TSTP Solution File: SEU355+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU355+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 : n027.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 18:33:23 EDT 2022

% Result   : Theorem 0.15s 0.51s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   58 (   9 unt;   0 def)
%            Number of atoms       :  215 (   4 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  262 ( 105   ~;  91   |;  40   &)
%                                         (   8 <=>;  18  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   3 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :  101 (  87   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f191,plain,
    $false,
    inference(avatar_sat_refutation,[],[f100,f140,f190]) ).

fof(f190,plain,
    spl9_2,
    inference(avatar_contradiction_clause,[],[f189]) ).

fof(f189,plain,
    ( $false
    | spl9_2 ),
    inference(subsumption_resolution,[],[f187,f85]) ).

fof(f85,plain,
    empty(sK7),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    empty(sK7),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f15,f63]) ).

fof(f63,plain,
    ( ? [X0] : empty(X0)
   => empty(sK7) ),
    introduced(choice_axiom,[]) ).

fof(f15,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).

fof(f187,plain,
    ( ~ empty(sK7)
    | spl9_2 ),
    inference(resolution,[],[f182,f141]) ).

fof(f141,plain,
    ( ~ relstr_element_smaller(sK3,sK7,sK4)
    | spl9_2 ),
    inference(forward_demodulation,[],[f99,f101]) ).

fof(f101,plain,
    empty_set = sK7,
    inference(resolution,[],[f72,f85]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).

fof(f99,plain,
    ( ~ relstr_element_smaller(sK3,empty_set,sK4)
    | spl9_2 ),
    inference(avatar_component_clause,[],[f97]) ).

fof(f97,plain,
    ( spl9_2
  <=> relstr_element_smaller(sK3,empty_set,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f182,plain,
    ! [X2] :
      ( relstr_element_smaller(sK3,X2,sK4)
      | ~ empty(X2) ),
    inference(subsumption_resolution,[],[f177,f77]) ).

fof(f77,plain,
    rel_str(sK3),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ( rel_str(sK3)
    & element(sK4,the_carrier(sK3))
    & ( ~ relstr_element_smaller(sK3,empty_set,sK4)
      | ~ relstr_set_smaller(sK3,empty_set,sK4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f35,f53,f52]) ).

fof(f52,plain,
    ( ? [X0] :
        ( rel_str(X0)
        & ? [X1] :
            ( element(X1,the_carrier(X0))
            & ( ~ relstr_element_smaller(X0,empty_set,X1)
              | ~ relstr_set_smaller(X0,empty_set,X1) ) ) )
   => ( rel_str(sK3)
      & ? [X1] :
          ( element(X1,the_carrier(sK3))
          & ( ~ relstr_element_smaller(sK3,empty_set,X1)
            | ~ relstr_set_smaller(sK3,empty_set,X1) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f53,plain,
    ( ? [X1] :
        ( element(X1,the_carrier(sK3))
        & ( ~ relstr_element_smaller(sK3,empty_set,X1)
          | ~ relstr_set_smaller(sK3,empty_set,X1) ) )
   => ( element(sK4,the_carrier(sK3))
      & ( ~ relstr_element_smaller(sK3,empty_set,sK4)
        | ~ relstr_set_smaller(sK3,empty_set,sK4) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f35,plain,
    ? [X0] :
      ( rel_str(X0)
      & ? [X1] :
          ( element(X1,the_carrier(X0))
          & ( ~ relstr_element_smaller(X0,empty_set,X1)
            | ~ relstr_set_smaller(X0,empty_set,X1) ) ) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,negated_conjecture,
    ~ ! [X0] :
        ( rel_str(X0)
       => ! [X1] :
            ( element(X1,the_carrier(X0))
           => ( relstr_set_smaller(X0,empty_set,X1)
              & relstr_element_smaller(X0,empty_set,X1) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

fof(f20,conjecture,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ( relstr_set_smaller(X0,empty_set,X1)
            & relstr_element_smaller(X0,empty_set,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_yellow_0) ).

fof(f177,plain,
    ! [X2] :
      ( ~ empty(X2)
      | relstr_element_smaller(sK3,X2,sK4)
      | ~ rel_str(sK3) ),
    inference(resolution,[],[f128,f76]) ).

fof(f76,plain,
    element(sK4,the_carrier(sK3)),
    inference(cnf_transformation,[],[f54]) ).

fof(f128,plain,
    ! [X8,X6,X7] :
      ( ~ element(X8,the_carrier(X6))
      | ~ empty(X7)
      | relstr_element_smaller(X6,X7,X8)
      | ~ rel_str(X6) ),
    inference(resolution,[],[f91,f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ~ in(X0,X1)
      | ~ empty(X1) ),
    inference(rectify,[],[f43]) ).

fof(f43,plain,
    ! [X1,X0] :
      ( ~ in(X1,X0)
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ~ ( empty(X0)
        & in(X1,X0) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X1,X0] :
      ~ ( empty(X1)
        & in(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).

fof(f91,plain,
    ! [X2,X0,X1] :
      ( in(sK8(X0,X1,X2),X1)
      | relstr_element_smaller(X0,X1,X2)
      | ~ rel_str(X0)
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ( in(sK8(X0,X1,X2),X1)
                & element(sK8(X0,X1,X2),the_carrier(X0))
                & ~ related(X0,X2,sK8(X0,X1,X2)) ) )
            & ( ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0))
                  | related(X0,X2,X4) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f66,f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( in(X3,X1)
          & element(X3,the_carrier(X0))
          & ~ related(X0,X2,X3) )
     => ( in(sK8(X0,X1,X2),X1)
        & element(sK8(X0,X1,X2),the_carrier(X0))
        & ~ related(X0,X2,sK8(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f66,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( in(X3,X1)
                  & element(X3,the_carrier(X0))
                  & ~ related(X0,X2,X3) ) )
            & ( ! [X4] :
                  ( ~ in(X4,X1)
                  | ~ element(X4,the_carrier(X0))
                  | related(X0,X2,X4) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( ( relstr_element_smaller(X0,X1,X2)
              | ? [X3] :
                  ( in(X3,X1)
                  & element(X3,the_carrier(X0))
                  & ~ related(X0,X2,X3) ) )
            & ( ! [X3] :
                  ( ~ in(X3,X1)
                  | ~ element(X3,the_carrier(X0))
                  | related(X0,X2,X3) )
              | ~ relstr_element_smaller(X0,X1,X2) ) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(nnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( relstr_element_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0))
                | related(X0,X2,X3) ) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(flattening,[],[f40]) ).

fof(f40,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( related(X0,X2,X3)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) )
          <=> relstr_element_smaller(X0,X1,X2) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1,X2] :
          ( element(X2,the_carrier(X0))
         => ( ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X2,X3) ) )
          <=> relstr_element_smaller(X0,X1,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_lattice3) ).

fof(f140,plain,
    spl9_1,
    inference(avatar_contradiction_clause,[],[f139]) ).

fof(f139,plain,
    ( $false
    | spl9_1 ),
    inference(subsumption_resolution,[],[f138,f85]) ).

fof(f138,plain,
    ( ~ empty(sK7)
    | spl9_1 ),
    inference(resolution,[],[f137,f104]) ).

fof(f104,plain,
    ( ~ relstr_set_smaller(sK3,sK7,sK4)
    | spl9_1 ),
    inference(backward_demodulation,[],[f95,f101]) ).

fof(f95,plain,
    ( ~ relstr_set_smaller(sK3,empty_set,sK4)
    | spl9_1 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f93,plain,
    ( spl9_1
  <=> relstr_set_smaller(sK3,empty_set,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f137,plain,
    ! [X0] :
      ( relstr_set_smaller(sK3,X0,sK4)
      | ~ empty(X0) ),
    inference(subsumption_resolution,[],[f133,f77]) ).

fof(f133,plain,
    ! [X0] :
      ( relstr_set_smaller(sK3,X0,sK4)
      | ~ rel_str(sK3)
      | ~ empty(X0) ),
    inference(resolution,[],[f125,f76]) ).

fof(f125,plain,
    ! [X8,X6,X7] :
      ( ~ element(X7,the_carrier(X6))
      | ~ empty(X8)
      | ~ rel_str(X6)
      | relstr_set_smaller(X6,X8,X7) ),
    inference(resolution,[],[f79,f83]) ).

fof(f79,plain,
    ! [X2,X0,X1] :
      ( in(sK5(X0,X1,X2),X2)
      | ~ rel_str(X0)
      | ~ element(X1,the_carrier(X0))
      | relstr_set_smaller(X0,X2,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( ( ! [X3] :
                  ( related(X0,X3,X1)
                  | ~ in(X3,X2)
                  | ~ element(X3,the_carrier(X0)) )
              | ~ relstr_set_smaller(X0,X2,X1) )
            & ( relstr_set_smaller(X0,X2,X1)
              | ( ~ related(X0,sK5(X0,X1,X2),X1)
                & in(sK5(X0,X1,X2),X2)
                & element(sK5(X0,X1,X2),the_carrier(X0)) ) ) )
          | ~ element(X1,the_carrier(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f56,f57]) ).

fof(f57,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ~ related(X0,X4,X1)
          & in(X4,X2)
          & element(X4,the_carrier(X0)) )
     => ( ~ related(X0,sK5(X0,X1,X2),X1)
        & in(sK5(X0,X1,X2),X2)
        & element(sK5(X0,X1,X2),the_carrier(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1,X2] :
          ( ( ( ! [X3] :
                  ( related(X0,X3,X1)
                  | ~ in(X3,X2)
                  | ~ element(X3,the_carrier(X0)) )
              | ~ relstr_set_smaller(X0,X2,X1) )
            & ( relstr_set_smaller(X0,X2,X1)
              | ? [X4] :
                  ( ~ related(X0,X4,X1)
                  & in(X4,X2)
                  & element(X4,the_carrier(X0)) ) ) )
          | ~ element(X1,the_carrier(X0)) ) ),
    inference(rectify,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X2,X1] :
          ( ( ( ! [X3] :
                  ( related(X0,X3,X2)
                  | ~ in(X3,X1)
                  | ~ element(X3,the_carrier(X0)) )
              | ~ relstr_set_smaller(X0,X1,X2) )
            & ( relstr_set_smaller(X0,X1,X2)
              | ? [X3] :
                  ( ~ related(X0,X3,X2)
                  & in(X3,X1)
                  & element(X3,the_carrier(X0)) ) ) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(nnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X2,X1] :
          ( ( ! [X3] :
                ( related(X0,X3,X2)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) )
          <=> relstr_set_smaller(X0,X1,X2) )
          | ~ element(X2,the_carrier(X0)) ) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ( relstr_set_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( related(X0,X3,X2)
                | ~ in(X3,X1)
                | ~ element(X3,the_carrier(X0)) ) )
          | ~ element(X2,the_carrier(X0)) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X2,X1] :
          ( element(X2,the_carrier(X0))
         => ( relstr_set_smaller(X0,X1,X2)
          <=> ! [X3] :
                ( element(X3,the_carrier(X0))
               => ( in(X3,X1)
                 => related(X0,X3,X2) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_lattice3) ).

fof(f100,plain,
    ( ~ spl9_1
    | ~ spl9_2 ),
    inference(avatar_split_clause,[],[f75,f97,f93]) ).

fof(f75,plain,
    ( ~ relstr_element_smaller(sK3,empty_set,sK4)
    | ~ relstr_set_smaller(sK3,empty_set,sK4) ),
    inference(cnf_transformation,[],[f54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : SEU355+1 : TPTP v8.1.0. Released v3.3.0.
% 0.02/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.33  % Computer : n027.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit   : 300
% 0.10/0.33  % WCLimit    : 300
% 0.10/0.33  % DateTime   : Tue Aug 30 15:32:01 EDT 2022
% 0.10/0.33  % CPUTime    : 
% 0.15/0.48  % (21395)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.48  % (21394)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.49  % (21404)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)
% 0.15/0.49  TRYING [1]
% 0.15/0.49  TRYING [2]
% 0.15/0.49  % (21395)First to succeed.
% 0.15/0.50  % (21412)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.15/0.50  TRYING [3]
% 0.15/0.50  TRYING [4]
% 0.15/0.50  % (21411)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 (2999ds/467Mi)
% 0.15/0.50  % (21403)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 (2999ds/75Mi)
% 0.15/0.51  % (21395)Refutation found. Thanks to Tanya!
% 0.15/0.51  % SZS status Theorem for theBenchmark
% 0.15/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.51  % (21395)------------------------------
% 0.15/0.51  % (21395)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.51  % (21395)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.51  % (21395)Termination reason: Refutation
% 0.15/0.51  
% 0.15/0.51  % (21395)Memory used [KB]: 5500
% 0.15/0.51  % (21395)Time elapsed: 0.106 s
% 0.15/0.51  % (21395)Instructions burned: 5 (million)
% 0.15/0.51  % (21395)------------------------------
% 0.15/0.51  % (21395)------------------------------
% 0.15/0.51  % (21387)Success in time 0.173 s
%------------------------------------------------------------------------------