TSTP Solution File: SEU223+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU223+3 : 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 : n005.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 18:32:38 EDT 2022

% Result   : Theorem 0.19s 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   49 (  15 unt;   0 def)
%            Number of atoms       :  200 (  65 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  244 (  93   ~;  81   |;  50   &)
%                                         (   4 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   7 con; 0-2 aty)
%            Number of variables   :   88 (  72   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f533,plain,
    $false,
    inference(subsumption_resolution,[],[f532,f194]) ).

fof(f194,plain,
    sF18 != sF17,
    inference(definition_folding,[],[f133,f193,f192,f189]) ).

fof(f189,plain,
    sF15 = relation_dom_restriction(sK1,sK2),
    introduced(function_definition,[]) ).

fof(f192,plain,
    apply(sF15,sK3) = sF17,
    introduced(function_definition,[]) ).

fof(f193,plain,
    sF18 = apply(sK1,sK3),
    introduced(function_definition,[]) ).

fof(f133,plain,
    apply(relation_dom_restriction(sK1,sK2),sK3) != apply(sK1,sK3),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( relation(sK1)
    & in(sK3,relation_dom(relation_dom_restriction(sK1,sK2)))
    & function(sK1)
    & apply(relation_dom_restriction(sK1,sK2),sK3) != apply(sK1,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f88,f89]) ).

fof(f89,plain,
    ( ? [X0,X1,X2] :
        ( relation(X0)
        & in(X2,relation_dom(relation_dom_restriction(X0,X1)))
        & function(X0)
        & apply(relation_dom_restriction(X0,X1),X2) != apply(X0,X2) )
   => ( relation(sK1)
      & in(sK3,relation_dom(relation_dom_restriction(sK1,sK2)))
      & function(sK1)
      & apply(relation_dom_restriction(sK1,sK2),sK3) != apply(sK1,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ? [X0,X1,X2] :
      ( relation(X0)
      & in(X2,relation_dom(relation_dom_restriction(X0,X1)))
      & function(X0)
      & apply(relation_dom_restriction(X0,X1),X2) != apply(X0,X2) ),
    inference(rectify,[],[f73]) ).

fof(f73,plain,
    ? [X1,X2,X0] :
      ( relation(X1)
      & in(X0,relation_dom(relation_dom_restriction(X1,X2)))
      & function(X1)
      & apply(relation_dom_restriction(X1,X2),X0) != apply(X1,X0) ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ? [X0,X1,X2] :
      ( apply(relation_dom_restriction(X1,X2),X0) != apply(X1,X0)
      & in(X0,relation_dom(relation_dom_restriction(X1,X2)))
      & relation(X1)
      & function(X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ~ ! [X0,X1,X2] :
        ( ( relation(X1)
          & function(X1) )
       => ( in(X0,relation_dom(relation_dom_restriction(X1,X2)))
         => apply(relation_dom_restriction(X1,X2),X0) = apply(X1,X0) ) ),
    inference(rectify,[],[f39]) ).

fof(f39,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( relation(X2)
          & function(X2) )
       => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
         => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    inference(negated_conjecture,[],[f38]) ).

fof(f38,conjecture,
    ! [X1,X2,X0] :
      ( ( relation(X2)
        & function(X2) )
     => ( in(X1,relation_dom(relation_dom_restriction(X2,X0)))
       => apply(relation_dom_restriction(X2,X0),X1) = apply(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t70_funct_1) ).

fof(f532,plain,
    sF18 = sF17,
    inference(forward_demodulation,[],[f531,f192]) ).

fof(f531,plain,
    sF18 = apply(sF15,sK3),
    inference(forward_demodulation,[],[f528,f193]) ).

fof(f528,plain,
    apply(sF15,sK3) = apply(sK1,sK3),
    inference(resolution,[],[f445,f191]) ).

fof(f191,plain,
    in(sK3,sF16),
    inference(definition_folding,[],[f135,f190,f189]) ).

fof(f190,plain,
    sF16 = relation_dom(sF15),
    introduced(function_definition,[]) ).

fof(f135,plain,
    in(sK3,relation_dom(relation_dom_restriction(sK1,sK2))),
    inference(cnf_transformation,[],[f90]) ).

fof(f445,plain,
    ! [X0] :
      ( ~ in(X0,sF16)
      | apply(sF15,X0) = apply(sK1,X0) ),
    inference(forward_demodulation,[],[f444,f190]) ).

fof(f444,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sF15,X0) = apply(sK1,X0) ),
    inference(subsumption_resolution,[],[f443,f136]) ).

fof(f136,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f443,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sF15,X0) = apply(sK1,X0)
      | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f442,f338]) ).

fof(f338,plain,
    function(sF15),
    inference(subsumption_resolution,[],[f337,f136]) ).

fof(f337,plain,
    ( function(sF15)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f336,f134]) ).

fof(f134,plain,
    function(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f336,plain,
    ( ~ function(sK1)
    | ~ relation(sK1)
    | function(sF15) ),
    inference(superposition,[],[f168,f189]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( function(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X1,X0] :
      ( ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) )
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ( relation(X1)
        & function(X1) )
     => ( function(relation_dom_restriction(X1,X0))
        & relation(relation_dom_restriction(X1,X0)) ) ),
    inference(rectify,[],[f24]) ).

fof(f24,axiom,
    ! [X1,X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_dom_restriction(X0,X1))
        & relation(relation_dom_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_funct_1) ).

fof(f442,plain,
    ! [X0] :
      ( apply(sF15,X0) = apply(sK1,X0)
      | ~ in(X0,relation_dom(sF15))
      | ~ function(sF15)
      | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f440,f134]) ).

fof(f440,plain,
    ! [X0] :
      ( apply(sF15,X0) = apply(sK1,X0)
      | ~ function(sK1)
      | ~ in(X0,relation_dom(sF15))
      | ~ relation(sK1)
      | ~ function(sF15) ),
    inference(superposition,[],[f195,f189]) ).

fof(f195,plain,
    ! [X2,X3,X1] :
      ( ~ in(X3,relation_dom(relation_dom_restriction(X2,X1)))
      | ~ relation(X2)
      | ~ function(X2)
      | ~ function(relation_dom_restriction(X2,X1))
      | apply(X2,X3) = apply(relation_dom_restriction(X2,X1),X3) ),
    inference(subsumption_resolution,[],[f187,f167]) ).

fof(f167,plain,
    ! [X0,X1] :
      ( relation(relation_dom_restriction(X0,X1))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f187,plain,
    ! [X2,X3,X1] :
      ( ~ relation(relation_dom_restriction(X2,X1))
      | ~ function(relation_dom_restriction(X2,X1))
      | ~ relation(X2)
      | apply(X2,X3) = apply(relation_dom_restriction(X2,X1),X3)
      | ~ function(X2)
      | ~ in(X3,relation_dom(relation_dom_restriction(X2,X1))) ),
    inference(equality_resolution,[],[f142]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( ~ function(X2)
      | ~ in(X3,relation_dom(X0))
      | apply(X2,X3) = apply(X0,X3)
      | relation_dom_restriction(X2,X1) != X0
      | ~ relation(X2)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ( ( ( ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ( in(sK4(X0,X2),relation_dom(X0))
                & apply(X2,sK4(X0,X2)) != apply(X0,sK4(X0,X2)) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) )
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f93,f94]) ).

fof(f94,plain,
    ! [X0,X2] :
      ( ? [X4] :
          ( in(X4,relation_dom(X0))
          & apply(X2,X4) != apply(X0,X4) )
     => ( in(sK4(X0,X2),relation_dom(X0))
        & apply(X2,sK4(X0,X2)) != apply(X0,sK4(X0,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f93,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ( ( ( ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ? [X4] :
                  ( in(X4,relation_dom(X0))
                  & apply(X2,X4) != apply(X0,X4) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) )
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f92]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ( ( ( ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ? [X3] :
                  ( in(X3,relation_dom(X0))
                  & apply(X2,X3) != apply(X0,X3) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) )
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f91]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ( ( ( ! [X3] :
                    ( ~ in(X3,relation_dom(X0))
                    | apply(X2,X3) = apply(X0,X3) )
                & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
              | relation_dom_restriction(X2,X1) != X0 )
            & ( relation_dom_restriction(X2,X1) = X0
              | ? [X3] :
                  ( in(X3,relation_dom(X0))
                  & apply(X2,X3) != apply(X0,X3) )
              | relation_dom(X0) != set_intersection2(relation_dom(X2),X1) ) )
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ function(X2)
          | ( ( ! [X3] :
                  ( ~ in(X3,relation_dom(X0))
                  | apply(X2,X3) = apply(X0,X3) )
              & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
          <=> relation_dom_restriction(X2,X1) = X0 )
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( ! [X3] :
                  ( ~ in(X3,relation_dom(X0))
                  | apply(X2,X3) = apply(X0,X3) )
              & relation_dom(X0) = set_intersection2(relation_dom(X2),X1) )
          <=> relation_dom_restriction(X2,X1) = X0 )
          | ~ relation(X2)
          | ~ function(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( relation_dom(X0) = set_intersection2(relation_dom(X2),X1)
              & ! [X3] :
                  ( in(X3,relation_dom(X0))
                 => apply(X2,X3) = apply(X0,X3) ) )
          <=> relation_dom_restriction(X2,X1) = X0 ) ) ),
    inference(rectify,[],[f40]) ).

fof(f40,axiom,
    ! [X1,X0] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X1,X3) = apply(X2,X3) )
              & relation_dom(X1) = set_intersection2(relation_dom(X2),X0) )
          <=> relation_dom_restriction(X2,X0) = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t68_funct_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SEU223+3 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n005.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:52:18 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.46  % (29149)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.46  % (29140)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.47  % (29149)First to succeed.
% 0.19/0.49  % (29149)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (29149)------------------------------
% 0.19/0.49  % (29149)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (29149)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (29149)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (29149)Memory used [KB]: 5628
% 0.19/0.49  % (29149)Time elapsed: 0.084 s
% 0.19/0.49  % (29149)Instructions burned: 13 (million)
% 0.19/0.49  % (29149)------------------------------
% 0.19/0.49  % (29149)------------------------------
% 0.19/0.49  % (29123)Success in time 0.141 s
%------------------------------------------------------------------------------