TSTP Solution File: SET906+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET906+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 : n025.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 18:26:03 EDT 2022

% Result   : Theorem 1.31s 0.57s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   39 (   8 unt;   0 def)
%            Number of atoms       :  202 (  70 equ)
%            Maximal formula atoms :   14 (   5 avg)
%            Number of connectives :  251 (  88   ~;  92   |;  53   &)
%                                         (   9 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :  114 (  97   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f168,plain,
    $false,
    inference(subsumption_resolution,[],[f166,f57]) ).

fof(f57,plain,
    ~ in(sK2,sK3),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3)
    & ~ in(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f34,f35]) ).

fof(f35,plain,
    ( ? [X0,X1,X2] :
        ( subset(set_union2(unordered_pair(X1,X0),X2),X2)
        & ~ in(X1,X2) )
   => ( subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3)
      & ~ in(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0,X1,X2] :
      ( subset(set_union2(unordered_pair(X1,X0),X2),X2)
      & ~ in(X1,X2) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ? [X1,X2,X0] :
      ( subset(set_union2(unordered_pair(X2,X1),X0),X0)
      & ~ in(X2,X0) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,plain,
    ~ ! [X0,X2,X1] :
        ( subset(set_union2(unordered_pair(X2,X1),X0),X0)
       => in(X2,X0) ),
    inference(rectify,[],[f14]) ).

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

fof(f13,conjecture,
    ! [X2,X1,X0] :
      ( subset(set_union2(unordered_pair(X0,X1),X2),X2)
     => in(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_zfmisc_1) ).

fof(f166,plain,
    in(sK2,sK3),
    inference(resolution,[],[f164,f77]) ).

fof(f77,plain,
    ! [X3,X1] : in(X3,unordered_pair(X3,X1)),
    inference(equality_resolution,[],[f76]) ).

fof(f76,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | unordered_pair(X3,X1) != X0 ),
    inference(equality_resolution,[],[f55]) ).

fof(f55,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | X2 != X3
      | unordered_pair(X2,X1) != X0 ),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ( ( ~ in(sK0(X0,X1,X2),X0)
            | ( sK0(X0,X1,X2) != X2
              & sK0(X0,X1,X2) != X1 ) )
          & ( in(sK0(X0,X1,X2),X0)
            | sK0(X0,X1,X2) = X2
            | sK0(X0,X1,X2) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f31,f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ( X2 != X4
              & X1 != X4 ) )
          & ( in(X4,X0)
            | X2 = X4
            | X1 = X4 ) )
     => ( ( ~ in(sK0(X0,X1,X2),X0)
          | ( sK0(X0,X1,X2) != X2
            & sK0(X0,X1,X2) != X1 ) )
        & ( in(sK0(X0,X1,X2),X0)
          | sK0(X0,X1,X2) = X2
          | sK0(X0,X1,X2) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f31,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X2,X1) != X0 )
      & ( unordered_pair(X2,X1) = X0
        | ? [X4] :
            ( ( ~ in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( in(X4,X0)
              | X2 = X4
              | X1 = X4 ) ) ) ),
    inference(rectify,[],[f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( in(X3,X2)
              | X1 = X3
              | X0 = X3 ) ) ) ),
    inference(flattening,[],[f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ( ! [X3] :
            ( ( X1 = X3
              | X0 = X3
              | ~ in(X3,X2) )
            & ( in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) ) )
        | unordered_pair(X1,X0) != X2 )
      & ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ~ in(X3,X2)
              | ( X1 != X3
                & X0 != X3 ) )
            & ( in(X3,X2)
              | X1 = X3
              | X0 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( ( X1 = X3
            | X0 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X1,X0) = X2 ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( ! [X3] :
          ( ( X1 = X3
            | X0 = X3 )
        <=> in(X3,X2) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f164,plain,
    ! [X0] :
      ( ~ in(X0,unordered_pair(sK2,sK1))
      | in(X0,sK3) ),
    inference(resolution,[],[f149,f81]) ).

fof(f81,plain,
    ! [X2,X0,X4] :
      ( in(X4,set_union2(X2,X0))
      | ~ in(X4,X0) ),
    inference(equality_resolution,[],[f68]) ).

fof(f68,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X1)
      | ~ in(X4,X0)
      | set_union2(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X2,X0) = X1
        | ( ( ( ~ in(sK6(X0,X1,X2),X2)
              & ~ in(sK6(X0,X1,X2),X0) )
            | ~ in(sK6(X0,X1,X2),X1) )
          & ( in(sK6(X0,X1,X2),X2)
            | in(sK6(X0,X1,X2),X0)
            | in(sK6(X0,X1,X2),X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( ~ in(X4,X2)
                & ~ in(X4,X0) ) )
            & ( in(X4,X2)
              | in(X4,X0)
              | ~ in(X4,X1) ) )
        | set_union2(X2,X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f47,f48]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( ~ in(X3,X2)
              & ~ in(X3,X0) )
            | ~ in(X3,X1) )
          & ( in(X3,X2)
            | in(X3,X0)
            | in(X3,X1) ) )
     => ( ( ( ~ in(sK6(X0,X1,X2),X2)
            & ~ in(sK6(X0,X1,X2),X0) )
          | ~ in(sK6(X0,X1,X2),X1) )
        & ( in(sK6(X0,X1,X2),X2)
          | in(sK6(X0,X1,X2),X0)
          | in(sK6(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ( set_union2(X2,X0) = X1
        | ? [X3] :
            ( ( ( ~ in(X3,X2)
                & ~ in(X3,X0) )
              | ~ in(X3,X1) )
            & ( in(X3,X2)
              | in(X3,X0)
              | in(X3,X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( ~ in(X4,X2)
                & ~ in(X4,X0) ) )
            & ( in(X4,X2)
              | in(X4,X0)
              | ~ in(X4,X1) ) )
        | set_union2(X2,X0) != X1 ) ),
    inference(rectify,[],[f46]) ).

fof(f46,plain,
    ! [X2,X1,X0] :
      ( ( set_union2(X0,X2) = X1
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_union2(X0,X2) != X1 ) ),
    inference(flattening,[],[f45]) ).

fof(f45,plain,
    ! [X2,X1,X0] :
      ( ( set_union2(X0,X2) = X1
        | ? [X3] :
            ( ( ( ~ in(X3,X0)
                & ~ in(X3,X2) )
              | ~ in(X3,X1) )
            & ( in(X3,X0)
              | in(X3,X2)
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ( ~ in(X3,X0)
                & ~ in(X3,X2) ) )
            & ( in(X3,X0)
              | in(X3,X2)
              | ~ in(X3,X1) ) )
        | set_union2(X0,X2) != X1 ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X2,X1,X0] :
      ( set_union2(X0,X2) = X1
    <=> ! [X3] :
          ( in(X3,X1)
        <=> ( in(X3,X0)
            | in(X3,X2) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X2,X1] :
      ( set_union2(X0,X1) = X2
    <=> ! [X3] :
          ( ( in(X3,X1)
            | in(X3,X0) )
        <=> in(X3,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

fof(f149,plain,
    ! [X1] :
      ( ~ in(X1,set_union2(sK3,unordered_pair(sK2,sK1)))
      | in(X1,sK3) ),
    inference(resolution,[],[f74,f90]) ).

fof(f90,plain,
    subset(set_union2(sK3,unordered_pair(sK2,sK1)),sK3),
    inference(superposition,[],[f58,f59]) ).

fof(f59,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

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

fof(f58,plain,
    subset(set_union2(unordered_pair(sK2,sK1),sK3),sK3),
    inference(cnf_transformation,[],[f36]) ).

fof(f74,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | in(X2,X1)
      | ~ in(X2,X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
     => ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    inference(unused_predicate_definition_removal,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET906+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
% 0.13/0.35  % Computer : n025.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 14:48:00 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.31/0.55  % (20015)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.31/0.56  % (20015)First to succeed.
% 1.31/0.56  % (20035)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)
% 1.31/0.56  % (20036)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.31/0.56  % (20027)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)
% 1.31/0.57  % (20028)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.31/0.57  % (20015)Refutation found. Thanks to Tanya!
% 1.31/0.57  % SZS status Theorem for theBenchmark
% 1.31/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.57  % (20015)------------------------------
% 1.31/0.57  % (20015)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.57  % (20015)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.57  % (20015)Termination reason: Refutation
% 1.31/0.57  
% 1.31/0.57  % (20015)Memory used [KB]: 1023
% 1.31/0.57  % (20015)Time elapsed: 0.130 s
% 1.31/0.57  % (20015)Instructions burned: 5 (million)
% 1.31/0.57  % (20015)------------------------------
% 1.31/0.57  % (20015)------------------------------
% 1.31/0.57  % (20012)Success in time 0.21 s
%------------------------------------------------------------------------------