TSTP Solution File: SET800+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET800+4 : 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_uns --cores 0 -t %d %s

% Computer : n024.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 18:22:18 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   40 (   9 unt;   0 def)
%            Number of atoms       :  179 (   0 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  182 (  43   ~;  27   |;  82   &)
%                                         (   7 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   8 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   6 usr;   1 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-3 aty)
%            Number of variables   :  141 ( 102   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f129,plain,
    $false,
    inference(subsumption_resolution,[],[f126,f89]) ).

fof(f89,plain,
    member(sK5,sK4),
    inference(unit_resulting_resolution,[],[f64,f77,f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( member(X2,X0)
      | ~ member(X2,X1)
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ! [X2] :
          ( ~ member(X2,X1)
          | member(X2,X0) ) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
     => ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).

fof(f77,plain,
    member(sK5,sK3),
    inference(unit_resulting_resolution,[],[f60,f55]) ).

fof(f55,plain,
    ! [X2,X3,X0,X1] :
      ( member(X0,X1)
      | ~ greatest_lower_bound(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1,X2,X3] :
      ( ~ greatest_lower_bound(X0,X1,X2,X3)
      | ( lower_bound(X0,X2,X1)
        & member(X0,X1)
        & ! [X4] :
            ( ~ lower_bound(X4,X2,X1)
            | apply(X2,X4,X0)
            | ~ member(X4,X3) ) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X3,X2,X0,X1] :
      ( ~ greatest_lower_bound(X3,X2,X0,X1)
      | ( lower_bound(X3,X0,X2)
        & member(X3,X2)
        & ! [X4] :
            ( ~ lower_bound(X4,X0,X2)
            | apply(X0,X4,X3)
            | ~ member(X4,X1) ) ) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X0,X3,X1,X2] :
      ( ( member(X3,X2)
        & ! [X4] :
            ( apply(X0,X4,X3)
            | ~ lower_bound(X4,X0,X2)
            | ~ member(X4,X1) )
        & lower_bound(X3,X0,X2) )
      | ~ greatest_lower_bound(X3,X2,X0,X1) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X3,X1,X2] :
      ( greatest_lower_bound(X3,X2,X0,X1)
     => ( member(X3,X2)
        & ! [X4] :
            ( ( lower_bound(X4,X0,X2)
              & member(X4,X1) )
           => apply(X0,X4,X3) )
        & lower_bound(X3,X0,X2) ) ),
    inference(unused_predicate_definition_removal,[],[f25]) ).

fof(f25,plain,
    ! [X0,X3,X1,X2] :
      ( greatest_lower_bound(X3,X2,X0,X1)
    <=> ( member(X3,X2)
        & ! [X4] :
            ( ( lower_bound(X4,X0,X2)
              & member(X4,X1) )
           => apply(X0,X4,X3) )
        & lower_bound(X3,X0,X2) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,axiom,
    ! [X5,X3,X2,X0] :
      ( greatest_lower_bound(X0,X2,X5,X3)
    <=> ( ! [X7] :
            ( ( member(X7,X3)
              & lower_bound(X7,X5,X2) )
           => apply(X5,X7,X0) )
        & lower_bound(X0,X5,X2)
        & member(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greatest_lower_bound) ).

fof(f60,plain,
    greatest_lower_bound(sK5,sK3,sK1,sK2),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ( subset(sK3,sK4)
    & subset(sK4,sK2)
    & greatest_lower_bound(sK6,sK4,sK1,sK2)
    & ~ apply(sK1,sK6,sK5)
    & greatest_lower_bound(sK5,sK3,sK1,sK2)
    & subset(sK3,sK2)
    & order(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f45,f48,f47,f46]) ).

fof(f46,plain,
    ( ? [X0,X1] :
        ( ? [X2,X3] :
            ( subset(X2,X3)
            & subset(X3,X1)
            & ? [X4,X5] :
                ( greatest_lower_bound(X5,X3,X0,X1)
                & ~ apply(X0,X5,X4)
                & greatest_lower_bound(X4,X2,X0,X1) )
            & subset(X2,X1) )
        & order(X0,X1) )
   => ( ? [X3,X2] :
          ( subset(X2,X3)
          & subset(X3,sK2)
          & ? [X5,X4] :
              ( greatest_lower_bound(X5,X3,sK1,sK2)
              & ~ apply(sK1,X5,X4)
              & greatest_lower_bound(X4,X2,sK1,sK2) )
          & subset(X2,sK2) )
      & order(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ( ? [X3,X2] :
        ( subset(X2,X3)
        & subset(X3,sK2)
        & ? [X5,X4] :
            ( greatest_lower_bound(X5,X3,sK1,sK2)
            & ~ apply(sK1,X5,X4)
            & greatest_lower_bound(X4,X2,sK1,sK2) )
        & subset(X2,sK2) )
   => ( subset(sK3,sK4)
      & subset(sK4,sK2)
      & ? [X5,X4] :
          ( greatest_lower_bound(X5,sK4,sK1,sK2)
          & ~ apply(sK1,X5,X4)
          & greatest_lower_bound(X4,sK3,sK1,sK2) )
      & subset(sK3,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ( ? [X5,X4] :
        ( greatest_lower_bound(X5,sK4,sK1,sK2)
        & ~ apply(sK1,X5,X4)
        & greatest_lower_bound(X4,sK3,sK1,sK2) )
   => ( greatest_lower_bound(sK6,sK4,sK1,sK2)
      & ~ apply(sK1,sK6,sK5)
      & greatest_lower_bound(sK5,sK3,sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f45,plain,
    ? [X0,X1] :
      ( ? [X2,X3] :
          ( subset(X2,X3)
          & subset(X3,X1)
          & ? [X4,X5] :
              ( greatest_lower_bound(X5,X3,X0,X1)
              & ~ apply(X0,X5,X4)
              & greatest_lower_bound(X4,X2,X0,X1) )
          & subset(X2,X1) )
      & order(X0,X1) ),
    inference(rectify,[],[f36]) ).

fof(f36,plain,
    ? [X1,X0] :
      ( ? [X3,X2] :
          ( subset(X3,X2)
          & subset(X2,X0)
          & ? [X5,X4] :
              ( greatest_lower_bound(X4,X2,X1,X0)
              & ~ apply(X1,X4,X5)
              & greatest_lower_bound(X5,X3,X1,X0) )
          & subset(X3,X0) )
      & order(X1,X0) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ? [X0,X1] :
      ( ? [X3,X2] :
          ( ? [X4,X5] :
              ( ~ apply(X1,X4,X5)
              & greatest_lower_bound(X4,X2,X1,X0)
              & greatest_lower_bound(X5,X3,X1,X0) )
          & subset(X2,X0)
          & subset(X3,X0)
          & subset(X3,X2) )
      & order(X1,X0) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f24,plain,
    ~ ! [X0,X1] :
        ( order(X1,X0)
       => ! [X3,X2] :
            ( ( subset(X2,X0)
              & subset(X3,X0)
              & subset(X3,X2) )
           => ! [X4,X5] :
                ( ( greatest_lower_bound(X4,X2,X1,X0)
                  & greatest_lower_bound(X5,X3,X1,X0) )
               => apply(X1,X4,X5) ) ) ),
    inference(rectify,[],[f23]) ).

fof(f23,negated_conjecture,
    ~ ! [X3,X5] :
        ( order(X5,X3)
       => ! [X9,X8] :
            ( ( subset(X8,X3)
              & subset(X8,X9)
              & subset(X9,X3) )
           => ! [X11,X10] :
                ( ( greatest_lower_bound(X11,X9,X5,X3)
                  & greatest_lower_bound(X10,X8,X5,X3) )
               => apply(X5,X11,X10) ) ) ),
    inference(negated_conjecture,[],[f22]) ).

fof(f22,conjecture,
    ! [X3,X5] :
      ( order(X5,X3)
     => ! [X9,X8] :
          ( ( subset(X8,X3)
            & subset(X8,X9)
            & subset(X9,X3) )
         => ! [X11,X10] :
              ( ( greatest_lower_bound(X11,X9,X5,X3)
                & greatest_lower_bound(X10,X8,X5,X3) )
             => apply(X5,X11,X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).

fof(f64,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f49]) ).

fof(f126,plain,
    ~ member(sK5,sK4),
    inference(unit_resulting_resolution,[],[f61,f83,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1,X4] :
      ( apply(X2,X1,X4)
      | ~ member(X4,X0)
      | ~ lower_bound(X1,X2,X0) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X1,X2,X0)
        | ( member(sK0(X0,X1,X2),X0)
          & ~ apply(X2,X1,sK0(X0,X1,X2)) ) )
      & ( ! [X4] :
            ( ~ member(X4,X0)
            | apply(X2,X1,X4) )
        | ~ lower_bound(X1,X2,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f41,f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ apply(X2,X1,X3) )
     => ( member(sK0(X0,X1,X2),X0)
        & ~ apply(X2,X1,sK0(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( lower_bound(X1,X2,X0)
        | ? [X3] :
            ( member(X3,X0)
            & ~ apply(X2,X1,X3) ) )
      & ( ! [X4] :
            ( ~ member(X4,X0)
            | apply(X2,X1,X4) )
        | ~ lower_bound(X1,X2,X0) ) ),
    inference(rectify,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0,X2] :
      ( ( lower_bound(X0,X2,X1)
        | ? [X3] :
            ( member(X3,X1)
            & ~ apply(X2,X0,X3) ) )
      & ( ! [X3] :
            ( ~ member(X3,X1)
            | apply(X2,X0,X3) )
        | ~ lower_bound(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X1,X0,X2] :
      ( lower_bound(X0,X2,X1)
    <=> ! [X3] :
          ( ~ member(X3,X1)
          | apply(X2,X0,X3) ) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( lower_bound(X0,X2,X1)
    <=> ! [X3] :
          ( member(X3,X1)
         => apply(X2,X0,X3) ) ),
    inference(rectify,[],[f15]) ).

fof(f15,axiom,
    ! [X7,X3,X5] :
      ( lower_bound(X7,X5,X3)
    <=> ! [X2] :
          ( member(X2,X3)
         => apply(X5,X7,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_bound) ).

fof(f83,plain,
    lower_bound(sK6,sK1,sK4),
    inference(unit_resulting_resolution,[],[f62,f56]) ).

fof(f56,plain,
    ! [X2,X3,X0,X1] :
      ( ~ greatest_lower_bound(X0,X1,X2,X3)
      | lower_bound(X0,X2,X1) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f62,plain,
    greatest_lower_bound(sK6,sK4,sK1,sK2),
    inference(cnf_transformation,[],[f49]) ).

fof(f61,plain,
    ~ apply(sK1,sK6,sK5),
    inference(cnf_transformation,[],[f49]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET800+4 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:23:04 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (2485)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.50  % (2492)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.50  % (2492)First to succeed.
% 0.19/0.51  % (2496)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.51  % (2492)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (2492)------------------------------
% 0.19/0.51  % (2492)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (2492)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (2492)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (2492)Memory used [KB]: 6012
% 0.19/0.51  % (2492)Time elapsed: 0.102 s
% 0.19/0.51  % (2492)Instructions burned: 3 (million)
% 0.19/0.51  % (2492)------------------------------
% 0.19/0.51  % (2492)------------------------------
% 0.19/0.51  % (2484)Success in time 0.165 s
%------------------------------------------------------------------------------