TSTP Solution File: DAT035_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT035_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n011.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 : Sun May  5 05:05:42 EDT 2024

% Result   : Theorem 2.46s 0.70s
% Output   : Refutation 2.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   66 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  115 (  22 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  108 (  50   ~;  40   |;   6   &)
%                                         (   8 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  171 (  51 atm;  38 fun;  35 num;  47 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   5 usr;   5 prp; 0-2 aty)
%            Number of functors    :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   62 (  56   !;   6   ?;  62   :)

% 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(func_def_11,type,
    sK2: $int ).

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

tff(f7478,plain,
    $false,
    inference(avatar_sat_refutation,[],[f1703,f2399,f3124,f3937,f7476]) ).

tff(f7476,plain,
    ( ~ spl3_4
    | ~ spl3_12 ),
    inference(avatar_contradiction_clause,[],[f7475]) ).

tff(f7475,plain,
    ( $false
    | ~ spl3_4
    | ~ spl3_12 ),
    inference(subsumption_resolution,[],[f7427,f2398]) ).

tff(f2398,plain,
    ( $less(1,sK2)
    | ~ spl3_12 ),
    inference(avatar_component_clause,[],[f2396]) ).

tff(f2396,plain,
    ( spl3_12
  <=> $less(1,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).

tff(f7427,plain,
    ( ~ $less(1,sK2)
    | ~ spl3_4 ),
    inference(resolution,[],[f187,f1702]) ).

tff(f1702,plain,
    ( $less($sum(sK2,count(sK0)),$sum(1,count(sK0)))
    | ~ spl3_4 ),
    inference(avatar_component_clause,[],[f1700]) ).

tff(f1700,plain,
    ( spl3_4
  <=> $less($sum(sK2,count(sK0)),$sum(1,count(sK0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

tff(f187,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less($sum(X1,X2),$sum(X0,X2))
      | ~ $less(X0,X1) ),
    inference(resolution,[],[f26,f124]) ).

tff(f124,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(resolution,[],[f24,f23]) ).

tff(f23,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f24,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X1,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_143,[]) ).

tff(f26,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X0,X2),$sum(X1,X2))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_145,[]) ).

tff(f3937,plain,
    ~ spl3_3,
    inference(avatar_contradiction_clause,[],[f3936]) ).

tff(f3936,plain,
    ( $false
    | ~ spl3_3 ),
    inference(subsumption_resolution,[],[f3909,f54]) ).

tff(f54,plain,
    $less(0,sK2),
    inference(cnf_transformation,[],[f44]) ).

tff(f44,plain,
    ( $less($sum(count(sK0),sK2),count(add(sK1,sK0)))
    & $less(0,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f43]) ).

tff(f43,plain,
    ( ? [X0: collection,X1: $int,X2: $int] :
        ( $less($sum(count(X0),X2),count(add(X1,X0)))
        & $less(0,X2) )
   => ( $less($sum(count(sK0),sK2),count(add(sK1,sK0)))
      & $less(0,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: collection,X1: $int,X2: $int] :
      ( $less($sum(count(X0),X2),count(add(X1,X0)))
      & $less(0,X2) ),
    inference(ennf_transformation,[],[f15]) ).

tff(f15,plain,
    ~ ! [X0: collection,X1: $int,X2: $int] :
        ( $less(0,X2)
       => ~ $less($sum(count(X0),X2),count(add(X1,X0))) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,negated_conjecture,
    ~ ! [X0: collection,X1: $int,X2: $int] :
        ( $greater(X2,0)
       => $greatereq($sum(count(X0),X2),count(add(X1,X0))) ),
    inference(negated_conjecture,[],[f13]) ).

tff(f13,conjecture,
    ! [X0: collection,X1: $int,X2: $int] :
      ( $greater(X2,0)
     => $greatereq($sum(count(X0),X2),count(add(X1,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f3909,plain,
    ( ~ $less(0,sK2)
    | ~ spl3_3 ),
    inference(resolution,[],[f624,f1708]) ).

tff(f1708,plain,
    ( ~ $less(count(sK0),$sum(sK2,count(sK0)))
    | ~ spl3_3 ),
    inference(backward_demodulation,[],[f131,f1698]) ).

tff(f1698,plain,
    ( ( count(sK0) = count(add(sK1,sK0)) )
    | ~ spl3_3 ),
    inference(avatar_component_clause,[],[f1696]) ).

tff(f1696,plain,
    ( spl3_3
  <=> ( count(sK0) = count(add(sK1,sK0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f131,plain,
    ~ $less(count(add(sK1,sK0)),$sum(sK2,count(sK0))),
    inference(resolution,[],[f124,f82]) ).

tff(f82,plain,
    $less($sum(sK2,count(sK0)),count(add(sK1,sK0))),
    inference(forward_demodulation,[],[f55,f18]) ).

tff(f18,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f55,plain,
    $less($sum(count(sK0),sK2),count(add(sK1,sK0))),
    inference(cnf_transformation,[],[f44]) ).

tff(f624,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,$sum(X1,X0))
      | ~ $less(0,X1) ),
    inference(superposition,[],[f191,f20]) ).

tff(f20,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f191,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X1,X0),$sum(X2,X1))
      | ~ $less(X0,X2) ),
    inference(superposition,[],[f26,f18]) ).

tff(f3124,plain,
    ( ~ spl3_4
    | ~ spl3_11 ),
    inference(avatar_contradiction_clause,[],[f3123]) ).

tff(f3123,plain,
    ( $false
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(subsumption_resolution,[],[f2708,f23]) ).

tff(f2708,plain,
    ( $less($sum(1,count(sK0)),$sum(1,count(sK0)))
    | ~ spl3_4
    | ~ spl3_11 ),
    inference(backward_demodulation,[],[f1702,f2394]) ).

tff(f2394,plain,
    ( ( 1 = sK2 )
    | ~ spl3_11 ),
    inference(avatar_component_clause,[],[f2392]) ).

tff(f2392,plain,
    ( spl3_11
  <=> ( 1 = sK2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_11])]) ).

tff(f2399,plain,
    ( spl3_11
    | spl3_12 ),
    inference(avatar_split_clause,[],[f2388,f2396,f2392]) ).

tff(f2388,plain,
    ( $less(1,sK2)
    | ( 1 = sK2 ) ),
    inference(resolution,[],[f2301,f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f2301,plain,
    ~ $less(sK2,1),
    inference(resolution,[],[f409,f54]) ).

tff(f409,plain,
    ! [X0: $int] :
      ( ~ $less(X0,1)
      | ~ $less(0,X0) ),
    inference(superposition,[],[f105,f20]) ).

tff(f105,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(1,X0))
      | ~ $less(X0,X1) ),
    inference(superposition,[],[f29,f18]) ).

tff(f29,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$sum(X0,1))
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_161,[]) ).

tff(f1703,plain,
    ( spl3_3
    | spl3_4 ),
    inference(avatar_split_clause,[],[f1679,f1700,f1696]) ).

tff(f1679,plain,
    ( $less($sum(sK2,count(sK0)),$sum(1,count(sK0)))
    | ( count(sK0) = count(add(sK1,sK0)) ) ),
    inference(superposition,[],[f82,f319]) ).

tff(f319,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(1,count(X1)) )
      | ( count(X1) = count(add(X0,X1)) ) ),
    inference(resolution,[],[f84,f67]) ).

tff(f67,plain,
    ! [X0: $int,X1: collection] :
      ( ~ in(X0,X1)
      | ( count(X1) = count(add(X0,X1)) ) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: collection] :
      ( ( in(X0,X1)
        | ( count(X1) != count(add(X0,X1)) ) )
      & ( ( count(X1) = count(add(X0,X1)) )
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
    <=> ( count(X1) = count(add(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(f84,plain,
    ! [X0: $int,X1: collection] :
      ( in(X0,X1)
      | ( count(add(X0,X1)) = $sum(1,count(X1)) ) ),
    inference(forward_demodulation,[],[f65,f18]) ).

tff(f65,plain,
    ! [X0: $int,X1: collection] :
      ( ( count(add(X0,X1)) = $sum(count(X1),1) )
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: collection] :
      ( ( ~ in(X0,X1)
        | ( count(add(X0,X1)) != $sum(count(X1),1) ) )
      & ( ( count(add(X0,X1)) = $sum(count(X1),1) )
        | in(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT035_1 : TPTP v8.1.2. Released v5.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n011.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Fri May  3 12:57:19 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (16951)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (16955)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37  % (16955)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37  % (16955)Terminated due to inappropriate strategy.
% 0.14/0.37  % (16955)------------------------------
% 0.14/0.37  % (16955)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37  % (16955)Termination reason: Inappropriate
% 0.14/0.37  
% 0.14/0.37  % (16955)Memory used [KB]: 766
% 0.14/0.37  % (16955)Time elapsed: 0.002 s
% 0.14/0.37  % (16955)Instructions burned: 3 (million)
% 0.14/0.37  % (16955)------------------------------
% 0.14/0.37  % (16955)------------------------------
% 0.14/0.37  % (16954)WARNING: value z3 for option sas not known
% 0.14/0.37  % (16952)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37  % (16953)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37  % (16954)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37  % (16956)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38  % (16957)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38  % (16958)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38  % (16952)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (16952)Terminated due to inappropriate strategy.
% 0.14/0.38  % (16952)------------------------------
% 0.14/0.38  % (16952)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (16952)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (16952)Memory used [KB]: 766
% 0.14/0.38  % (16952)Time elapsed: 0.003 s
% 0.14/0.38  % (16952)Instructions burned: 3 (million)
% 0.14/0.38  % (16953)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (16953)Terminated due to inappropriate strategy.
% 0.14/0.38  % (16953)------------------------------
% 0.14/0.38  % (16953)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (16953)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (16953)Memory used [KB]: 767
% 0.14/0.38  % (16953)Time elapsed: 0.003 s
% 0.14/0.38  % (16953)Instructions burned: 3 (million)
% 0.14/0.38  % (16952)------------------------------
% 0.14/0.38  % (16952)------------------------------
% 0.14/0.38  % (16953)------------------------------
% 0.14/0.38  % (16953)------------------------------
% 0.14/0.38  % (16959)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.39  % (16959)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (16959)Terminated due to inappropriate strategy.
% 0.14/0.39  % (16959)------------------------------
% 0.14/0.39  % (16959)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (16959)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (16959)Memory used [KB]: 766
% 0.14/0.39  % (16959)Time elapsed: 0.002 s
% 0.14/0.39  % (16959)Instructions burned: 3 (million)
% 0.14/0.39  % (16959)------------------------------
% 0.14/0.39  % (16959)------------------------------
% 0.22/0.39  % (16960)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.22/0.39  % (16961)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.22/0.40  % (16962)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.46/0.69  % (16961)First to succeed.
% 2.46/0.69  % (16961)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16951"
% 2.46/0.70  % (16961)Refutation found. Thanks to Tanya!
% 2.46/0.70  % SZS status Theorem for theBenchmark
% 2.46/0.70  % SZS output start Proof for theBenchmark
% See solution above
% 2.46/0.70  % (16961)------------------------------
% 2.46/0.70  % (16961)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.46/0.70  % (16961)Termination reason: Refutation
% 2.46/0.70  
% 2.46/0.70  % (16961)Memory used [KB]: 2844
% 2.46/0.70  % (16961)Time elapsed: 0.303 s
% 2.46/0.70  % (16961)Instructions burned: 637 (million)
% 2.46/0.70  % (16951)Success in time 0.331 s
%------------------------------------------------------------------------------