TSTP Solution File: SET366+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET366+4 : 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 18:24:33 EDT 2022

% Result   : Theorem 1.41s 0.56s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   25 (  11 unt;   0 def)
%            Number of atoms       :   60 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   62 (  27   ~;  16   |;  10   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   43 (  38   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f92,plain,
    $false,
    inference(resolution,[],[f90,f88]) ).

fof(f88,plain,
    ~ subset(empty_set,sK1),
    inference(resolution,[],[f83,f76]) ).

fof(f76,plain,
    ~ member(empty_set,power_set(sK1)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ~ member(empty_set,power_set(sK1)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f26,f46]) ).

fof(f46,plain,
    ( ? [X0] : ~ member(empty_set,power_set(X0))
   => ~ member(empty_set,power_set(sK1)) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0] : ~ member(empty_set,power_set(X0)),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X0] : member(empty_set,power_set(X0)),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X0] : member(empty_set,power_set(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI47) ).

fof(f83,plain,
    ! [X0,X1] :
      ( member(X1,power_set(X0))
      | ~ subset(X1,X0) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ~ member(X1,power_set(X0)) )
      & ( member(X1,power_set(X0))
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | ~ member(X0,power_set(X1)) )
      & ( member(X0,power_set(X1))
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> member(X0,power_set(X1)) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0] :
      ( subset(X2,X0)
    <=> member(X2,power_set(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).

fof(f90,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f61,f75]) ).

fof(f75,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).

fof(f61,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ member(X3,X1)
          & member(X3,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ member(X3,X1)
            & member(X3,X0) ) ) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( member(X2,X0)
            | ~ member(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ member(X2,X0)
            & member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
          | ~ member(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f1]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SET366+4 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % 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 13:43:22 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 1.41/0.55  % (2402)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.41/0.56  % (2402)First to succeed.
% 1.41/0.56  % (2402)Refutation found. Thanks to Tanya!
% 1.41/0.56  % SZS status Theorem for theBenchmark
% 1.41/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.56  % (2402)------------------------------
% 1.41/0.56  % (2402)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.41/0.56  % (2402)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.41/0.56  % (2402)Termination reason: Refutation
% 1.41/0.56  
% 1.41/0.56  % (2402)Memory used [KB]: 895
% 1.41/0.56  % (2402)Time elapsed: 0.126 s
% 1.41/0.56  % (2402)Instructions burned: 2 (million)
% 1.41/0.56  % (2402)------------------------------
% 1.41/0.56  % (2402)------------------------------
% 1.41/0.56  % (2399)Success in time 0.203 s
%------------------------------------------------------------------------------