TSTP Solution File: SET978+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET978+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_sat --cores 0 -t %d %s

% Computer : n020.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 18:26:15 EDT 2022

% Result   : Theorem 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   43 (  17 unt;   0 def)
%            Number of atoms       :   83 (  21 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   75 (  35   ~;  21   |;  10   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   63 (  51   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f147,plain,
    $false,
    inference(avatar_sat_refutation,[],[f47,f98,f146]) ).

fof(f146,plain,
    spl12_1,
    inference(avatar_contradiction_clause,[],[f145]) ).

fof(f145,plain,
    ( $false
    | spl12_1 ),
    inference(subsumption_resolution,[],[f144,f42]) ).

fof(f42,plain,
    ( ~ disjoint(sF7,sF9)
    | spl12_1 ),
    inference(avatar_component_clause,[],[f40]) ).

fof(f40,plain,
    ( spl12_1
  <=> disjoint(sF7,sF9) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f144,plain,
    disjoint(sF7,sF9),
    inference(superposition,[],[f139,f35]) ).

fof(f35,plain,
    sF9 = cartesian_product2(sF8,sK3),
    introduced(function_definition,[]) ).

fof(f139,plain,
    ! [X0] : disjoint(sF7,cartesian_product2(sF8,X0)),
    inference(superposition,[],[f78,f33]) ).

fof(f33,plain,
    sF7 = cartesian_product2(sF6,sK0),
    introduced(function_definition,[]) ).

fof(f78,plain,
    ! [X10,X11] : disjoint(cartesian_product2(sF6,X10),cartesian_product2(sF8,X11)),
    inference(resolution,[],[f25,f56]) ).

fof(f56,plain,
    disjoint(sF6,sF8),
    inference(subsumption_resolution,[],[f55,f27]) ).

fof(f27,plain,
    sK1 != sK2,
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( ( ~ disjoint(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK3))
      | ~ disjoint(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK3,singleton(sK1))) )
    & sK1 != sK2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f16,f17]) ).

fof(f17,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( ~ disjoint(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X3))
          | ~ disjoint(cartesian_product2(X0,singleton(X2)),cartesian_product2(X3,singleton(X1))) )
        & X1 != X2 )
   => ( ( ~ disjoint(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK3))
        | ~ disjoint(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK3,singleton(sK1))) )
      & sK1 != sK2 ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2,X3] :
      ( ( ~ disjoint(cartesian_product2(singleton(X2),X0),cartesian_product2(singleton(X1),X3))
        | ~ disjoint(cartesian_product2(X0,singleton(X2)),cartesian_product2(X3,singleton(X1))) )
      & X1 != X2 ),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ? [X2,X0,X3,X1] :
      ( ( ~ disjoint(cartesian_product2(singleton(X3),X2),cartesian_product2(singleton(X0),X1))
        | ~ disjoint(cartesian_product2(X2,singleton(X3)),cartesian_product2(X1,singleton(X0))) )
      & X0 != X3 ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,plain,
    ~ ! [X3,X0,X1,X2] :
        ( X0 != X3
       => ( disjoint(cartesian_product2(X2,singleton(X3)),cartesian_product2(X1,singleton(X0)))
          & disjoint(cartesian_product2(singleton(X3),X2),cartesian_product2(singleton(X0),X1)) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X1,X3,X2,X0] :
        ( X0 != X1
       => ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
          & disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X1,X3,X2,X0] :
      ( X0 != X1
     => ( disjoint(cartesian_product2(singleton(X0),X2),cartesian_product2(singleton(X1),X3))
        & disjoint(cartesian_product2(X2,singleton(X0)),cartesian_product2(X3,singleton(X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t131_zfmisc_1) ).

fof(f55,plain,
    ( disjoint(sF6,sF8)
    | sK1 = sK2 ),
    inference(superposition,[],[f49,f34]) ).

fof(f34,plain,
    singleton(sK1) = sF8,
    introduced(function_definition,[]) ).

fof(f49,plain,
    ! [X0] :
      ( disjoint(sF6,singleton(X0))
      | sK2 = X0 ),
    inference(superposition,[],[f26,f32]) ).

fof(f32,plain,
    singleton(sK2) = sF6,
    introduced(function_definition,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( disjoint(singleton(X1),singleton(X0))
      | X0 = X1 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( disjoint(singleton(X1),singleton(X0))
      | X0 = X1 ),
    inference(rectify,[],[f10]) ).

fof(f10,plain,
    ! [X1,X0] :
      ( disjoint(singleton(X0),singleton(X1))
      | X0 = X1 ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( X0 != X1
     => disjoint(singleton(X0),singleton(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_zfmisc_1) ).

fof(f25,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X3,X0)
      | disjoint(cartesian_product2(X3,X1),cartesian_product2(X0,X2)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2,X3] :
      ( ( ~ disjoint(X3,X0)
        & ~ disjoint(X1,X2) )
      | disjoint(cartesian_product2(X3,X1),cartesian_product2(X0,X2)) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X3,X2,X1,X0] :
      ( ( ~ disjoint(X0,X3)
        & ~ disjoint(X2,X1) )
      | disjoint(cartesian_product2(X0,X2),cartesian_product2(X3,X1)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ! [X1,X3,X2,X0] :
      ( ( disjoint(X2,X1)
        | disjoint(X0,X3) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X3,X1)) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X3,X2,X1] :
      ( ( disjoint(X0,X1)
        | disjoint(X2,X3) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(f98,plain,
    spl12_2,
    inference(avatar_split_clause,[],[f97,f44]) ).

fof(f44,plain,
    ( spl12_2
  <=> disjoint(sF10,sF11) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f97,plain,
    disjoint(sF10,sF11),
    inference(superposition,[],[f92,f37]) ).

fof(f37,plain,
    cartesian_product2(sK3,sF8) = sF11,
    introduced(function_definition,[]) ).

fof(f92,plain,
    ! [X0] : disjoint(sF10,cartesian_product2(X0,sF8)),
    inference(superposition,[],[f71,f36]) ).

fof(f36,plain,
    sF10 = cartesian_product2(sK0,sF6),
    introduced(function_definition,[]) ).

fof(f71,plain,
    ! [X10,X11] : disjoint(cartesian_product2(X10,sF6),cartesian_product2(X11,sF8)),
    inference(resolution,[],[f24,f56]) ).

fof(f24,plain,
    ! [X2,X3,X0,X1] :
      ( ~ disjoint(X1,X2)
      | disjoint(cartesian_product2(X3,X1),cartesian_product2(X0,X2)) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f47,plain,
    ( ~ spl12_1
    | ~ spl12_2 ),
    inference(avatar_split_clause,[],[f38,f44,f40]) ).

fof(f38,plain,
    ( ~ disjoint(sF10,sF11)
    | ~ disjoint(sF7,sF9) ),
    inference(definition_folding,[],[f28,f37,f34,f36,f32,f35,f34,f33,f32]) ).

fof(f28,plain,
    ( ~ disjoint(cartesian_product2(singleton(sK2),sK0),cartesian_product2(singleton(sK1),sK3))
    | ~ disjoint(cartesian_product2(sK0,singleton(sK2)),cartesian_product2(sK3,singleton(sK1))) ),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET978+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_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n020.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 14:35:15 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.20/0.53  % (29358)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.53  % (29358)First to succeed.
% 0.20/0.54  % (29366)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.20/0.54  % (29358)Refutation found. Thanks to Tanya!
% 0.20/0.54  % SZS status Theorem for theBenchmark
% 0.20/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.54  % (29358)------------------------------
% 0.20/0.54  % (29358)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54  % (29358)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54  % (29358)Termination reason: Refutation
% 0.20/0.54  
% 0.20/0.54  % (29358)Memory used [KB]: 5500
% 0.20/0.54  % (29358)Time elapsed: 0.096 s
% 0.20/0.54  % (29358)Instructions burned: 5 (million)
% 0.20/0.54  % (29358)------------------------------
% 0.20/0.54  % (29358)------------------------------
% 0.20/0.54  % (29353)Success in time 0.183 s
%------------------------------------------------------------------------------