TSTP Solution File: SEU150+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU150+2 : 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 : n027.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 18:26:55 EDT 2022

% Result   : Theorem 0.15s 0.52s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (  14 unt;   0 def)
%            Number of atoms       :  167 ( 117 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  199 (  73   ~;  74   |;  40   &)
%                                         (   6 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   99 (  83   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f648,plain,
    $false,
    inference(subsumption_resolution,[],[f647,f287]) ).

fof(f287,plain,
    sK8 != sK9,
    inference(cnf_transformation,[],[f193]) ).

fof(f193,plain,
    ( singleton(sK10) = unordered_pair(sK9,sK8)
    & sK8 != sK9 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f191,f192]) ).

fof(f192,plain,
    ( ? [X0,X1,X2] :
        ( unordered_pair(X1,X0) = singleton(X2)
        & X0 != X1 )
   => ( singleton(sK10) = unordered_pair(sK9,sK8)
      & sK8 != sK9 ) ),
    introduced(choice_axiom,[]) ).

fof(f191,plain,
    ? [X0,X1,X2] :
      ( unordered_pair(X1,X0) = singleton(X2)
      & X0 != X1 ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ? [X1,X2,X0] :
      ( singleton(X0) = unordered_pair(X2,X1)
      & X1 != X2 ),
    inference(ennf_transformation,[],[f75]) ).

fof(f75,plain,
    ~ ! [X2,X1,X0] :
        ( singleton(X0) = unordered_pair(X2,X1)
       => X1 = X2 ),
    inference(rectify,[],[f74]) ).

fof(f74,negated_conjecture,
    ~ ! [X0,X2,X1] :
        ( singleton(X0) = unordered_pair(X1,X2)
       => X1 = X2 ),
    inference(negated_conjecture,[],[f73]) ).

fof(f73,conjecture,
    ! [X0,X2,X1] :
      ( singleton(X0) = unordered_pair(X1,X2)
     => X1 = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).

fof(f647,plain,
    sK8 = sK9,
    inference(backward_demodulation,[],[f628,f629]) ).

fof(f629,plain,
    sK10 = sK8,
    inference(resolution,[],[f626,f366]) ).

fof(f366,plain,
    ! [X2,X4] : in(X4,unordered_pair(X4,X2)),
    inference(equality_resolution,[],[f365]) ).

fof(f365,plain,
    ! [X2,X0,X4] :
      ( in(X4,X0)
      | unordered_pair(X4,X2) != X0 ),
    inference(equality_resolution,[],[f272]) ).

fof(f272,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X1 != X4
      | unordered_pair(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f181]) ).

fof(f181,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ( ( ( sK6(X0,X1,X2) != X2
              & sK6(X0,X1,X2) != X1 )
            | ~ in(sK6(X0,X1,X2),X0) )
          & ( sK6(X0,X1,X2) = X2
            | sK6(X0,X1,X2) = X1
            | in(sK6(X0,X1,X2),X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f179,f180]) ).

fof(f180,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X2 != X3
              & X1 != X3 )
            | ~ in(X3,X0) )
          & ( X2 = X3
            | X1 = X3
            | in(X3,X0) ) )
     => ( ( ( sK6(X0,X1,X2) != X2
            & sK6(X0,X1,X2) != X1 )
          | ~ in(sK6(X0,X1,X2),X0) )
        & ( sK6(X0,X1,X2) = X2
          | sK6(X0,X1,X2) = X1
          | in(sK6(X0,X1,X2),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f179,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ( X2 != X3
                & X1 != X3 )
              | ~ in(X3,X0) )
            & ( X2 = X3
              | X1 = X3
              | in(X3,X0) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X0)
              | ( X2 != X4
                & X1 != X4 ) )
            & ( X2 = X4
              | X1 = X4
              | ~ in(X4,X0) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(rectify,[],[f178]) ).

fof(f178,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ( X2 != X3
                & X1 != X3 )
              | ~ in(X3,X0) )
            & ( X2 = X3
              | X1 = X3
              | in(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(flattening,[],[f177]) ).

fof(f177,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ( X2 != X3
                & X1 != X3 )
              | ~ in(X3,X0) )
            & ( X2 = X3
              | X1 = X3
              | in(X3,X0) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) ) )
        | unordered_pair(X1,X2) != X0 ) ),
    inference(nnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X1,X2) = X0
    <=> ! [X3] :
          ( in(X3,X0)
        <=> ( X2 = X3
            | X1 = X3 ) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X2,X0,X1] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f626,plain,
    ! [X5] :
      ( ~ in(X5,unordered_pair(sK8,sK9))
      | sK10 = X5 ),
    inference(superposition,[],[f357,f417]) ).

fof(f417,plain,
    unordered_pair(sK8,sK9) = unordered_pair(sK10,sK10),
    inference(backward_demodulation,[],[f343,f295]) ).

fof(f295,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f343,plain,
    unordered_pair(sK9,sK8) = unordered_pair(sK10,sK10),
    inference(definition_unfolding,[],[f288,f282]) ).

fof(f282,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,axiom,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).

fof(f288,plain,
    singleton(sK10) = unordered_pair(sK9,sK8),
    inference(cnf_transformation,[],[f193]) ).

fof(f357,plain,
    ! [X2,X1] :
      ( ~ in(X2,unordered_pair(X1,X1))
      | X1 = X2 ),
    inference(equality_resolution,[],[f330]) ).

fof(f330,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ in(X2,X0)
      | unordered_pair(X1,X1) != X0 ),
    inference(definition_unfolding,[],[f249,f282]) ).

fof(f249,plain,
    ! [X2,X0,X1] :
      ( X1 = X2
      | ~ in(X2,X0)
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f161]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ( ( ~ in(sK3(X0,X1),X0)
            | sK3(X0,X1) != X1 )
          & ( in(sK3(X0,X1),X0)
            | sK3(X0,X1) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f159,f160]) ).

fof(f160,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ in(X3,X0)
            | X1 != X3 )
          & ( in(X3,X0)
            | X1 = X3 ) )
     => ( ( ~ in(sK3(X0,X1),X0)
          | sK3(X0,X1) != X1 )
        & ( in(sK3(X0,X1),X0)
          | sK3(X0,X1) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 )
      & ( singleton(X1) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | X1 != X3 )
            & ( in(X3,X0)
              | X1 = X3 ) ) ) ),
    inference(rectify,[],[f158]) ).

fof(f158,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( X0 = X2
              | ~ in(X2,X1) )
            & ( in(X2,X1)
              | X0 != X2 ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( X0 = X2
        <=> in(X2,X1) )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f628,plain,
    sK10 = sK9,
    inference(resolution,[],[f626,f364]) ).

fof(f364,plain,
    ! [X1,X4] : in(X4,unordered_pair(X1,X4)),
    inference(equality_resolution,[],[f363]) ).

fof(f363,plain,
    ! [X0,X1,X4] :
      ( in(X4,X0)
      | unordered_pair(X1,X4) != X0 ),
    inference(equality_resolution,[],[f273]) ).

fof(f273,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X0)
      | X2 != X4
      | unordered_pair(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f181]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem    : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.10/0.31  % Computer : n027.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.15/0.31  % WCLimit    : 300
% 0.15/0.31  % DateTime   : Tue Aug 30 15:06:31 EDT 2022
% 0.15/0.31  % CPUTime    : 
% 0.15/0.47  % (19858)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.15/0.47  % (19848)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.48  % (19850)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.15/0.48  % (19864)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.15/0.48  % (19856)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.15/0.48  % (19857)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.48  % (19856)Instruction limit reached!
% 0.15/0.48  % (19856)------------------------------
% 0.15/0.48  % (19856)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.49  % (19857)Instruction limit reached!
% 0.15/0.49  % (19857)------------------------------
% 0.15/0.49  % (19857)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.49  % (19849)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.15/0.49  % (19866)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.15/0.49  % (19856)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.49  % (19856)Termination reason: Unknown
% 0.15/0.49  % (19856)Termination phase: Function definition elimination
% 0.15/0.49  
% 0.15/0.49  % (19856)Memory used [KB]: 1535
% 0.15/0.49  % (19856)Time elapsed: 0.005 s
% 0.15/0.49  % (19856)Instructions burned: 4 (million)
% 0.15/0.49  % (19856)------------------------------
% 0.15/0.49  % (19856)------------------------------
% 0.15/0.49  % (19857)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.49  % (19857)Termination reason: Unknown
% 0.15/0.49  % (19857)Termination phase: Saturation
% 0.15/0.49  
% 0.15/0.49  % (19857)Memory used [KB]: 6140
% 0.15/0.49  % (19857)Time elapsed: 0.008 s
% 0.15/0.49  % (19857)Instructions burned: 7 (million)
% 0.15/0.49  % (19857)------------------------------
% 0.15/0.49  % (19857)------------------------------
% 0.15/0.50  % (19865)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.15/0.51  % (19845)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.15/0.51  % (19848)First to succeed.
% 0.15/0.52  % (19848)Refutation found. Thanks to Tanya!
% 0.15/0.52  % SZS status Theorem for theBenchmark
% 0.15/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.52  % (19848)------------------------------
% 0.15/0.52  % (19848)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.15/0.52  % (19848)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.15/0.52  % (19848)Termination reason: Refutation
% 0.15/0.52  
% 0.15/0.52  % (19848)Memory used [KB]: 6268
% 0.15/0.52  % (19848)Time elapsed: 0.142 s
% 0.15/0.52  % (19848)Instructions burned: 15 (million)
% 0.15/0.52  % (19848)------------------------------
% 0.15/0.52  % (19848)------------------------------
% 0.15/0.52  % (19841)Success in time 0.196 s
%------------------------------------------------------------------------------