TSTP Solution File: SEU126+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 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 18:26:46 EDT 2022

% Result   : Theorem 1.29s 0.52s
% Output   : Refutation 1.29s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   40 (   9 unt;   0 def)
%            Number of atoms       :  161 (  34 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  182 (  61   ~;  69   |;  37   &)
%                                         (   7 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-3 aty)
%            Number of variables   :   89 (  76   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f133,plain,
    $false,
    inference(subsumption_resolution,[],[f127,f72]) ).

fof(f72,plain,
    set_union2(sK2,sK3) != sK3,
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( subset(sK2,sK3)
    & set_union2(sK2,sK3) != sK3 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f50,f51]) ).

fof(f51,plain,
    ( ? [X0,X1] :
        ( subset(X0,X1)
        & set_union2(X0,X1) != X1 )
   => ( subset(sK2,sK3)
      & set_union2(sK2,sK3) != sK3 ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0,X1] :
      ( subset(X0,X1)
      & set_union2(X0,X1) != X1 ),
    inference(rectify,[],[f29]) ).

fof(f29,plain,
    ? [X1,X0] :
      ( subset(X1,X0)
      & set_union2(X1,X0) != X0 ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ~ ! [X0,X1] :
        ( subset(X1,X0)
       => set_union2(X1,X0) = X0 ),
    inference(rectify,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X1,X0] :
        ( subset(X0,X1)
       => set_union2(X0,X1) = X1 ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X1,X0] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f127,plain,
    set_union2(sK2,sK3) = sK3,
    inference(superposition,[],[f55,f123]) ).

fof(f123,plain,
    set_union2(sK3,sK2) = sK3,
    inference(subsumption_resolution,[],[f122,f108]) ).

fof(f108,plain,
    ! [X1] :
      ( in(sK0(sK3,X1,sK2),X1)
      | in(sK0(sK3,X1,sK2),sK3)
      | set_union2(X1,sK2) = sK3 ),
    inference(factoring,[],[f93]) ).

fof(f93,plain,
    ! [X2,X1] :
      ( in(sK0(X1,X2,sK2),sK3)
      | in(sK0(X1,X2,sK2),X2)
      | in(sK0(X1,X2,sK2),X1)
      | set_union2(X2,sK2) = X1 ),
    inference(resolution,[],[f82,f56]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( in(sK0(X0,X1,X2),X2)
      | in(sK0(X0,X1,X2),X1)
      | in(sK0(X0,X1,X2),X0)
      | set_union2(X1,X2) = X0 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 )
      & ( set_union2(X1,X2) = X0
        | ( ( ~ in(sK0(X0,X1,X2),X0)
            | ( ~ in(sK0(X0,X1,X2),X1)
              & ~ in(sK0(X0,X1,X2),X2) ) )
          & ( in(sK0(X0,X1,X2),X0)
            | in(sK0(X0,X1,X2),X1)
            | in(sK0(X0,X1,X2),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f39,f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ( ~ in(X4,X1)
              & ~ in(X4,X2) ) )
          & ( in(X4,X0)
            | in(X4,X1)
            | in(X4,X2) ) )
     => ( ( ~ in(sK0(X0,X1,X2),X0)
          | ( ~ in(sK0(X0,X1,X2),X1)
            & ~ in(sK0(X0,X1,X2),X2) ) )
        & ( in(sK0(X0,X1,X2),X0)
          | in(sK0(X0,X1,X2),X1)
          | in(sK0(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 )
      & ( set_union2(X1,X2) = X0
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ( ~ in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( in(X4,X0)
              | in(X4,X1)
              | in(X4,X2) ) ) ) ),
    inference(rectify,[],[f38]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 )
      & ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) ) ),
    inference(flattening,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X1,X2) != X0 )
      & ( set_union2(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) ) ),
    inference(nnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X2) )
        <=> in(X3,X0) )
    <=> set_union2(X1,X2) = X0 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X2,X0,X1] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            | in(X3,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f82,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | in(X0,sK3) ),
    inference(resolution,[],[f73,f68]) ).

fof(f68,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | in(X2,X1)
      | ~ in(X2,X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ in(sK1(X0,X1),X1)
          & in(sK1(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f46,f47]) ).

fof(f47,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ in(X3,X1)
          & in(X3,X0) )
     => ( ~ in(sK1(X0,X1),X1)
        & in(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    inference(rectify,[],[f45]) ).

fof(f45,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
          | ~ in(X2,X1) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f73,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f52]) ).

fof(f122,plain,
    ( set_union2(sK3,sK2) = sK3
    | ~ in(sK0(sK3,sK3,sK2),sK3) ),
    inference(duplicate_literal_removal,[],[f121]) ).

fof(f121,plain,
    ( ~ in(sK0(sK3,sK3,sK2),sK3)
    | set_union2(sK3,sK2) = sK3
    | set_union2(sK3,sK2) = sK3 ),
    inference(resolution,[],[f117,f58]) ).

fof(f58,plain,
    ! [X2,X0,X1] :
      ( ~ in(sK0(X0,X1,X2),X1)
      | set_union2(X1,X2) = X0
      | ~ in(sK0(X0,X1,X2),X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f117,plain,
    ! [X2] :
      ( in(sK0(X2,X2,sK2),sK3)
      | set_union2(X2,sK2) = X2 ),
    inference(subsumption_resolution,[],[f109,f58]) ).

fof(f109,plain,
    ! [X2] :
      ( in(sK0(X2,X2,sK2),X2)
      | set_union2(X2,sK2) = X2
      | in(sK0(X2,X2,sK2),sK3) ),
    inference(factoring,[],[f93]) ).

fof(f55,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU126+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:52:06 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.49  % (22449)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)
% 0.20/0.52  % (22473)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.29/0.52  % (22449)First to succeed.
% 1.29/0.52  % (22449)Refutation found. Thanks to Tanya!
% 1.29/0.52  % SZS status Theorem for theBenchmark
% 1.29/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.29/0.52  % (22449)------------------------------
% 1.29/0.52  % (22449)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.29/0.52  % (22449)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.29/0.52  % (22449)Termination reason: Refutation
% 1.29/0.52  
% 1.29/0.52  % (22449)Memory used [KB]: 6012
% 1.29/0.52  % (22449)Time elapsed: 0.101 s
% 1.29/0.52  % (22449)Instructions burned: 4 (million)
% 1.29/0.52  % (22449)------------------------------
% 1.29/0.52  % (22449)------------------------------
% 1.29/0.52  % (22447)Success in time 0.174 s
%------------------------------------------------------------------------------