TSTP Solution File: SET900+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET900+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 : n006.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 18:26:02 EDT 2022

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   26 (   7 unt;   0 def)
%            Number of atoms       :   77 (  61 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   95 (  44   ~;  25   |;  24   &)
%                                         (   0 <=>;   2  =>;   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   41 (  32   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f63,plain,
    $false,
    inference(subsumption_resolution,[],[f62,f33]) ).

fof(f33,plain,
    sK4 != sF5,
    inference(definition_folding,[],[f30,f32]) ).

fof(f32,plain,
    singleton(sK3) = sF5,
    introduced(function_definition,[]) ).

fof(f30,plain,
    sK4 != singleton(sK3),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( ! [X2] :
        ( sK3 = X2
        | ~ in(X2,sK4) )
    & sK4 != singleton(sK3)
    & empty_set != sK4 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1] :
        ( ! [X2] :
            ( X0 = X2
            | ~ in(X2,X1) )
        & singleton(X0) != X1
        & empty_set != X1 )
   => ( ! [X2] :
          ( sK3 = X2
          | ~ in(X2,sK4) )
      & sK4 != singleton(sK3)
      & empty_set != sK4 ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1] :
      ( ! [X2] :
          ( X0 = X2
          | ~ in(X2,X1) )
      & singleton(X0) != X1
      & empty_set != X1 ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ? [X1,X0] :
      ( ! [X2] :
          ( X1 = X2
          | ~ in(X2,X0) )
      & singleton(X1) != X0
      & empty_set != X0 ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X0,X1] :
        ~ ( singleton(X1) != X0
          & empty_set != X0
          & ! [X2] :
              ~ ( X1 != X2
                & in(X2,X0) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X0,X1] :
      ~ ( singleton(X1) != X0
        & empty_set != X0
        & ! [X2] :
            ~ ( X1 != X2
              & in(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).

fof(f62,plain,
    sK4 = sF5,
    inference(backward_demodulation,[],[f32,f61]) ).

fof(f61,plain,
    sK4 = singleton(sK3),
    inference(equality_resolution,[],[f41]) ).

fof(f41,plain,
    ! [X1] :
      ( sK3 != X1
      | singleton(X1) = sK4 ),
    inference(subsumption_resolution,[],[f40,f29]) ).

fof(f29,plain,
    empty_set != sK4,
    inference(cnf_transformation,[],[f22]) ).

fof(f40,plain,
    ! [X1] :
      ( singleton(X1) = sK4
      | sK3 != X1
      | empty_set = sK4 ),
    inference(duplicate_literal_removal,[],[f38]) ).

fof(f38,plain,
    ! [X1] :
      ( sK3 != X1
      | empty_set = sK4
      | singleton(X1) = sK4
      | singleton(X1) = sK4 ),
    inference(superposition,[],[f25,f36]) ).

fof(f36,plain,
    ! [X0] :
      ( sK0(X0,sK4) = sK3
      | singleton(X0) = sK4 ),
    inference(subsumption_resolution,[],[f34,f29]) ).

fof(f34,plain,
    ! [X0] :
      ( sK0(X0,sK4) = sK3
      | singleton(X0) = sK4
      | empty_set = sK4 ),
    inference(resolution,[],[f26,f31]) ).

fof(f31,plain,
    ! [X2] :
      ( ~ in(X2,sK4)
      | sK3 = X2 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( in(sK0(X0,X1),X1)
      | empty_set = X1
      | singleton(X0) = X1 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( in(sK0(X0,X1),X1)
        & sK0(X0,X1) != X0 )
      | singleton(X0) = X1
      | empty_set = X1 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f13,f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X1)
          & X0 != X2 )
     => ( in(sK0(X0,X1),X1)
        & sK0(X0,X1) != X0 ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X1)
          & X0 != X2 )
      | singleton(X0) = X1
      | empty_set = X1 ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( in(X2,X0)
          & X1 != X2 )
      | singleton(X1) = X0
      | empty_set = X0 ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ~ ( empty_set != X0
        & ! [X2] :
            ~ ( in(X2,X0)
              & X1 != X2 )
        & singleton(X1) != X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).

fof(f25,plain,
    ! [X0,X1] :
      ( sK0(X0,X1) != X0
      | singleton(X0) = X1
      | empty_set = X1 ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SET900+1 : 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
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:27:40 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.19/0.48  % (30905)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.49  % (30925)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)
% 0.19/0.49  % (30915)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)
% 0.19/0.49  % (30926)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/482Mi)
% 0.19/0.49  % (30913)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.19/0.49  % (30908)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.19/0.49  % (30901)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 (3000ds/191324Mi)
% 0.19/0.49  % (30914)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.19/0.49  % (30926)First to succeed.
% 0.19/0.49  % (30932)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/355Mi)
% 0.19/0.49  % (30905)Also succeeded, but the first one will report.
% 0.19/0.50  % (30926)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (30926)------------------------------
% 0.19/0.50  % (30926)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (30926)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (30926)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (30926)Memory used [KB]: 5373
% 0.19/0.50  % (30926)Time elapsed: 0.078 s
% 0.19/0.50  % (30926)Instructions burned: 2 (million)
% 0.19/0.50  % (30926)------------------------------
% 0.19/0.50  % (30926)------------------------------
% 0.19/0.50  % (30898)Success in time 0.156 s
%------------------------------------------------------------------------------