TSTP Solution File: SET979+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET979+1 : 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 : n015.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 18:22:56 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   20 (   8 unt;   0 def)
%            Number of atoms       :   34 (  33 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  17   ~;   7   |;   6   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   41 (  32   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f35,plain,
    $false,
    inference(subsumption_resolution,[],[f34,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] : set_union2(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) = cartesian_product2(set_union2(X1,X2),X0),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
      & set_union2(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) = cartesian_product2(set_union2(X1,X2),X0) ),
    inference(rectify,[],[f15]) ).

fof(f15,plain,
    ! [X1,X2,X0] :
      ( cartesian_product2(X1,set_union2(X2,X0)) = set_union2(cartesian_product2(X1,X2),cartesian_product2(X1,X0))
      & set_union2(cartesian_product2(X2,X1),cartesian_product2(X0,X1)) = cartesian_product2(set_union2(X2,X0),X1) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X2,X0] :
      ( cartesian_product2(set_union2(X0,X1),X2) = set_union2(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
      & cartesian_product2(X2,set_union2(X0,X1)) = set_union2(cartesian_product2(X2,X0),cartesian_product2(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_zfmisc_1) ).

fof(f34,plain,
    cartesian_product2(set_union2(singleton(sK2),singleton(sK1)),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0)),
    inference(subsumption_resolution,[],[f32,f31]) ).

fof(f31,plain,
    ! [X2,X0,X1] : cartesian_product2(X0,set_union2(X1,X2)) = set_union2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
    inference(cnf_transformation,[],[f24]) ).

fof(f32,plain,
    ( set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,set_union2(singleton(sK2),singleton(sK1)))
    | cartesian_product2(set_union2(singleton(sK2),singleton(sK1)),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0)) ),
    inference(definition_unfolding,[],[f27,f26,f26]) ).

fof(f26,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X1,X0] : unordered_pair(X1,X0) = set_union2(singleton(X1),singleton(X0)),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t41_enumset1) ).

fof(f27,plain,
    ( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
    | set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
    | set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f20,f21]) ).

fof(f21,plain,
    ( ? [X0,X1,X2] :
        ( cartesian_product2(unordered_pair(X2,X1),X0) != set_union2(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X0))
        | cartesian_product2(X0,unordered_pair(X2,X1)) != set_union2(cartesian_product2(X0,singleton(X2)),cartesian_product2(X0,singleton(X1))) )
   => ( cartesian_product2(unordered_pair(sK2,sK1),sK0) != set_union2(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK0))
      | set_union2(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK0,singleton(sK1))) != cartesian_product2(sK0,unordered_pair(sK2,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2] :
      ( cartesian_product2(unordered_pair(X2,X1),X0) != set_union2(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X0))
      | cartesian_product2(X0,unordered_pair(X2,X1)) != set_union2(cartesian_product2(X0,singleton(X2)),cartesian_product2(X0,singleton(X1))) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X2,X0] :
      ( set_union2(cartesian_product2(singleton(X0),X1),cartesian_product2(singleton(X2),X1)) != cartesian_product2(unordered_pair(X0,X2),X1)
      | set_union2(cartesian_product2(X1,singleton(X0)),cartesian_product2(X1,singleton(X2))) != cartesian_product2(X1,unordered_pair(X0,X2)) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ! [X1,X2,X0] :
        ( set_union2(cartesian_product2(singleton(X0),X1),cartesian_product2(singleton(X2),X1)) = cartesian_product2(unordered_pair(X0,X2),X1)
        & set_union2(cartesian_product2(X1,singleton(X0)),cartesian_product2(X1,singleton(X2))) = cartesian_product2(X1,unordered_pair(X0,X2)) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
        & cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X2,X1] :
      ( cartesian_product2(X2,unordered_pair(X0,X1)) = set_union2(cartesian_product2(X2,singleton(X0)),cartesian_product2(X2,singleton(X1)))
      & cartesian_product2(unordered_pair(X0,X1),X2) = set_union2(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t132_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET979+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:44:51 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.53  % (1673)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.54  % (1670)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.55  % (1673)First to succeed.
% 0.20/0.56  % (1691)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.20/0.56  % (1673)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (1673)------------------------------
% 0.20/0.56  % (1673)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (1673)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (1673)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (1673)Memory used [KB]: 5884
% 0.20/0.56  % (1673)Time elapsed: 0.006 s
% 0.20/0.56  % (1673)Instructions burned: 2 (million)
% 0.20/0.56  % (1673)------------------------------
% 0.20/0.56  % (1673)------------------------------
% 0.20/0.56  % (1668)Success in time 0.202 s
%------------------------------------------------------------------------------