TSTP Solution File: DAT049_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT049_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 : n007.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 16:04:01 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   65 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :  112 (  34 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  105 (  49   ~;  37   |;   6   &)
%                                         (  12 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number arithmetic     :   84 (   0 atm;  31 fun;  24 num;  29 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :   11 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   56 (  52   !;   4   ?;  56   :)

% 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(func_def_9,type,
    sK0: collection ).

tff(func_def_10,type,
    sK1: $int ).

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

tff(pred_def_4,type,
    sP2: $int > $o ).

tff(f130,plain,
    $false,
    inference(avatar_sat_refutation,[],[f99,f115,f117,f129]) ).

tff(f129,plain,
    ( ~ spl3_1
    | spl3_2 ),
    inference(avatar_contradiction_clause,[],[f128]) ).

tff(f128,plain,
    ( $false
    | ~ spl3_1
    | spl3_2 ),
    inference(subsumption_resolution,[],[f127,f97]) ).

tff(f97,plain,
    ( ~ in(sK1,sK0)
    | spl3_2 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f96,plain,
    ( spl3_2
  <=> in(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f127,plain,
    ( in(sK1,sK0)
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f110,f94]) ).

tff(f94,plain,
    ( sP2(count(sK0))
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f92]) ).

tff(f92,plain,
    ( spl3_1
  <=> sP2(count(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f110,plain,
    ( ~ sP2(count(sK0))
    | in(sK1,sK0) ),
    inference(evaluation,[],[f108]) ).

tff(f108,plain,
    ( in(sK1,sK0)
    | ~ sP2($sum(-1,$sum(count(sK0),1))) ),
    inference(superposition,[],[f103,f58]) ).

tff(f58,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: collection] :
      ( ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) )
      & ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) ) ),
    inference(rectify,[],[f42]) ).

tff(f42,plain,
    ! [X1: $int,X0: collection] :
      ( ( ( count(add(X1,X0)) = $sum(count(X0),1) )
        | in(X1,X0) )
      & ( ~ in(X1,X0)
        | ( count(add(X1,X0)) != $sum(count(X0),1) ) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X1: $int,X0: collection] :
      ( ( count(add(X1,X0)) = $sum(count(X0),1) )
    <=> ~ in(X1,X0) ),
    inference(rectify,[],[f8]) ).

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

tff(f103,plain,
    ~ sP2($sum(-1,count(add(sK1,sK0)))),
    inference(superposition,[],[f90,f17]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
    introduced(theory_axiom_140,[]) ).

tff(f90,plain,
    ~ sP2($sum(count(add(sK1,sK0)),-1)),
    inference(subsumption_resolution,[],[f88,f74]) ).

tff(f74,plain,
    ! [X0: collection,X1: $int] : in(X1,add(X1,X0)),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,plain,
    ! [X0: collection,X1: $int] : in(X1,add(X1,X0)),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X2: collection,X1: $int] : in(X1,add(X1,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).

tff(f88,plain,
    ( ~ in(sK1,add(sK1,sK0))
    | ~ sP2($sum(count(add(sK1,sK0)),-1)) ),
    inference(superposition,[],[f79,f85]) ).

tff(f85,plain,
    ! [X0: $int,X1: collection] :
      ( ( $sum(count(X1),-1) = count(remove(X0,X1)) )
      | ~ in(X0,X1) ),
    inference(evaluation,[],[f72]) ).

tff(f72,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) ) ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,plain,
    ! [X0: $int,X1: collection] :
      ( ( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ( $sum(count(X1),$uminus(1)) != count(remove(X0,X1)) ) ) ),
    inference(nnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: collection] :
      ( ( $sum(count(X1),$uminus(1)) = count(remove(X0,X1)) )
    <=> in(X0,X1) ),
    inference(rectify,[],[f15]) ).

tff(f15,plain,
    ! [X17: $int,X18: collection] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $sum(count(X18),$uminus(1)) ) ),
    inference(theory_normalization,[],[f10]) ).

tff(f10,axiom,
    ! [X17: $int,X18: collection] :
      ( in(X17,X18)
    <=> ( count(remove(X17,X18)) = $difference(count(X18),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax5) ).

tff(f79,plain,
    ~ sP2(count(remove(sK1,add(sK1,sK0)))),
    introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP2])]) ).

tff(f117,plain,
    ( ~ spl3_2
    | ~ spl3_3 ),
    inference(avatar_contradiction_clause,[],[f116]) ).

tff(f116,plain,
    ( $false
    | ~ spl3_2
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f114,f105]) ).

tff(f105,plain,
    ( ~ sP2($sum(count(sK0),-1))
    | ~ spl3_2 ),
    inference(subsumption_resolution,[],[f101,f98]) ).

tff(f98,plain,
    ( in(sK1,sK0)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f101,plain,
    ( ~ in(sK1,sK0)
    | ~ sP2($sum(count(sK0),-1)) ),
    inference(superposition,[],[f90,f70]) ).

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

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

tff(f51,plain,
    ! [X1: collection,X0: $int] :
      ( ( ( count(add(X0,X1)) = count(X1) )
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ( count(add(X0,X1)) != count(X1) ) ) ),
    inference(nnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X1: collection,X0: $int] :
      ( ( count(add(X0,X1)) = count(X1) )
    <=> in(X0,X1) ),
    inference(rectify,[],[f9]) ).

tff(f9,axiom,
    ! [X15: $int,X16: collection] :
      ( in(X15,X16)
    <=> ( count(add(X15,X16)) = count(X16) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

tff(f114,plain,
    ( sP2($sum(count(sK0),-1))
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f112]) ).

tff(f112,plain,
    ( spl3_3
  <=> sP2($sum(count(sK0),-1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f115,plain,
    ( ~ spl3_2
    | spl3_3 ),
    inference(avatar_split_clause,[],[f86,f112,f96]) ).

tff(f86,plain,
    ( sP2($sum(count(sK0),-1))
    | ~ in(sK1,sK0) ),
    inference(superposition,[],[f80,f85]) ).

tff(f80,plain,
    sP2(count(remove(sK1,sK0))),
    inference(inequality_splitting,[],[f78,f79]) ).

tff(f78,plain,
    count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,plain,
    count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f41,f55]) ).

tff(f55,plain,
    ( ? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) )
   => ( count(remove(sK1,add(sK1,sK0))) != count(remove(sK1,sK0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: collection,X1: $int] : ( count(remove(X1,add(X1,X0))) != count(remove(X1,X0)) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X1: $int,X0: collection] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X1: $int,X0: collection] : ( count(remove(X1,add(X1,X0))) = count(remove(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f99,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f87,f96,f92]) ).

tff(f87,plain,
    ( in(sK1,sK0)
    | sP2(count(sK0)) ),
    inference(superposition,[],[f80,f75]) ).

tff(f75,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(X1) = count(remove(X0,X1)) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(X1) != count(remove(X0,X1)) ) )
      & ( ( count(X1) = count(remove(X0,X1)) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
    <=> ( count(X1) = count(remove(X0,X1)) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X19: $int,X20: collection] :
      ( ( count(remove(X19,X20)) = count(X20) )
    <=> ~ in(X19,X20) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax6) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT049=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
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 29 20:03:15 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.51  % (18782)dis+1011_1:64_drc=off:flr=on:nwc=2.0:sac=on:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.20/0.51  % (18803)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)
% 0.20/0.51  % (18783)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)
% 0.20/0.51  % (18783)Instruction limit reached!
% 0.20/0.51  % (18783)------------------------------
% 0.20/0.51  % (18783)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (18783)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (18783)Termination reason: Unknown
% 0.20/0.51  % (18783)Termination phase: Unused predicate definition removal
% 0.20/0.51  
% 0.20/0.51  % (18783)Memory used [KB]: 895
% 0.20/0.51  % (18783)Time elapsed: 0.002 s
% 0.20/0.51  % (18783)Instructions burned: 2 (million)
% 0.20/0.51  % (18783)------------------------------
% 0.20/0.51  % (18783)------------------------------
% 0.20/0.52  % (18795)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)
% 0.20/0.52  % (18795)Instruction limit reached!
% 0.20/0.52  % (18795)------------------------------
% 0.20/0.52  % (18795)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (18795)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (18795)Termination reason: Unknown
% 0.20/0.52  % (18795)Termination phase: Saturation
% 0.20/0.52  
% 0.20/0.52  % (18795)Memory used [KB]: 1023
% 0.20/0.52  % (18795)Time elapsed: 0.005 s
% 0.20/0.52  % (18795)Instructions burned: 3 (million)
% 0.20/0.52  % (18795)------------------------------
% 0.20/0.52  % (18795)------------------------------
% 0.20/0.52  % (18803)Refutation not found, incomplete strategy% (18803)------------------------------
% 0.20/0.52  % (18803)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (18803)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (18803)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52  
% 0.20/0.52  % (18803)Memory used [KB]: 5500
% 0.20/0.52  % (18803)Time elapsed: 0.071 s
% 0.20/0.52  % (18803)Instructions burned: 3 (million)
% 0.20/0.52  % (18803)------------------------------
% 0.20/0.52  % (18803)------------------------------
% 0.20/0.52  % (18787)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)
% 0.20/0.52  % (18787)First to succeed.
% 0.20/0.52  % (18787)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (18787)------------------------------
% 0.20/0.53  % (18787)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (18787)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (18787)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (18787)Memory used [KB]: 5500
% 0.20/0.53  % (18787)Time elapsed: 0.074 s
% 0.20/0.53  % (18787)Instructions burned: 3 (million)
% 0.20/0.53  % (18787)------------------------------
% 0.20/0.53  % (18787)------------------------------
% 0.20/0.53  % (18779)Success in time 0.171 s
%------------------------------------------------------------------------------