
      ( ( ? [X3,X4] :
            ( ordered_pair(X4,X3) = X0
            & member(X4,universal_class)
            & member(X3,universal_class) )
        | X0 != X2
        | X0 != X1 )
      & ( ordered_pair(X1,X2) != X0
        | ~ member(X1,universal_class)
        | ~ member(X2,universal_class) ) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ~ ! [X0] :
      ? [X1,X2] :
        ( ( member(X2,universal_class)
          & member(X1,universal_class)
          & ordered_pair(X1,X2) = X0 )
        | ( X0 = X1
          & X0 = X2
          & ~ ? [X3,X4] :
                ( ordered_pair(X4,X3) = X0
                & member(X4,universal_class)
                & member(X3,universal_class) ) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0] :
      ? [X2,X3] :
        ( ( ordered_pair(X2,X3) = X0
          & member(X3,universal_class)
          & member(X2,universal_class) )
        | ( X0 = X2
          & ~ ? [X4,X1] :
                ( member(X4,universal_class)
                & ordered_pair(X1,X4) = X0
                & member(X1,universal_class) )
          & X0 = X3 ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0] :
    ? [X2,X3] :
      ( ( ordered_pair(X2,X3) = X0
        & member(X3,universal_class)
        & member(X2,universal_class) )
      | ( X0 = X2
        & ~ ? [X4,X1] :
              ( member(X4,universal_class)
              & ordered_pair(X1,X4) = X0
              & member(X1,universal_class) )
        & X0 = X3 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_first_and_second) ).

fof(f298,plain,
    ~ member(sK4,universal_class),
    inference(subsumption_resolution,[],[f297,f291]) ).

fof(f291,plain,
    member(sK5,universal_class),
    inference(equality_resolution,[],[f290]) ).

fof(f290,plain,
    ! [X1] :
      ( member(sK5,universal_class)
      | sK3 != X1 ),
    inference(equality_resolution,[],[f222]) ).

fof(f222,plain,
    ! [X2,X1] :
      ( member(sK5,universal_class)
      | sK3 != X2
      | sK3 != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f297,plain,
    ( ~ member(sK5,universal_class)
    | ~ member(sK4,universal_class) ),
    inference(trivial_inequality_removal,[],[f296]) ).

fof(f296,plain,
    ( ~ member(sK4,universal_class)
    | sK3 != sK3
    | ~ member(sK5,universal_class) ),
    inference(superposition,[],[f282,f289]) ).

fof(f289,plain,
    sK3 = unordered_pair(unordered_pair(sK5,sK5),unordered_pair(sK5,unordered_pair(sK4,sK4))),
    inference(equality_resolution,[],[f288]) ).

fof(f288,plain,
    ! [X1] :
      ( sK3 = unordered_pair(unordered_pair(sK5,sK5),unordered_pair(sK5,unordered_pair(sK4,sK4)))
      | sK3 != X1 ),
    inference(equality_resolution,[],[f281]) ).

fof(f281,plain,
    ! [X2,X1] :
      ( sK3 = unordered_pair(unordered_pair(sK5,sK5),unordered_pair(sK5,unordered_pair(sK4,sK4)))
      | sK3 != X2
      | sK3 != X1 ),
    inference(definition_unfolding,[],[f223,f245]) ).

fof(f245,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
    inference(definition_unfolding,[],[f169,f224,f224]) ).

fof(f224,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).

fof(f169,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ! [X1,X0] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X0))),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).

fof(f223,plain,
    ! [X2,X1] :
      ( sK3 = ordered_pair(sK5,sK4)
      | sK3 != X2
      | sK3 != X1 ),
    inference(cnf_transformation,[],[f138]) ).

fof(f282,plain,
    ! [X2,X1] :
      ( unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) != sK3
      | ~ member(X1,universal_class)
      | ~ member(X2,universal_class) ),
    inference(definition_unfolding,[],[f220,f245]) ).

fof(f220,plain,
    ! [X2,X1] :
      ( sK3 != ordered_pair(X1,X2)
      | ~ member(X1,universal_class)
      | ~ member(X2,universal_class) ),
    inference(cnf_transformation,[],[f138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SET108+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 13:15:25 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.55  % (2027)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.56  % (1999)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)
% 0.20/0.56  % (2007)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.56  % (2019)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.56  % (2007)Instruction limit reached!
% 0.20/0.56  % (2007)------------------------------
% 0.20/0.56  % (2007)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (2007)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (2007)Termination reason: Unknown
% 0.20/0.56  % (2007)Termination phase: Preprocessing 2
% 0.20/0.56  
% 0.20/0.56  % (2007)Memory used [KB]: 895
% 0.20/0.56  % (2007)Time elapsed: 0.003 s
% 0.20/0.56  % (2007)Instructions burned: 2 (million)
% 0.20/0.56  % (2007)------------------------------
% 0.20/0.56  % (2007)------------------------------
% 1.42/0.57  % (2009)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.42/0.58  % (2015)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)
% 1.42/0.58  % (2003)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.80/0.59  % (2019)First to succeed.
% 1.80/0.59  % (2001)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 (2999ds/37Mi)
% 1.80/0.59  % (2019)Refutation found. Thanks to Tanya!
% 1.80/0.59  % SZS status Theorem for theBenchmark
% 1.80/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.80/0.59  % (2019)------------------------------
% 1.80/0.59  % (2019)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.80/0.59  % (2019)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.80/0.59  % (2019)Termination reason: Refutation
% 1.80/0.59  
% 1.80/0.59  % (2019)Memory used [KB]: 5628
% 1.80/0.59  % (2019)Time elapsed: 0.159 s
% 1.80/0.59  % (2019)Instructions burned: 10 (million)
% 1.80/0.59  % (2019)------------------------------
% 1.80/0.59  % (2019)------------------------------
% 1.80/0.59  % (1998)Success in time 0.235 s
%------------------------------------------------------------------------------