%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT046_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 : n001.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 16:04:00 EDT 2022

% Result   : Theorem 0.19s 0.55s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   49 (  12 unt;   7 typ;   0 def)
%            Number of atoms       :   96 (  32 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   92 (  38   ~;  37   |;   9   &)
%                                         (   8 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :   87 (   0 atm;  15 fun;  53 num;  19 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   4 usr;   5 con; 0-2 aty)
%            Number of variables   :   34 (  34   !;   0   ?;  34   :)

% 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_3,type,
    count: collection > $int ).

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

tff(pred_def_4,type,
    sP0: $int > $o ).

tff(f117,plain,
    $false,
    inference(avatar_sat_refutation,[],[f102,f112,f116]) ).

tff(f116,plain,
    ~ spl1_1,
    inference(avatar_contradiction_clause,[],[f115]) ).

tff(f115,plain,
    ( $false
    | ~ spl1_1 ),
    inference(subsumption_resolution,[],[f114,f58]) ).

tff(f58,plain,
    ! [X0: $int] : ~ in(X0,empty),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ~ in(X0,empty),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

tff(f114,plain,
    ( in(1,empty)
    | ~ spl1_1 ),
    inference(evaluation,[],[f113]) ).

tff(f113,plain,
    ( ( 1 = 3 )
    | in(1,empty)
    | ~ spl1_1 ),
    inference(resolution,[],[f90,f70]) ).

tff(f70,plain,
    ! [X2: $int,X0: collection,X1: $int] :
      ( ~ in(X2,add(X1,X0))
      | in(X2,X0)
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: collection,X1: $int,X2: $int] :
      ( ( in(X2,add(X1,X0))
        | ( ( X1 != X2 )
          & ~ in(X2,X0) ) )
      & ( ( X1 = X2 )
        | in(X2,X0)
        | ~ in(X2,add(X1,X0)) ) ),
    inference(rectify,[],[f51]) ).

tff(f51,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( ( in(X2,add(X0,X1))
        | ( ( X0 != X2 )
          & ~ in(X2,X1) ) )
      & ( ( X0 = X2 )
        | in(X2,X1)
        | ~ in(X2,add(X0,X1)) ) ),
    inference(flattening,[],[f50]) ).

tff(f50,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( ( in(X2,add(X0,X1))
        | ( ( X0 != X2 )
          & ~ in(X2,X1) ) )
      & ( ( X0 = X2 )
        | in(X2,X1)
        | ~ in(X2,add(X0,X1)) ) ),
    inference(nnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X1: collection,X0: $int,X2: $int] :
      ( in(X2,add(X0,X1))
    <=> ( ( X0 = X2 )
        | in(X2,X1) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X7: $int,X6: collection,X5: $int] :
      ( ( in(X5,X6)
        | ( X5 = X7 ) )
    <=> in(X5,add(X7,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).

tff(f90,plain,
    ( in(1,add(3,empty))
    | ~ spl1_1 ),
    inference(avatar_component_clause,[],[f89]) ).

tff(f89,plain,
    ( spl1_1
  <=> in(1,add(3,empty)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).

tff(f112,plain,
    spl1_3,
    inference(avatar_contradiction_clause,[],[f111]) ).

tff(f111,plain,
    ( $false
    | spl1_3 ),
    inference(subsumption_resolution,[],[f110,f80]) ).

tff(f80,plain,
    sP0(2),
    inference(inequality_splitting,[],[f66,f79]) ).

tff(f79,plain,
    ~ sP0(count(add(1,add(3,empty)))),
    introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP0])]) ).

tff(f66,plain,
    count(add(1,add(3,empty))) != 2,
    inference(cnf_transformation,[],[f36]) ).

tff(f36,plain,
    count(add(1,add(3,empty))) != 2,
    inference(flattening,[],[f14]) ).

tff(f14,negated_conjecture,
    ( ( ~ count(add(1,add(3,empty))) )
    = 2 ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    count(add(1,add(3,empty))) = 2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).

tff(f110,plain,
    ( ~ sP0(2)
    | spl1_3 ),
    inference(evaluation,[],[f109]) ).

tff(f109,plain,
    ( ~ sP0($sum(2,0))
    | spl1_3 ),
    inference(superposition,[],[f108,f81]) ).

tff(f81,plain,
    0 = count(empty),
    inference(equality_resolution,[],[f60]) ).

tff(f60,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
      | ( empty != X0 ) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: collection] :
      ( ( ( 0 = count(X0) )
        | ( empty != X0 ) )
      & ( ( empty = X0 )
        | ( 0 != count(X0) ) ) ),
    inference(nnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: collection] :
      ( ( 0 = count(X0) )
    <=> ( empty = X0 ) ),
    inference(rectify,[],[f7]) ).

tff(f7,axiom,
    ! [X12: collection] :
      ( ( empty = X12 )
    <=> ( 0 = count(X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

tff(f108,plain,
    ( ~ sP0($sum(2,count(empty)))
    | spl1_3 ),
    inference(subsumption_resolution,[],[f107,f58]) ).

tff(f107,plain,
    ( ~ sP0($sum(2,count(empty)))
    | in(3,empty)
    | spl1_3 ),
    inference(evaluation,[],[f104]) ).

tff(f104,plain,
    ( in(3,empty)
    | ~ sP0($sum($sum(count(empty),1),1))
    | spl1_3 ),
    inference(superposition,[],[f101,f61]) ).

tff(f61,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(add(X1,X0)) = $sum(count(X0),1) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f45]) ).

tff(f45,plain,
    ! [X0: collection,X1: $int] :
      ( ( ~ in(X1,X0)
        | ( count(add(X1,X0)) != $sum(count(X0),1) ) )
      & ( ( count(add(X1,X0)) = $sum(count(X0),1) )
        | in(X1,X0) ) ),
    inference(rectify,[],[f44]) ).

tff(f44,plain,
    ! [X1: collection,X0: $int] :
      ( ( ~ in(X0,X1)
        | ( $sum(count(X1),1) != count(add(X0,X1)) ) )
      & ( ( $sum(count(X1),1) = count(add(X0,X1)) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X1: collection,X0: $int] :
      ( ~ in(X0,X1)
    <=> ( $sum(count(X1),1) = count(add(X0,X1)) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,axiom,
    ! [X13: $int,X14: collection] :
      ( ( count(add(X13,X14)) = $sum(count(X14),1) )
    <=> ~ in(X13,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f101,plain,
    ( ~ sP0($sum(count(add(3,empty)),1))
    | spl1_3 ),
    inference(avatar_component_clause,[],[f99]) ).

tff(f99,plain,
    ( spl1_3
  <=> sP0($sum(count(add(3,empty)),1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).

tff(f102,plain,
    ( ~ spl1_3
    | spl1_1 ),
    inference(avatar_split_clause,[],[f87,f89,f99]) ).

tff(f87,plain,
    ( in(1,add(3,empty))
    | ~ sP0($sum(count(add(3,empty)),1)) ),
    inference(superposition,[],[f79,f61]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : DAT046=1 : TPTP v8.1.0. Released v5.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n001.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 20:39:15 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.53  % (27192)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)
% 0.19/0.54  % (27191)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)
% 0.19/0.55  % (27207)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.55  % (27208)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/47Mi)
% 0.19/0.55  % (27191)First to succeed.
% 0.19/0.55  % (27199)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)
% 0.19/0.55  % (27191)Refutation found. Thanks to Tanya!
% 0.19/0.55  % SZS status Theorem for theBenchmark
% 0.19/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.55  % (27191)------------------------------
% 0.19/0.55  % (27191)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.55  % (27191)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (27191)Termination reason: Refutation
% 0.19/0.55  
% 0.19/0.55  % (27191)Memory used [KB]: 5500
% 0.19/0.55  % (27191)Time elapsed: 0.127 s
% 0.19/0.55  % (27191)Instructions burned: 3 (million)
% 0.19/0.55  % (27191)------------------------------
% 0.19/0.55  % (27191)------------------------------
% 0.19/0.55  % (27183)Success in time 0.203 s
%------------------------------------------------------------------------------