TSTP Solution File: SET027+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n003.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 18:23:15 EDT 2022

% Result   : Theorem 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   27 (   8 unt;   0 def)
%            Number of atoms       :   74 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   73 (  26   ~;  16   |;  23   &)
%                                         (   2 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   50 (  35   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f47,plain,
    $false,
    inference(resolution,[],[f43,f18]) ).

fof(f18,plain,
    ~ subset(sK0,sK1),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,plain,
    ( ~ subset(sK0,sK1)
    & subset(sK2,sK1)
    & subset(sK0,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f10]) ).

fof(f10,plain,
    ( ? [X0,X1,X2] :
        ( ~ subset(X0,X1)
        & subset(X2,X1)
        & subset(X0,X2) )
   => ( ~ subset(sK0,sK1)
      & subset(sK2,sK1)
      & subset(sK0,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f9,plain,
    ? [X0,X1,X2] :
      ( ~ subset(X0,X1)
      & subset(X2,X1)
      & subset(X0,X2) ),
    inference(rectify,[],[f8]) ).

fof(f8,plain,
    ? [X2,X1,X0] :
      ( ~ subset(X2,X1)
      & subset(X0,X1)
      & subset(X2,X0) ),
    inference(flattening,[],[f7]) ).

fof(f7,plain,
    ? [X1,X0,X2] :
      ( ~ subset(X2,X1)
      & subset(X0,X1)
      & subset(X2,X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,plain,
    ~ ! [X1,X0,X2] :
        ( ( subset(X0,X1)
          & subset(X2,X0) )
       => subset(X2,X1) ),
    inference(rectify,[],[f4]) ).

fof(f4,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( subset(X0,X1)
          & subset(X1,X2) )
       => subset(X0,X2) ),
    inference(negated_conjecture,[],[f3]) ).

fof(f3,conjecture,
    ! [X1,X2,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X2) )
     => subset(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_transitivity_of_subset) ).

fof(f43,plain,
    subset(sK0,sK1),
    inference(resolution,[],[f33,f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( member(sK3(X0,X1),X0)
          & ~ member(sK3(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f13,f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1) )
     => ( member(sK3(X0,X1),X0)
        & ~ member(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( member(X3,X0)
            & ~ member(X3,X1) ) ) ),
    inference(rectify,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

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

fof(f33,plain,
    member(sK3(sK0,sK1),sK1),
    inference(resolution,[],[f28,f17]) ).

fof(f17,plain,
    subset(sK2,sK1),
    inference(cnf_transformation,[],[f11]) ).

fof(f28,plain,
    ! [X0] :
      ( ~ subset(sK2,X0)
      | member(sK3(sK0,sK1),X0) ),
    inference(resolution,[],[f25,f22]) ).

fof(f22,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X0)
      | member(X2,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f25,plain,
    member(sK3(sK0,sK1),sK2),
    inference(resolution,[],[f24,f16]) ).

fof(f16,plain,
    subset(sK0,sK2),
    inference(cnf_transformation,[],[f11]) ).

fof(f24,plain,
    ! [X0] :
      ( ~ subset(sK0,X0)
      | member(sK3(sK0,sK1),X0) ),
    inference(resolution,[],[f22,f23]) ).

fof(f23,plain,
    member(sK3(sK0,sK1),sK0),
    inference(resolution,[],[f21,f18]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f15]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : SET027+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n003.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 12:57:37 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (5576)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.21/0.50  % (5568)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.21/0.50  % (5584)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)
% 0.21/0.51  % (5584)First to succeed.
% 0.21/0.51  % (5584)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
% 0.21/0.51  % (5584)------------------------------
% 0.21/0.51  % (5584)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (5584)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (5584)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (5584)Memory used [KB]: 5373
% 0.21/0.51  % (5584)Time elapsed: 0.089 s
% 0.21/0.51  % (5584)Instructions burned: 2 (million)
% 0.21/0.51  % (5584)------------------------------
% 0.21/0.51  % (5584)------------------------------
% 0.21/0.51  % (5554)Success in time 0.153 s
%------------------------------------------------------------------------------