TSTP Solution File: SWV408+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWV408+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 : n029.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 18:56:45 EDT 2022

% Result   : Theorem 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   49 (  11 unt;   0 def)
%            Number of atoms       :  139 (  17 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  146 (  56   ~;  49   |;  31   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-3 aty)
%            Number of variables   :   86 (  63   !;  23   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f553,plain,
    $false,
    inference(avatar_sat_refutation,[],[f292,f316,f552]) ).

fof(f552,plain,
    ~ spl5_5,
    inference(avatar_contradiction_clause,[],[f551]) ).

fof(f551,plain,
    ( $false
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f550,f291]) ).

fof(f291,plain,
    ( strictly_less_than(sK4,findmin_pqp_res(sK1))
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f289]) ).

fof(f289,plain,
    ( spl5_5
  <=> strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f550,plain,
    ( ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f544,f474]) ).

fof(f474,plain,
    ( ~ less_than(findmin_pqp_res(sK1),sK0(sK4,findmin_pqp_res(sK1),sK3))
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f473,f200]) ).

fof(f200,plain,
    ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
    inference(cnf_transformation,[],[f149]) ).

fof(f149,plain,
    ( contains_slb(sK3,sK4)
    & ! [X4] :
        ( ~ less_than(findmin_pqp_res(sK1),X4)
        | ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,X4) )
    & strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK3,sK2)))
    & ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f147,f148]) ).

fof(f148,plain,
    ( ? [X0,X1,X2,X3] :
        ( contains_slb(X2,X3)
        & ! [X4] :
            ( ~ less_than(findmin_pqp_res(X0),X4)
            | ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,X4) )
        & strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
        & ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) )
   => ( contains_slb(sK3,sK4)
      & ! [X4] :
          ( ~ less_than(findmin_pqp_res(sK1),X4)
          | ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,X4) )
      & strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK3,sK2)))
      & ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f147,plain,
    ? [X0,X1,X2,X3] :
      ( contains_slb(X2,X3)
      & ! [X4] :
          ( ~ less_than(findmin_pqp_res(X0),X4)
          | ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,X4) )
      & strictly_less_than(X3,findmin_cpq_res(triple(X0,X2,X1)))
      & ~ pair_in_list(update_slb(X2,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ? [X0,X2,X1,X3] :
      ( contains_slb(X1,X3)
      & ! [X4] :
          ( ~ less_than(findmin_pqp_res(X0),X4)
          | ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
      & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
      & ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ? [X1,X2,X3,X0] :
      ( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
      & ! [X4] :
          ( ~ less_than(findmin_pqp_res(X0),X4)
          | ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
      & strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
      & contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ ! [X1,X2,X3,X0] :
        ( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
          & contains_slb(X1,X3) )
       => ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
          | ? [X4] :
              ( less_than(findmin_pqp_res(X0),X4)
              & pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) ) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    ! [X1,X2,X3,X0] :
      ( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
        & contains_slb(X1,X3) )
     => ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
        | ? [X4] :
            ( less_than(findmin_pqp_res(X0),X4)
            & pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).

fof(f473,plain,
    ( pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
    | ~ less_than(findmin_pqp_res(sK1),sK0(sK4,findmin_pqp_res(sK1),sK3))
    | ~ spl5_5 ),
    inference(subsumption_resolution,[],[f472,f291]) ).

fof(f472,plain,
    ( ~ less_than(findmin_pqp_res(sK1),sK0(sK4,findmin_pqp_res(sK1),sK3))
    | ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
    | pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)) ),
    inference(subsumption_resolution,[],[f470,f203]) ).

fof(f203,plain,
    contains_slb(sK3,sK4),
    inference(cnf_transformation,[],[f149]) ).

fof(f470,plain,
    ( ~ contains_slb(sK3,sK4)
    | pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
    | ~ less_than(findmin_pqp_res(sK1),sK0(sK4,findmin_pqp_res(sK1),sK3))
    | ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
    inference(resolution,[],[f156,f202]) ).

fof(f202,plain,
    ! [X4] :
      ( ~ pair_in_list(update_slb(sK3,findmin_pqp_res(sK1)),sK4,X4)
      | ~ less_than(findmin_pqp_res(sK1),X4) ),
    inference(cnf_transformation,[],[f149]) ).

fof(f156,plain,
    ! [X2,X0,X1] :
      ( pair_in_list(update_slb(X2,X1),X0,sK0(X0,X1,X2))
      | ~ strictly_less_than(X0,X1)
      | pair_in_list(update_slb(X2,X1),X0,X1)
      | ~ contains_slb(X2,X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( pair_in_list(update_slb(X2,X1),X0,X1)
      | ~ contains_slb(X2,X0)
      | ~ strictly_less_than(X0,X1)
      | ( less_than(X1,sK0(X0,X1,X2))
        & pair_in_list(update_slb(X2,X1),X0,sK0(X0,X1,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f98,f112]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( less_than(X1,X3)
          & pair_in_list(update_slb(X2,X1),X0,X3) )
     => ( less_than(X1,sK0(X0,X1,X2))
        & pair_in_list(update_slb(X2,X1),X0,sK0(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( pair_in_list(update_slb(X2,X1),X0,X1)
      | ~ contains_slb(X2,X0)
      | ~ strictly_less_than(X0,X1)
      | ? [X3] :
          ( less_than(X1,X3)
          & pair_in_list(update_slb(X2,X1),X0,X3) ) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X2,X1,X0] :
      ( pair_in_list(update_slb(X2,X1),X0,X1)
      | ? [X3] :
          ( less_than(X1,X3)
          & pair_in_list(update_slb(X2,X1),X0,X3) )
      | ~ contains_slb(X2,X0)
      | ~ strictly_less_than(X0,X1) ),
    inference(ennf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X2,X1,X0] :
      ( ( contains_slb(X2,X0)
        & strictly_less_than(X0,X1) )
     => ( pair_in_list(update_slb(X2,X1),X0,X1)
        | ? [X3] :
            ( less_than(X1,X3)
            & pair_in_list(update_slb(X2,X1),X0,X3) ) ) ),
    inference(rectify,[],[f42]) ).

fof(f42,axiom,
    ! [X1,X2,X0] :
      ( ( contains_slb(X0,X1)
        & strictly_less_than(X1,X2) )
     => ( ? [X3] :
            ( pair_in_list(update_slb(X0,X2),X1,X3)
            & less_than(X2,X3) )
        | pair_in_list(update_slb(X0,X2),X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_l45) ).

fof(f544,plain,
    ( less_than(findmin_pqp_res(sK1),sK0(sK4,findmin_pqp_res(sK1),sK3))
    | ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
    inference(resolution,[],[f421,f200]) ).

fof(f421,plain,
    ! [X9] :
      ( pair_in_list(update_slb(sK3,X9),sK4,X9)
      | less_than(X9,sK0(sK4,X9,sK3))
      | ~ strictly_less_than(sK4,X9) ),
    inference(resolution,[],[f157,f203]) ).

fof(f157,plain,
    ! [X2,X0,X1] :
      ( ~ contains_slb(X2,X0)
      | less_than(X1,sK0(X0,X1,X2))
      | pair_in_list(update_slb(X2,X1),X0,X1)
      | ~ strictly_less_than(X0,X1) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f316,plain,
    ~ spl5_2,
    inference(avatar_contradiction_clause,[],[f315]) ).

fof(f315,plain,
    ( $false
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f300,f152]) ).

fof(f152,plain,
    ! [X0] : ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : ~ contains_slb(create_slb,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).

fof(f300,plain,
    ( contains_slb(create_slb,sK4)
    | ~ spl5_2 ),
    inference(backward_demodulation,[],[f203,f277]) ).

fof(f277,plain,
    ( create_slb = sK3
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f275,plain,
    ( spl5_2
  <=> create_slb = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f292,plain,
    ( spl5_2
    | spl5_5 ),
    inference(avatar_split_clause,[],[f268,f289,f275]) ).

fof(f268,plain,
    ( strictly_less_than(sK4,findmin_pqp_res(sK1))
    | create_slb = sK3 ),
    inference(superposition,[],[f210,f209]) ).

fof(f209,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X2,X1))
      | create_slb = X2 ),
    inference(definition_unfolding,[],[f192,f185]) ).

fof(f185,plain,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).

fof(f192,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X2,X1))
      | create_slb = X2 ),
    inference(cnf_transformation,[],[f140]) ).

fof(f140,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X2,X1))
      | create_slb = X2 ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X1,X2,X3] :
      ( findmin_cpq_res(triple(X1,X3,X2)) = findmin_pqp_res(X1)
      | create_slb = X3 ),
    inference(ennf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X1,X2,X3] :
      ( create_slb != X3
     => findmin_cpq_res(triple(X1,X3,X2)) = findmin_pqp_res(X1) ),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X3,X0,X2,X1] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).

fof(f210,plain,
    strictly_less_than(sK4,removemin_cpq_res(triple(sK1,sK3,sK2))),
    inference(definition_unfolding,[],[f201,f185]) ).

fof(f201,plain,
    strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK3,sK2))),
    inference(cnf_transformation,[],[f149]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWV408+1 : TPTP v8.1.0. Released v3.3.0.
% 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
% 0.13/0.36  % Computer : n029.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Tue Aug 30 19:32:42 EDT 2022
% 0.13/0.36  % CPUTime    : 
% 0.21/0.48  % (10639)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.50  % (10647)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 (2999ds/355Mi)
% 0.21/0.51  % (10639)First to succeed.
% 0.21/0.51  % (10639)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Theorem for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (10639)------------------------------
% 0.21/0.52  % (10639)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (10639)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (10639)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (10639)Memory used [KB]: 5884
% 0.21/0.52  % (10639)Time elapsed: 0.076 s
% 0.21/0.52  % (10639)Instructions burned: 25 (million)
% 0.21/0.52  % (10639)------------------------------
% 0.21/0.52  % (10639)------------------------------
% 0.21/0.52  % (10617)Success in time 0.145 s
%------------------------------------------------------------------------------