TSTP Solution File: SET909+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET909+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 : n023.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 18:26:04 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   42 (  16 unt;   0 def)
%            Number of atoms       :  200 (  90 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  249 (  91   ~;  94   |;  51   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-3 aty)
%            Number of variables   :  121 ( 101   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f122,plain,
    $false,
    inference(resolution,[],[f116,f79]) ).

fof(f79,plain,
    ! [X0,X4] : in(X4,unordered_pair(X0,X4)),
    inference(equality_resolution,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X4] :
      ( in(X4,X1)
      | unordered_pair(X0,X4) != X1 ),
    inference(equality_resolution,[],[f61]) ).

fof(f61,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | X2 != X4
      | unordered_pair(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X2) = X1
        | ( ( ~ in(sK5(X0,X1,X2),X1)
            | ( sK5(X0,X1,X2) != X2
              & sK5(X0,X1,X2) != X0 ) )
          & ( in(sK5(X0,X1,X2),X1)
            | sK5(X0,X1,X2) = X2
            | sK5(X0,X1,X2) = X0 ) ) )
      & ( ! [X4] :
            ( ( X2 = X4
              | X0 = X4
              | ~ in(X4,X1) )
            & ( in(X4,X1)
              | ( X2 != X4
                & X0 != X4 ) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f39,f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ( X2 != X3
              & X0 != X3 ) )
          & ( in(X3,X1)
            | X2 = X3
            | X0 = X3 ) )
     => ( ( ~ in(sK5(X0,X1,X2),X1)
          | ( sK5(X0,X1,X2) != X2
            & sK5(X0,X1,X2) != X0 ) )
        & ( in(sK5(X0,X1,X2),X1)
          | sK5(X0,X1,X2) = X2
          | sK5(X0,X1,X2) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X2) = X1
        | ? [X3] :
            ( ( ~ in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( in(X3,X1)
              | X2 = X3
              | X0 = X3 ) ) )
      & ( ! [X3] :
            ( ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X0,X2) != X1 ) ),
    inference(nnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X2) = X1
    <=> ! [X3] :
          ( ( X2 = X3
            | X0 = X3 )
        <=> in(X3,X1) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X2,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f116,plain,
    ! [X9] : ~ in(X9,unordered_pair(sK2,sK3)),
    inference(subsumption_resolution,[],[f114,f76]) ).

fof(f76,plain,
    ! [X2] : ~ in(X2,empty_set),
    inference(equality_resolution,[],[f52]) ).

fof(f52,plain,
    ! [X2,X0] :
      ( ~ in(X2,X0)
      | empty_set != X0 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK0(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f27,f28]) ).

fof(f28,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK0(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(rectify,[],[f26]) ).

fof(f26,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

fof(f114,plain,
    ! [X9] :
      ( ~ in(X9,unordered_pair(sK2,sK3))
      | in(X9,empty_set) ),
    inference(superposition,[],[f83,f99]) ).

fof(f99,plain,
    empty_set = set_union2(sK1,unordered_pair(sK2,sK3)),
    inference(superposition,[],[f67,f55]) ).

fof(f55,plain,
    empty_set = set_union2(unordered_pair(sK2,sK3),sK1),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    empty_set = set_union2(unordered_pair(sK2,sK3),sK1),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f31,f32]) ).

fof(f32,plain,
    ( ? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X2),X0)
   => empty_set = set_union2(unordered_pair(sK2,sK3),sK1) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ? [X0,X1,X2] : empty_set = set_union2(unordered_pair(X1,X2),X0),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ? [X1,X0,X2] : empty_set = set_union2(unordered_pair(X0,X2),X1),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ~ ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X2),X1),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X0,X2,X1] : empty_set != set_union2(unordered_pair(X0,X1),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_zfmisc_1) ).

fof(f67,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f83,plain,
    ! [X2,X3,X0] :
      ( in(X3,set_union2(X2,X0))
      | ~ in(X3,X0) ),
    inference(equality_resolution,[],[f73]) ).

fof(f73,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,X0)
      | set_union2(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) ) )
        | set_union2(X2,X0) != X1 )
      & ( set_union2(X2,X0) = X1
        | ( ( ~ in(sK7(X0,X1,X2),X1)
            | ( ~ in(sK7(X0,X1,X2),X0)
              & ~ in(sK7(X0,X1,X2),X2) ) )
          & ( in(sK7(X0,X1,X2),X1)
            | in(sK7(X0,X1,X2),X0)
            | in(sK7(X0,X1,X2),X2) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f48,f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X1)
            | ( ~ in(X4,X0)
              & ~ in(X4,X2) ) )
          & ( in(X4,X1)
            | in(X4,X0)
            | in(X4,X2) ) )
     => ( ( ~ in(sK7(X0,X1,X2),X1)
          | ( ~ in(sK7(X0,X1,X2),X0)
            & ~ in(sK7(X0,X1,X2),X2) ) )
        & ( in(sK7(X0,X1,X2),X1)
          | in(sK7(X0,X1,X2),X0)
          | in(sK7(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) ) )
        | set_union2(X2,X0) != X1 )
      & ( set_union2(X2,X0) = X1
        | ? [X4] :
            ( ( ~ in(X4,X1)
              | ( ~ in(X4,X0)
                & ~ in(X4,X2) ) )
            & ( in(X4,X1)
              | in(X4,X0)
              | in(X4,X2) ) ) ) ),
    inference(rectify,[],[f47]) ).

fof(f47,plain,
    ! [X1,X0,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X2,X1) != X0 )
      & ( set_union2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) ) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X1,X0,X2] :
      ( ( ! [X3] :
            ( ( in(X3,X1)
              | in(X3,X2)
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) ) )
        | set_union2(X2,X1) != X0 )
      & ( set_union2(X2,X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( ~ in(X3,X1)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X1)
              | in(X3,X2) ) ) ) ),
    inference(nnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X2) )
        <=> in(X3,X0) )
    <=> set_union2(X2,X1) = X0 ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X1,X0] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X0)
            | in(X3,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET909+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n023.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 15:02:05 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.46  % (10313)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.46  % (10305)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.47  % (10313)First to succeed.
% 0.20/0.47  % (10313)Refutation found. Thanks to Tanya!
% 0.20/0.47  % SZS status Theorem for theBenchmark
% 0.20/0.47  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.47  % (10313)------------------------------
% 0.20/0.47  % (10313)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.47  % (10313)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.47  % (10313)Termination reason: Refutation
% 0.20/0.47  
% 0.20/0.47  % (10313)Memory used [KB]: 1023
% 0.20/0.47  % (10313)Time elapsed: 0.009 s
% 0.20/0.47  % (10313)Instructions burned: 4 (million)
% 0.20/0.47  % (10313)------------------------------
% 0.20/0.47  % (10313)------------------------------
% 0.20/0.47  % (10290)Success in time 0.117 s
%------------------------------------------------------------------------------