TSTP Solution File: SET882+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET882+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 : n011.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 18:26:00 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   39 (  13 unt;   0 def)
%            Number of atoms       :  124 (  79 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  142 (  57   ~;  48   |;  26   &)
%                                         (   6 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   62 (  55   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f181,plain,
    $false,
    inference(subsumption_resolution,[],[f180,f51]) ).

fof(f51,plain,
    sF7 != sF8,
    inference(definition_folding,[],[f34,f50,f49,f48,f47]) ).

fof(f47,plain,
    sF5 = unordered_pair(sK2,sK1),
    introduced(function_definition,[]) ).

fof(f48,plain,
    sF6 = singleton(sK1),
    introduced(function_definition,[]) ).

fof(f49,plain,
    set_difference(sF5,sF6) = sF7,
    introduced(function_definition,[]) ).

fof(f50,plain,
    singleton(sK2) = sF8,
    introduced(function_definition,[]) ).

fof(f34,plain,
    set_difference(unordered_pair(sK2,sK1),singleton(sK1)) != singleton(sK2),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ( sK1 != sK2
    & set_difference(unordered_pair(sK2,sK1),singleton(sK1)) != singleton(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f20]) ).

fof(f20,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & singleton(X1) != set_difference(unordered_pair(X1,X0),singleton(X0)) )
   => ( sK1 != sK2
      & set_difference(unordered_pair(sK2,sK1),singleton(sK1)) != singleton(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( X0 != X1
      & singleton(X1) != set_difference(unordered_pair(X1,X0),singleton(X0)) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,plain,
    ~ ! [X1,X0] :
        ( X0 != X1
       => singleton(X1) = set_difference(unordered_pair(X1,X0),singleton(X0)) ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X0] :
        ( X0 != X1
       => singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X0] :
      ( X0 != X1
     => singleton(X0) = set_difference(unordered_pair(X0,X1),singleton(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).

fof(f180,plain,
    sF7 = sF8,
    inference(forward_demodulation,[],[f179,f49]) ).

fof(f179,plain,
    set_difference(sF5,sF6) = sF8,
    inference(forward_demodulation,[],[f178,f50]) ).

fof(f178,plain,
    set_difference(sF5,sF6) = singleton(sK2),
    inference(subsumption_resolution,[],[f169,f35]) ).

fof(f35,plain,
    sK1 != sK2,
    inference(cnf_transformation,[],[f21]) ).

fof(f169,plain,
    ( sK1 = sK2
    | set_difference(sF5,sF6) = singleton(sK2) ),
    inference(superposition,[],[f120,f47]) ).

fof(f120,plain,
    ! [X0] :
      ( singleton(X0) = set_difference(unordered_pair(X0,sK1),sF6)
      | sK1 = X0 ),
    inference(resolution,[],[f108,f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ~ in(X0,sF6)
      | sK1 = X0 ),
    inference(superposition,[],[f44,f48]) ).

fof(f44,plain,
    ! [X3,X0] :
      ( ~ in(X3,singleton(X0))
      | X0 = X3 ),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X3,X0,X1] :
      ( X0 = X3
      | ~ in(X3,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ( ( ~ in(sK4(X0,X1),X1)
            | sK4(X0,X1) != X0 )
          & ( in(sK4(X0,X1),X1)
            | sK4(X0,X1) = X0 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f26,f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | X0 != X2 )
          & ( in(X2,X1)
            | X0 = X2 ) )
     => ( ( ~ in(sK4(X0,X1),X1)
          | sK4(X0,X1) != X0 )
        & ( in(sK4(X0,X1),X1)
          | sK4(X0,X1) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( singleton(X0) = X1
        | ? [X2] :
            ( ( ~ in(X2,X1)
              | X0 != X2 )
            & ( in(X2,X1)
              | X0 = X2 ) ) )
      & ( ! [X3] :
            ( ( X0 = X3
              | ~ in(X3,X1) )
            & ( in(X3,X1)
              | X0 != X3 ) )
        | singleton(X0) != X1 ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) )
      & ( ! [X2] :
            ( ( X1 = X2
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | X1 != X2 ) )
        | singleton(X1) != X0 ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( singleton(X1) = X0
    <=> ! [X2] :
          ( X1 = X2
        <=> in(X2,X0) ) ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f108,plain,
    ! [X5] :
      ( in(X5,sF6)
      | singleton(X5) = set_difference(unordered_pair(X5,sK1),sF6) ),
    inference(resolution,[],[f31,f52]) ).

fof(f52,plain,
    in(sK1,sF6),
    inference(superposition,[],[f46,f48]) ).

fof(f46,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f45]) ).

fof(f45,plain,
    ! [X3,X1] :
      ( in(X3,X1)
      | singleton(X3) != X1 ),
    inference(equality_resolution,[],[f38]) ).

fof(f38,plain,
    ! [X3,X0,X1] :
      ( in(X3,X1)
      | X0 != X3
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,X0)
      | singleton(X1) = set_difference(unordered_pair(X1,X2),X0)
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( ( ( in(X2,X0)
            | X1 = X2 )
          & ~ in(X1,X0) )
        | singleton(X1) != set_difference(unordered_pair(X1,X2),X0) )
      & ( singleton(X1) = set_difference(unordered_pair(X1,X2),X0)
        | ( ~ in(X2,X0)
          & X1 != X2 )
        | in(X1,X0) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0,X2] :
      ( ( ( ( in(X2,X1)
            | X0 = X2 )
          & ~ in(X0,X1) )
        | singleton(X0) != set_difference(unordered_pair(X0,X2),X1) )
      & ( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
        | ( ~ in(X2,X1)
          & X0 != X2 )
        | in(X0,X1) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0,X2] :
      ( ( ( ( in(X2,X1)
            | X0 = X2 )
          & ~ in(X0,X1) )
        | singleton(X0) != set_difference(unordered_pair(X0,X2),X1) )
      & ( singleton(X0) = set_difference(unordered_pair(X0,X2),X1)
        | ( ~ in(X2,X1)
          & X0 != X2 )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0,X2] :
      ( ( ( in(X2,X1)
          | X0 = X2 )
        & ~ in(X0,X1) )
    <=> singleton(X0) = set_difference(unordered_pair(X0,X2),X1) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X2,X1] :
      ( ( ~ in(X0,X2)
        & ( in(X1,X2)
          | X0 = X1 ) )
    <=> singleton(X0) = set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET882+1 : 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 : n011.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 14:25:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.50  % (28821)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/48Mi)
% 0.19/0.50  % (28829)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.19/0.50  % (28829)First to succeed.
% 0.19/0.51  % (28827)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 0.19/0.51  % (28823)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.19/0.51  % (28828)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.19/0.51  % (28845)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/355Mi)
% 0.19/0.51  % (28838)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 (3000ds/498Mi)
% 0.19/0.52  % (28831)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 (3000ds/75Mi)
% 0.19/0.52  % (28837)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 0.19/0.52  % (28830)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 (3000ds/68Mi)
% 0.19/0.52  % (28817)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.19/0.52  % (28818)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 (3000ds/37Mi)
% 0.19/0.52  % (28829)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (28829)------------------------------
% 0.19/0.52  % (28829)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (28829)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (28829)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (28829)Memory used [KB]: 5500
% 0.19/0.52  % (28829)Time elapsed: 0.118 s
% 0.19/0.52  % (28829)Instructions burned: 8 (million)
% 0.19/0.52  % (28829)------------------------------
% 0.19/0.52  % (28829)------------------------------
% 0.19/0.52  % (28815)Success in time 0.174 s
%------------------------------------------------------------------------------