TSTP Solution File: SET884+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET884+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 : n014.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 0.22s 0.55s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   47 (  11 unt;   3 typ;   0 def)
%            Number of atoms       :  192 ( 113 equ)
%            Maximal formula atoms :   14 (   4 avg)
%            Number of connectives :  240 (  92   ~;  80   |;  51   &)
%                                         (  10 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :  105 (  89   !;  16   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_5,type,
    sQ8_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_6,type,
    sQ9_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_7,type,
    sQ10_eqProxy: ( $real * $real ) > $o ).

fof(f185,plain,
    $false,
    inference(subsumption_resolution,[],[f184,f83]) ).

fof(f83,plain,
    sK3 != sK4,
    inference(literal_reordering,[],[f51]) ).

fof(f51,plain,
    sK3 != sK4,
    inference(cnf_transformation,[],[f32]) ).

fof(f32,plain,
    ( sK3 != sK2
    & sK3 != sK4
    & subset(singleton(sK3),unordered_pair(sK2,sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f30,f31]) ).

fof(f31,plain,
    ( ? [X0,X1,X2] :
        ( X0 != X1
        & X1 != X2
        & subset(singleton(X1),unordered_pair(X0,X2)) )
   => ( sK3 != sK2
      & sK3 != sK4
      & subset(singleton(sK3),unordered_pair(sK2,sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f30,plain,
    ? [X0,X1,X2] :
      ( X0 != X1
      & X1 != X2
      & subset(singleton(X1),unordered_pair(X0,X2)) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X1,X2,X0] :
      ( X1 != X2
      & X0 != X2
      & subset(singleton(X2),unordered_pair(X1,X0)) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X1,X0,X2] :
        ~ ( X1 != X2
          & X0 != X2
          & subset(singleton(X2),unordered_pair(X1,X0)) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ~ ( X0 != X1
          & subset(singleton(X0),unordered_pair(X1,X2))
          & X0 != X2 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X2,X1,X0] :
      ~ ( X0 != X1
        & subset(singleton(X0),unordered_pair(X1,X2))
        & X0 != X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_zfmisc_1) ).

fof(f184,plain,
    sK3 = sK4,
    inference(subsumption_resolution,[],[f182,f70]) ).

fof(f70,plain,
    sK3 != sK2,
    inference(literal_reordering,[],[f52]) ).

fof(f52,plain,
    sK3 != sK2,
    inference(cnf_transformation,[],[f32]) ).

fof(f182,plain,
    ( sK3 = sK2
    | sK3 = sK4 ),
    inference(resolution,[],[f160,f67]) ).

fof(f67,plain,
    ! [X2,X0,X4] :
      ( ~ in(X4,unordered_pair(X2,X0))
      | X0 = X4
      | X2 = X4 ),
    inference(literal_reordering,[],[f64]) ).

fof(f64,plain,
    ! [X2,X0,X4] :
      ( X2 = X4
      | ~ in(X4,unordered_pair(X2,X0))
      | X0 = X4 ),
    inference(equality_resolution,[],[f44]) ).

fof(f44,plain,
    ! [X2,X0,X1,X4] :
      ( X2 = X4
      | X0 = X4
      | ~ in(X4,X1)
      | unordered_pair(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X0) = X1
        | ( ( ( sK1(X0,X1,X2) != X2
              & sK1(X0,X1,X2) != X0 )
            | ~ in(sK1(X0,X1,X2),X1) )
          & ( sK1(X0,X1,X2) = X2
            | sK1(X0,X1,X2) = X0
            | in(sK1(X0,X1,X2),X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( X2 != X4
                & X0 != X4 ) )
            & ( X2 = X4
              | X0 = X4
              | ~ in(X4,X1) ) )
        | unordered_pair(X2,X0) != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f27,f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X2 != X3
              & X0 != X3 )
            | ~ in(X3,X1) )
          & ( X2 = X3
            | X0 = X3
            | in(X3,X1) ) )
     => ( ( ( sK1(X0,X1,X2) != X2
            & sK1(X0,X1,X2) != X0 )
          | ~ in(sK1(X0,X1,X2),X1) )
        & ( sK1(X0,X1,X2) = X2
          | sK1(X0,X1,X2) = X0
          | in(sK1(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X0) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X1)
              | ( X2 != X4
                & X0 != X4 ) )
            & ( X2 = X4
              | X0 = X4
              | ~ in(X4,X1) ) )
        | unordered_pair(X2,X0) != X1 ) ),
    inference(rectify,[],[f26]) ).

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

fof(f25,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X2,X0) = X1
        | ? [X3] :
            ( ( ( X2 != X3
                & X0 != X3 )
              | ~ in(X3,X1) )
            & ( X2 = X3
              | X0 = X3
              | in(X3,X1) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X1)
              | ( X2 != X3
                & X0 != X3 ) )
            & ( X2 = X3
              | X0 = X3
              | ~ in(X3,X1) ) )
        | unordered_pair(X2,X0) != X1 ) ),
    inference(nnf_transformation,[],[f15]) ).

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

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

fof(f160,plain,
    in(sK3,unordered_pair(sK2,sK4)),
    inference(resolution,[],[f133,f82]) ).

fof(f82,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(literal_reordering,[],[f59]) ).

fof(f59,plain,
    ! [X3] : in(X3,singleton(X3)),
    inference(equality_resolution,[],[f58]) ).

fof(f58,plain,
    ! [X3,X0] :
      ( in(X3,X0)
      | singleton(X3) != X0 ),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X3,X0,X1] :
      ( in(X3,X0)
      | X1 != X3
      | singleton(X1) != X0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ( ( ~ in(sK0(X0,X1),X0)
            | sK0(X0,X1) != X1 )
          & ( in(sK0(X0,X1),X0)
            | sK0(X0,X1) = X1 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | X1 != X3 ) )
        | singleton(X1) != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X0)
            | X1 != X2 )
          & ( in(X2,X0)
            | X1 = X2 ) )
     => ( ( ~ in(sK0(X0,X1),X0)
          | sK0(X0,X1) != X1 )
        & ( in(sK0(X0,X1),X0)
          | sK0(X0,X1) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( singleton(X1) = X0
        | ? [X2] :
            ( ( ~ in(X2,X0)
              | X1 != X2 )
            & ( in(X2,X0)
              | X1 = X2 ) ) )
      & ( ! [X3] :
            ( ( X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | X1 != X3 ) )
        | singleton(X1) != X0 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( 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,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( 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(f133,plain,
    ! [X2] :
      ( ~ in(X2,singleton(sK3))
      | in(X2,unordered_pair(sK2,sK4)) ),
    inference(resolution,[],[f80,f81]) ).

fof(f81,plain,
    subset(singleton(sK3),unordered_pair(sK2,sK4)),
    inference(literal_reordering,[],[f50]) ).

fof(f50,plain,
    subset(singleton(sK3),unordered_pair(sK2,sK4)),
    inference(cnf_transformation,[],[f32]) ).

fof(f80,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | ~ in(X2,X1)
      | in(X2,X0) ),
    inference(literal_reordering,[],[f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | in(X2,X0)
      | ~ in(X2,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
     => ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(unused_predicate_definition_removal,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f5]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : SET884+1 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.35  % Computer : n014.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Aug 30 14:29:03 EDT 2022
% 0.15/0.35  % CPUTime    : 
% 0.22/0.53  % (11443)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.22/0.54  TRYING [1]
% 0.22/0.54  % (11449)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.54  % (11450)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.22/0.54  % (11460)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.22/0.54  % (11457)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)
% 0.22/0.54  % (11452)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.22/0.54  % (11455)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.22/0.54  TRYING [1]
% 0.22/0.54  % (11458)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)
% 0.22/0.54  % (11467)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.22/0.54  % (11457)First to succeed.
% 0.22/0.54  % (11444)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.22/0.54  % (11469)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)
% 0.22/0.55  TRYING [2]
% 0.22/0.55  TRYING [1]
% 0.22/0.55  TRYING [2]
% 0.22/0.55  TRYING [3]
% 0.22/0.55  TRYING [3]
% 0.22/0.55  % (11458)Also succeeded, but the first one will report.
% 0.22/0.55  % (11463)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.22/0.55  % (11457)Refutation found. Thanks to Tanya!
% 0.22/0.55  % SZS status Theorem for theBenchmark
% 0.22/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.55  % (11457)------------------------------
% 0.22/0.55  % (11457)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.22/0.55  % (11457)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.22/0.55  % (11457)Termination reason: Refutation
% 0.22/0.55  
% 0.22/0.55  % (11457)Memory used [KB]: 5756
% 0.22/0.55  % (11457)Time elapsed: 0.006 s
% 0.22/0.55  % (11457)Instructions burned: 6 (million)
% 0.22/0.55  % (11457)------------------------------
% 0.22/0.55  % (11457)------------------------------
% 0.22/0.55  % (11442)Success in time 0.183 s
%------------------------------------------------------------------------------