TSTP Solution File: SET603+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET603+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_uns --cores 0 -t %d %s

% Computer : n014.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 18:21:34 EDT 2022

% Result   : Theorem 0.18s 0.47s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (  13 unt;   0 def)
%            Number of atoms       :   93 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   88 (  35   ~;  29   |;  13   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   75 (  71   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f119,plain,
    $false,
    inference(resolution,[],[f118,f31]) ).

fof(f31,plain,
    ~ equal_set(difference(sK0,empty_set),sK0),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ~ equal_set(difference(sK0,empty_set),sK0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f23,f24]) ).

fof(f24,plain,
    ( ? [X0] : ~ equal_set(difference(X0,empty_set),X0)
   => ~ equal_set(difference(sK0,empty_set),sK0) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0] : ~ equal_set(difference(X0,empty_set),X0),
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0] : equal_set(difference(X0,empty_set),X0),
    inference(rectify,[],[f13]) ).

fof(f13,negated_conjecture,
    ~ ! [X3] : equal_set(difference(X3,empty_set),X3),
    inference(negated_conjecture,[],[f12]) ).

fof(f12,conjecture,
    ! [X3] : equal_set(difference(X3,empty_set),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI30) ).

fof(f118,plain,
    ! [X1] : equal_set(difference(X1,empty_set),X1),
    inference(subsumption_resolution,[],[f117,f56]) ).

fof(f56,plain,
    ! [X0,X1] : subset(difference(X0,X1),X0),
    inference(duplicate_literal_removal,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( subset(difference(X0,X1),X0)
      | subset(difference(X0,X1),X0) ),
    inference(resolution,[],[f40,f38]) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ member(sK1(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f29]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
     => subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

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

fof(f40,plain,
    ! [X2,X3,X1] :
      ( member(sK1(difference(X1,X2),X3),X1)
      | subset(difference(X1,X2),X3) ),
    inference(resolution,[],[f37,f36]) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,difference(X0,X1))
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X0)
          & ~ member(X2,X1) )
        | ~ member(X2,difference(X0,X1)) )
      & ( member(X2,difference(X0,X1))
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    inference(flattening,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X2,X0)
          & ~ member(X2,X1) )
        | ~ member(X2,difference(X0,X1)) )
      & ( member(X2,difference(X0,X1))
        | ~ member(X2,X0)
        | member(X2,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,X0)
        & ~ member(X2,X1) )
    <=> member(X2,difference(X0,X1)) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X3,X0,X1] :
      ( member(X1,difference(X3,X0))
    <=> ( ~ member(X1,X0)
        & member(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference) ).

fof(f37,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f30]) ).

fof(f117,plain,
    ! [X1] :
      ( equal_set(difference(X1,empty_set),X1)
      | ~ subset(difference(X1,empty_set),X1) ),
    inference(resolution,[],[f109,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ~ subset(X0,X1)
      | equal_set(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | equal_set(X0,X1)
      | ~ subset(X0,X1) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ~ subset(X0,X1)
      | equal_set(X1,X0)
      | ~ subset(X1,X0) ),
    inference(flattening,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0] :
      ( equal_set(X1,X0)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X1,X0) ),
    inference(unused_predicate_definition_removal,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
    <=> equal_set(X1,X0) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( equal_set(X0,X1)
    <=> ( subset(X0,X1)
        & subset(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_set) ).

fof(f109,plain,
    ! [X3] : subset(X3,difference(X3,empty_set)),
    inference(resolution,[],[f106,f32]) ).

fof(f32,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f106,plain,
    ! [X0,X1] :
      ( member(sK1(X0,difference(X0,X1)),X1)
      | subset(X0,difference(X0,X1)) ),
    inference(duplicate_literal_removal,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( subset(X0,difference(X0,X1))
      | member(sK1(X0,difference(X0,X1)),X1)
      | subset(X0,difference(X0,X1)) ),
    inference(resolution,[],[f51,f37]) ).

fof(f51,plain,
    ! [X8,X6,X7] :
      ( ~ member(sK1(X6,difference(X7,X8)),X7)
      | member(sK1(X6,difference(X7,X8)),X8)
      | subset(X6,difference(X7,X8)) ),
    inference(resolution,[],[f34,f38]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SET603+4 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n014.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 30 14:05:03 EDT 2022
% 0.12/0.33  % CPUTime    : 
% 0.18/0.45  % (30077)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.18/0.46  % (30077)First to succeed.
% 0.18/0.47  % (30077)Refutation found. Thanks to Tanya!
% 0.18/0.47  % SZS status Theorem for theBenchmark
% 0.18/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47  % (30077)------------------------------
% 0.18/0.47  % (30077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.47  % (30077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.47  % (30077)Termination reason: Refutation
% 0.18/0.47  
% 0.18/0.47  % (30077)Memory used [KB]: 5884
% 0.18/0.47  % (30077)Time elapsed: 0.082 s
% 0.18/0.47  % (30077)Instructions burned: 3 (million)
% 0.18/0.47  % (30077)------------------------------
% 0.18/0.47  % (30077)------------------------------
% 0.18/0.47  % (30066)Success in time 0.134 s
%------------------------------------------------------------------------------