TSTP Solution File: DAT044_1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : DAT044_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 : n003.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 0.20s 0.51s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   59 (   7 unt;   8 typ;   0 def)
%            Number of atoms       :  121 (  18 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  127 (  57   ~;  49   |;   7   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  116 (  46 atm;  15 fun;  13 num;  42 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   4 usr;   4 prp; 0-2 aty)
%            Number of functors    :    9 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   57 (  51   !;   6   ?;  57   :)

% 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: $int ).

tff(func_def_10,type,
    sK1: collection ).

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

tff(f231,plain,
    $false,
    inference(avatar_sat_refutation,[],[f106,f120,f123,f230]) ).

tff(f230,plain,
    ~ spl2_4,
    inference(avatar_contradiction_clause,[],[f229]) ).

tff(f229,plain,
    ( $false
    | ~ spl2_4 ),
    inference(subsumption_resolution,[],[f228,f23]) ).

tff(f23,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_147,[]) ).

tff(f228,plain,
    ( $less(count(sK1),count(sK1))
    | ~ spl2_4 ),
    inference(evaluation,[],[f226]) ).

tff(f226,plain,
    ( $less(count(sK1),count(sK1))
    | ~ $less(0,1)
    | ~ spl2_4 ),
    inference(superposition,[],[f163,f20]) ).

tff(f20,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_142,[]) ).

tff(f163,plain,
    ( ! [X2: $int] :
        ( $less($sum(count(sK1),X2),count(sK1))
        | ~ $less(X2,1) )
    | ~ spl2_4 ),
    inference(superposition,[],[f148,f18]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
    introduced(theory_axiom_140,[]) ).

tff(f148,plain,
    ( ! [X1: $int] :
        ( $less($sum(X1,count(sK1)),count(sK1))
        | ~ $less(X1,1) )
    | ~ spl2_4 ),
    inference(resolution,[],[f137,f26]) ).

tff(f26,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X0,X2),$sum(X1,X2))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_150,[]) ).

tff(f137,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,$sum(1,count(sK1)))
        | $less(X0,count(sK1)) )
    | ~ spl2_4 ),
    inference(forward_demodulation,[],[f136,f18]) ).

tff(f136,plain,
    ( ! [X0: $int] :
        ( $less(X0,count(sK1))
        | ~ $less(X0,$sum(count(sK1),1)) )
    | ~ spl2_4 ),
    inference(subsumption_resolution,[],[f134,f132]) ).

tff(f132,plain,
    ( ~ in(sK0,sK1)
    | ~ spl2_4 ),
    inference(subsumption_resolution,[],[f130,f23]) ).

tff(f130,plain,
    ( $less(count(sK1),count(sK1))
    | ~ in(sK0,sK1)
    | ~ spl2_4 ),
    inference(superposition,[],[f105,f61]) ).

tff(f61,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(add(X1,X0)) = count(X0) )
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,plain,
    ! [X0: collection,X1: $int] :
      ( ( ( count(add(X1,X0)) = count(X0) )
        | ~ in(X1,X0) )
      & ( in(X1,X0)
        | ( count(add(X1,X0)) != count(X0) ) ) ),
    inference(nnf_transformation,[],[f31]) ).

tff(f31,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(add(X1,X0)) = count(X0) )
    <=> in(X1,X0) ),
    inference(rectify,[],[f9]) ).

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

tff(f105,plain,
    ( $less(count(add(sK0,sK1)),count(sK1))
    | ~ spl2_4 ),
    inference(avatar_component_clause,[],[f104]) ).

tff(f104,plain,
    ( spl2_4
  <=> $less(count(add(sK0,sK1)),count(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

tff(f134,plain,
    ( ! [X0: $int] :
        ( in(sK0,sK1)
        | $less(X0,count(sK1))
        | ~ $less(X0,$sum(count(sK1),1)) )
    | ~ spl2_4 ),
    inference(superposition,[],[f128,f73]) ).

tff(f73,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(add(X1,X0)) = $sum(count(X0),1) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,plain,
    ! [X0: collection,X1: $int] :
      ( ( ( 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,[],[f39]) ).

tff(f39,plain,
    ! [X0: collection,X1: $int] :
      ( ( 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(f128,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,count(add(sK0,sK1)))
        | $less(X0,count(sK1)) )
    | ~ spl2_4 ),
    inference(resolution,[],[f105,f24]) ).

tff(f24,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | ~ $less(X0,X1)
      | $less(X0,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f123,plain,
    ~ spl2_2,
    inference(avatar_contradiction_clause,[],[f122]) ).

tff(f122,plain,
    ( $false
    | ~ spl2_2 ),
    inference(subsumption_resolution,[],[f121,f23]) ).

tff(f121,plain,
    ( $less(sK0,sK0)
    | ~ spl2_2 ),
    inference(resolution,[],[f97,f78]) ).

tff(f78,plain,
    ! [X2: $int] :
      ( ~ in(X2,sK1)
      | $less(X2,sK0) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,plain,
    ( ! [X2: $int] :
        ( $less(X2,sK0)
        | ~ in(X2,sK1) )
    & ~ $less(count(sK1),count(add(sK0,sK1))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f54,f55]) ).

tff(f55,plain,
    ( ? [X0: $int,X1: collection] :
        ( ! [X2: $int] :
            ( $less(X2,X0)
            | ~ in(X2,X1) )
        & ~ $less(count(X1),count(add(X0,X1))) )
   => ( ! [X2: $int] :
          ( $less(X2,sK0)
          | ~ in(X2,sK1) )
      & ~ $less(count(sK1),count(add(sK0,sK1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f54,plain,
    ? [X0: $int,X1: collection] :
      ( ! [X2: $int] :
          ( $less(X2,X0)
          | ~ in(X2,X1) )
      & ~ $less(count(X1),count(add(X0,X1))) ),
    inference(rectify,[],[f42]) ).

tff(f42,plain,
    ? [X1: $int,X0: collection] :
      ( ! [X2: $int] :
          ( $less(X2,X1)
          | ~ in(X2,X0) )
      & ~ $less(count(X0),count(add(X1,X0))) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ~ ! [X0: collection,X1: $int] :
        ( ! [X2: $int] :
            ( in(X2,X0)
           => $less(X2,X1) )
       => $less(count(X0),count(add(X1,X0))) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X0: collection,X1: $int] :
        ( ! [X2: $int] :
            ( in(X2,X0)
           => $greater(X1,X2) )
       => $greater(count(add(X1,X0)),count(X0)) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X0: collection,X1: $int] :
      ( ! [X2: $int] :
          ( in(X2,X0)
         => $greater(X1,X2) )
     => $greater(count(add(X1,X0)),count(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f97,plain,
    ( in(sK0,sK1)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f96]) ).

tff(f96,plain,
    ( spl2_2
  <=> in(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f120,plain,
    ( spl2_2
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f114,f101,f96]) ).

tff(f101,plain,
    ( spl2_3
  <=> ( count(add(sK0,sK1)) = count(sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f114,plain,
    ( in(sK0,sK1)
    | ~ spl2_3 ),
    inference(trivial_inequality_removal,[],[f109]) ).

tff(f109,plain,
    ( in(sK0,sK1)
    | ( count(sK1) != count(sK1) )
    | ~ spl2_3 ),
    inference(superposition,[],[f60,f102]) ).

tff(f102,plain,
    ( ( count(add(sK0,sK1)) = count(sK1) )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f101]) ).

tff(f60,plain,
    ! [X0: collection,X1: $int] :
      ( ( count(add(X1,X0)) != count(X0) )
      | in(X1,X0) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f106,plain,
    ( spl2_3
    | spl2_4 ),
    inference(avatar_split_clause,[],[f88,f104,f101]) ).

tff(f88,plain,
    ( $less(count(add(sK0,sK1)),count(sK1))
    | ( count(add(sK0,sK1)) = count(sK1) ) ),
    inference(resolution,[],[f77,f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f77,plain,
    ~ $less(count(sK1),count(add(sK0,sK1))),
    inference(cnf_transformation,[],[f56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem    : DAT044=1 : TPTP v8.1.0. Released v5.0.0.
% 0.04/0.12  % 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 : n003.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 20:18:07 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (18319)lrs+10_1:1_ss=axioms:st=5.0:tha=off:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.49  % (18302)lrs+1010_1:1_aac=none:bce=on:nicw=on:nm=0:plsq=on:plsql=on:sac=on:sos=on:sp=frequency:spb=units:to=lpo:i=34:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/34Mi)
% 0.20/0.49  % (18301)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.20/0.50  % (18308)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)
% 0.20/0.50  % (18310)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50  % (18302)First to succeed.
% 0.20/0.50  % (18318)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.20/0.50  % (18326)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.20/0.50  % (18324)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)
% 0.20/0.50  % (18311)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.20/0.51  % (18302)Refutation found. Thanks to Tanya!
% 0.20/0.51  % SZS status Theorem for theBenchmark
% 0.20/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.51  % (18302)------------------------------
% 0.20/0.51  % (18302)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (18302)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (18302)Termination reason: Refutation
% 0.20/0.51  
% 0.20/0.51  % (18302)Memory used [KB]: 5628
% 0.20/0.51  % (18302)Time elapsed: 0.099 s
% 0.20/0.51  % (18302)Instructions burned: 9 (million)
% 0.20/0.51  % (18302)------------------------------
% 0.20/0.51  % (18302)------------------------------
% 0.20/0.51  % (18300)Success in time 0.163 s
%------------------------------------------------------------------------------