TSTP Solution File: DAT025_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT025_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : n026.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 16:03:56 EDT 2022

% Result   : Theorem 1.31s 0.58s
% Output   : Refutation 1.31s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   60 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :  158 (  17 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  174 (  69   ~;  48   |;  35   &)
%                                         (  11 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  179 (  38 atm;   7 fun;  84 num;  50 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :   10 (   5 usr;   6 con; 0-2 aty)
%            Number of variables   :   66 (  56   !;  10   ?;  66   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    collection: $tType ).

tff(func_def_0,type,
    empty: collection ).

tff(func_def_1,type,
    add: ( $int * collection ) > collection ).

tff(func_def_2,type,
    remove: ( $int * collection ) > collection ).

tff(func_def_8,type,
    sK0: collection ).

tff(func_def_9,type,
    sK1: $int ).

tff(pred_def_1,type,
    in: ( $int * collection ) > $o ).

tff(f247,plain,
    $false,
    inference(avatar_sat_refutation,[],[f80,f96,f154,f190,f246]) ).

tff(f246,plain,
    ~ spl2_1,
    inference(avatar_contradiction_clause,[],[f241]) ).

tff(f241,plain,
    ( $false
    | ~ spl2_1 ),
    inference(resolution,[],[f235,f44]) ).

tff(f44,plain,
    ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: $int,X1: collection] : ~ in(X0,remove(X0,X1)),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X3: $int,X4: collection] : ~ in(X3,remove(X3,X4)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f235,plain,
    ( in(1,remove(1,sK0))
    | ~ spl2_1 ),
    inference(resolution,[],[f204,f47]) ).

tff(f47,plain,
    ! [X2: $int,X0: $int,X1: collection] :
      ( ~ in(X0,remove(X2,X1))
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: collection,X2: $int] :
      ( ( in(X0,remove(X2,X1))
        | ~ in(X0,X1)
        | ( X0 = X2 ) )
      & ( ( in(X0,X1)
          & ( X0 != X2 ) )
        | ~ in(X0,remove(X2,X1)) ) ),
    inference(rectify,[],[f33]) ).

tff(f33,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( ( in(X2,remove(X1,X0))
        | ~ in(X2,X0)
        | ( X1 = X2 ) )
      & ( ( in(X2,X0)
          & ( X1 != X2 ) )
        | ~ in(X2,remove(X1,X0)) ) ),
    inference(flattening,[],[f32]) ).

tff(f32,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( ( in(X2,remove(X1,X0))
        | ~ in(X2,X0)
        | ( X1 = X2 ) )
      & ( ( in(X2,X0)
          & ( X1 != X2 ) )
        | ~ in(X2,remove(X1,X0)) ) ),
    inference(nnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( in(X2,remove(X1,X0))
    <=> ( in(X2,X0)
        & ( X1 != X2 ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X9: collection,X10: $int,X8: $int] :
      ( ( ( X8 != X10 )
        & in(X8,X9) )
    <=> in(X8,remove(X10,X9)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).

tff(f204,plain,
    ( in(1,remove(0,remove(1,sK0)))
    | ~ spl2_1 ),
    inference(backward_demodulation,[],[f161,f73]) ).

tff(f73,plain,
    ( ( 1 = sK1 )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f71]) ).

tff(f71,plain,
    ( spl2_1
  <=> ( 1 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

tff(f161,plain,
    in(sK1,remove(0,remove(1,sK0))),
    inference(resolution,[],[f39,f41]) ).

tff(f41,plain,
    ! [X2: $int] :
      ( ~ in(X2,sK0)
      | in(X2,remove(0,remove(1,sK0))) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ( ! [X1: $int] :
        ( ~ in(X1,sK0)
        | ~ $less(X1,0) )
    & ! [X2: $int] :
        ( ( in(X2,remove(0,remove(1,sK0)))
          | ~ in(X2,sK0) )
        & ( in(X2,sK0)
          | ~ in(X2,remove(0,remove(1,sK0))) ) )
    & in(sK1,sK0)
    & $less(sK1,2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f29,f28]) ).

tff(f28,plain,
    ( ? [X0: collection] :
        ( ! [X1: $int] :
            ( ~ in(X1,X0)
            | ~ $less(X1,0) )
        & ! [X2: $int] :
            ( ( in(X2,remove(0,remove(1,X0)))
              | ~ in(X2,X0) )
            & ( in(X2,X0)
              | ~ in(X2,remove(0,remove(1,X0))) ) )
        & ? [X3: $int] :
            ( in(X3,X0)
            & $less(X3,2) ) )
   => ( ! [X1: $int] :
          ( ~ in(X1,sK0)
          | ~ $less(X1,0) )
      & ! [X2: $int] :
          ( ( in(X2,remove(0,remove(1,sK0)))
            | ~ in(X2,sK0) )
          & ( in(X2,sK0)
            | ~ in(X2,remove(0,remove(1,sK0))) ) )
      & ? [X3: $int] :
          ( in(X3,sK0)
          & $less(X3,2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f29,plain,
    ( ? [X3: $int] :
        ( in(X3,sK0)
        & $less(X3,2) )
   => ( in(sK1,sK0)
      & $less(sK1,2) ) ),
    introduced(choice_axiom,[]) ).

tff(f27,plain,
    ? [X0: collection] :
      ( ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) )
      & ! [X2: $int] :
          ( ( in(X2,remove(0,remove(1,X0)))
            | ~ in(X2,X0) )
          & ( in(X2,X0)
            | ~ in(X2,remove(0,remove(1,X0))) ) )
      & ? [X3: $int] :
          ( in(X3,X0)
          & $less(X3,2) ) ),
    inference(nnf_transformation,[],[f26]) ).

tff(f26,plain,
    ? [X0: collection] :
      ( ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) )
      & ! [X2: $int] :
          ( in(X2,remove(0,remove(1,X0)))
        <=> in(X2,X0) )
      & ? [X3: $int] :
          ( in(X3,X0)
          & $less(X3,2) ) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ? [X0: collection] :
      ( ? [X3: $int] :
          ( in(X3,X0)
          & $less(X3,2) )
      & ! [X2: $int] :
          ( in(X2,remove(0,remove(1,X0)))
        <=> in(X2,X0) )
      & ! [X1: $int] :
          ( ~ in(X1,X0)
          | ~ $less(X1,0) ) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ~ ! [X0: collection] :
        ( ( ! [X2: $int] :
              ( in(X2,remove(0,remove(1,X0)))
            <=> in(X2,X0) )
          & ! [X1: $int] :
              ( in(X1,X0)
             => ~ $less(X1,0) ) )
       => ! [X3: $int] :
            ( in(X3,X0)
           => ~ $less(X3,2) ) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X0: collection] :
        ( ( ! [X1: $int] :
              ( in(X1,X0)
             => $greatereq(X1,0) )
          & ! [X2: $int] :
              ( in(X2,remove(0,remove(1,X0)))
            <=> in(X2,X0) ) )
       => ! [X3: $int] :
            ( in(X3,X0)
           => $greatereq(X3,2) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X0: collection] :
      ( ( ! [X1: $int] :
            ( in(X1,X0)
           => $greatereq(X1,0) )
        & ! [X2: $int] :
            ( in(X2,remove(0,remove(1,X0)))
          <=> in(X2,X0) ) )
     => ! [X3: $int] :
          ( in(X3,X0)
         => $greatereq(X3,2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f39,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f30]) ).

tff(f190,plain,
    ( ~ spl2_4
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f186,f75,f92]) ).

tff(f92,plain,
    ( spl2_4
  <=> $less(0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

tff(f75,plain,
    ( spl2_2
  <=> $less(sK1,1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f186,plain,
    ( ~ $less(0,sK1)
    | ~ spl2_2 ),
    inference(evaluation,[],[f185]) ).

tff(f185,plain,
    ( ~ $less($sum(1,$uminus(1)),sK1)
    | ~ spl2_2 ),
    inference(gaussian_variable_elimination,[],[f181]) ).

tff(f181,plain,
    ( ! [X0: $int] :
        ( ( 1 != $sum(X0,1) )
        | ~ $less(X0,sK1) )
    | ~ spl2_2 ),
    inference(constrained_resolution,[],[f77,f20]) ).

tff(f20,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_166,[]) ).

tff(f77,plain,
    ( $less(sK1,1)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f75]) ).

tff(f154,plain,
    ~ spl2_3,
    inference(avatar_contradiction_clause,[],[f149]) ).

tff(f149,plain,
    ( $false
    | ~ spl2_3 ),
    inference(resolution,[],[f113,f44]) ).

tff(f113,plain,
    ( in(0,remove(0,remove(1,sK0)))
    | ~ spl2_3 ),
    inference(resolution,[],[f41,f98]) ).

tff(f98,plain,
    ( in(0,sK0)
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f39,f90]) ).

tff(f90,plain,
    ( ( 0 = sK1 )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f88,plain,
    ( spl2_3
  <=> ( 0 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f96,plain,
    ( spl2_4
    | spl2_3 ),
    inference(avatar_split_clause,[],[f83,f88,f92]) ).

tff(f83,plain,
    ( ( 0 = sK1 )
    | $less(0,sK1) ),
    inference(resolution,[],[f63,f16]) ).

tff(f16,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f63,plain,
    ~ $less(sK1,0),
    inference(resolution,[],[f42,f39]) ).

tff(f42,plain,
    ! [X1: $int] :
      ( ~ in(X1,sK0)
      | ~ $less(X1,0) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f80,plain,
    ( spl2_2
    | spl2_1 ),
    inference(avatar_split_clause,[],[f67,f71,f75]) ).

tff(f67,plain,
    ( ( 1 = sK1 )
    | $less(sK1,1) ),
    inference(resolution,[],[f59,f16]) ).

tff(f59,plain,
    ~ $less(1,sK1),
    inference(evaluation,[],[f58]) ).

tff(f58,plain,
    ~ $less($sum(2,$uminus(1)),sK1),
    inference(gaussian_variable_elimination,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int] :
      ( ~ $less(X0,sK1)
      | ( 2 != $sum(X0,1) ) ),
    inference(constrained_resolution,[],[f38,f20]) ).

tff(f38,plain,
    $less(sK1,2),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT025=1 : TPTP v8.1.0. Released v5.0.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n026.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   : Mon Aug 29 20:31:05 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.55  % (10056)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.21/0.56  % (10072)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 1.31/0.56  % (10057)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 1.31/0.56  % (10061)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 1.31/0.57  % (10064)lrs+22_1:1_amm=sco:fsr=off:gve=force:sos=on:uwa=all:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.31/0.57  % (10053)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.31/0.57  % (10065)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.31/0.57  % (10053)Instruction limit reached!
% 1.31/0.57  % (10053)------------------------------
% 1.31/0.57  % (10053)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.57  % (10053)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.57  % (10053)Termination reason: Unknown
% 1.31/0.57  % (10053)Termination phase: Saturation
% 1.31/0.57  
% 1.31/0.57  % (10053)Memory used [KB]: 1023
% 1.31/0.57  % (10053)Time elapsed: 0.002 s
% 1.31/0.57  % (10053)Instructions burned: 2 (million)
% 1.31/0.57  % (10053)------------------------------
% 1.31/0.57  % (10053)------------------------------
% 1.31/0.57  % (10069)lrs+10_1:1_sd=10:sos=all:ss=axioms:st=5.0:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.31/0.58  % (10058)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/26Mi)
% 1.31/0.58  % (10070)dis+1002_1:5_av=off:nwc=2.0:sos=all:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.31/0.58  % (10077)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 1.31/0.58  % (10064)First to succeed.
% 1.31/0.58  % (10064)Refutation found. Thanks to Tanya!
% 1.31/0.58  % SZS status Theorem for theBenchmark
% 1.31/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 1.31/0.58  % (10064)------------------------------
% 1.31/0.58  % (10064)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.31/0.58  % (10064)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.31/0.58  % (10064)Termination reason: Refutation
% 1.31/0.58  
% 1.31/0.58  % (10064)Memory used [KB]: 5628
% 1.31/0.58  % (10064)Time elapsed: 0.132 s
% 1.31/0.58  % (10064)Instructions burned: 7 (million)
% 1.31/0.58  % (10064)------------------------------
% 1.31/0.58  % (10064)------------------------------
% 1.31/0.58  % (10049)Success in time 0.217 s
%------------------------------------------------------------------------------