TSTP Solution File: DAT062_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT062_1 : TPTP v8.2.0. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 : Mon May 20 19:51:18 EDT 2024

% Result   : Theorem 0.20s 0.40s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   51 (  17 unt;  10 typ;   0 def)
%            Number of atoms       :   95 (  16 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   92 (  38   ~;  29   |;  14   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   84 (  33 atm;  15 fun;  13 num;  23 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :   10 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   55 (  47   !;   8   ?;  55   :)

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

tff(func_def_0,type,
    empty: heap ).

tff(func_def_1,type,
    get: heap > heap ).

tff(func_def_2,type,
    app: ( heap * $int ) > heap ).

tff(func_def_3,type,
    toop: heap > $int ).

tff(func_def_4,type,
    length: heap > $int ).

tff(func_def_9,type,
    sK0: heap ).

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

tff(func_def_11,type,
    sK2: heap ).

tff(pred_def_1,type,
    lsls: ( heap * heap ) > $o ).

tff(f428,plain,
    $false,
    inference(avatar_sat_refutation,[],[f164,f420]) ).

tff(f420,plain,
    spl3_5,
    inference(avatar_contradiction_clause,[],[f419]) ).

tff(f419,plain,
    ( $false
    | spl3_5 ),
    inference(trivial_inequality_removal,[],[f375]) ).

tff(f375,plain,
    ( ( length(sK2) != length(sK2) )
    | spl3_5 ),
    inference(backward_demodulation,[],[f144,f365]) ).

tff(f365,plain,
    sK0 = sK2,
    inference(subsumption_resolution,[],[f360,f122]) ).

tff(f122,plain,
    ~ lsls(sK2,sK0),
    inference(resolution,[],[f119,f45]) ).

tff(f45,plain,
    ! [X3: heap] :
      ( $less(length(X3),length(sK0))
      | ~ lsls(X3,sK0) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f40,plain,
    ( ~ $less(length(sK2),length(app(sK0,sK1)))
    & lsls(sK2,app(sK0,sK1))
    & ! [X3: heap] :
        ( $less(length(X3),length(sK0))
        | ~ lsls(X3,sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f35,f39,f38]) ).

tff(f38,plain,
    ( ? [X0: heap,X1: $int] :
        ( ? [X2: heap] :
            ( ~ $less(length(X2),length(app(X0,X1)))
            & lsls(X2,app(X0,X1)) )
        & ! [X3: heap] :
            ( $less(length(X3),length(X0))
            | ~ lsls(X3,X0) ) )
   => ( ? [X2: heap] :
          ( ~ $less(length(X2),length(app(sK0,sK1)))
          & lsls(X2,app(sK0,sK1)) )
      & ! [X3: heap] :
          ( $less(length(X3),length(sK0))
          | ~ lsls(X3,sK0) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f39,plain,
    ( ? [X2: heap] :
        ( ~ $less(length(X2),length(app(sK0,sK1)))
        & lsls(X2,app(sK0,sK1)) )
   => ( ~ $less(length(sK2),length(app(sK0,sK1)))
      & lsls(sK2,app(sK0,sK1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f35,plain,
    ? [X0: heap,X1: $int] :
      ( ? [X2: heap] :
          ( ~ $less(length(X2),length(app(X0,X1)))
          & lsls(X2,app(X0,X1)) )
      & ! [X3: heap] :
          ( $less(length(X3),length(X0))
          | ~ lsls(X3,X0) ) ),
    inference(ennf_transformation,[],[f26]) ).

tff(f26,plain,
    ~ ! [X0: heap,X1: $int] :
        ( ! [X2: heap] :
            ( lsls(X2,app(X0,X1))
           => $less(length(X2),length(app(X0,X1))) )
        | ~ ! [X3: heap] :
              ( lsls(X3,X0)
             => $less(length(X3),length(X0)) ) ),
    inference(rectify,[],[f13]) ).

tff(f13,negated_conjecture,
    ~ ! [X1: heap,X0: $int] :
        ( ! [X2: heap] :
            ( lsls(X2,app(X1,X0))
           => $less(length(X2),length(app(X1,X0))) )
        | ~ ! [X2: heap] :
              ( lsls(X2,X1)
             => $less(length(X2),length(X1)) ) ),
    inference(negated_conjecture,[],[f12]) ).

tff(f12,conjecture,
    ! [X1: heap,X0: $int] :
      ( ! [X2: heap] :
          ( lsls(X2,app(X1,X0))
         => $less(length(X2),length(app(X1,X0))) )
      | ~ ! [X2: heap] :
            ( lsls(X2,X1)
           => $less(length(X2),length(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_lem_1a) ).

tff(f119,plain,
    ~ $less(length(sK2),length(sK0)),
    inference(resolution,[],[f114,f99]) ).

tff(f99,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f91,f14]) ).

tff(f14,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f91,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(resolution,[],[f23,f19]) ).

tff(f19,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f23,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f114,plain,
    ! [X0: $int] :
      ( ~ $less(X0,$sum(1,length(sK0)))
      | ~ $less(length(sK2),X0) ),
    inference(resolution,[],[f20,f66]) ).

tff(f66,plain,
    ~ $less(length(sK2),$sum(1,length(sK0))),
    inference(backward_demodulation,[],[f47,f55]) ).

tff(f55,plain,
    ! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0: $int,X1: heap] : ( length(app(X1,X0)) = $sum(1,length(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_23) ).

tff(f47,plain,
    ~ $less(length(sK2),length(app(sK0,sK1))),
    inference(cnf_transformation,[],[f40]) ).

tff(f20,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less(X1,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_143,[]) ).

tff(f360,plain,
    ( ( sK0 = sK2 )
    | lsls(sK2,sK0) ),
    inference(resolution,[],[f57,f46]) ).

tff(f46,plain,
    lsls(sK2,app(sK0,sK1)),
    inference(cnf_transformation,[],[f40]) ).

tff(f57,plain,
    ! [X2: heap,X0: $int,X1: heap] :
      ( ~ lsls(X1,app(X2,X0))
      | ( X1 = X2 )
      | lsls(X1,X2) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( ( lsls(X1,app(X2,X0))
        | ( ~ lsls(X1,X2)
          & ( X1 != X2 ) ) )
      & ( lsls(X1,X2)
        | ( X1 = X2 )
        | ~ lsls(X1,app(X2,X0)) ) ),
    inference(flattening,[],[f41]) ).

tff(f41,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( ( lsls(X1,app(X2,X0))
        | ( ~ lsls(X1,X2)
          & ( X1 != X2 ) ) )
      & ( lsls(X1,X2)
        | ( X1 = X2 )
        | ~ lsls(X1,app(X2,X0)) ) ),
    inference(nnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: heap,X2: heap] :
      ( lsls(X1,app(X2,X0))
    <=> ( lsls(X1,X2)
        | ( X1 = X2 ) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,axiom,
    ! [X0: $int,X2: heap,X1: heap] :
      ( lsls(X2,app(X1,X0))
    <=> ( lsls(X2,X1)
        | ( X1 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_27) ).

tff(f144,plain,
    ( ( length(sK0) != length(sK2) )
    | spl3_5 ),
    inference(avatar_component_clause,[],[f143]) ).

tff(f143,plain,
    ( spl3_5
  <=> ( length(sK0) = length(sK2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).

tff(f164,plain,
    ~ spl3_5,
    inference(avatar_contradiction_clause,[],[f163]) ).

tff(f163,plain,
    ( $false
    | ~ spl3_5 ),
    inference(subsumption_resolution,[],[f153,f19]) ).

tff(f153,plain,
    ( $less($sum(1,length(sK2)),$sum(1,length(sK2)))
    | ~ spl3_5 ),
    inference(backward_demodulation,[],[f92,f145]) ).

tff(f145,plain,
    ( ( length(sK0) = length(sK2) )
    | ~ spl3_5 ),
    inference(avatar_component_clause,[],[f143]) ).

tff(f92,plain,
    $less($sum(1,length(sK0)),$sum(1,length(sK2))),
    inference(forward_demodulation,[],[f90,f14]) ).

tff(f90,plain,
    $less($sum(1,length(sK0)),$sum(length(sK2),1)),
    inference(resolution,[],[f23,f66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : DAT062_1 : TPTP v8.2.0. Released v5.5.0.
% 0.06/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n020.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   : Sun May 19 23:26:53 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.35  % (11845)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36  % (11848)WARNING: value z3 for option sas not known
% 0.13/0.36  % (11847)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (11849)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (11846)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (11851)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)
% 0.13/0.36  % (11850)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)
% 0.13/0.36  % (11848)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)
% 0.13/0.36  % (11852)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)
% 0.13/0.37  % (11849)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11847)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11847)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11847)------------------------------
% 0.13/0.37  % (11847)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (11846)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37  % (11849)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11849)------------------------------
% 0.13/0.37  % (11849)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (11849)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11849)Memory used [KB]: 749
% 0.13/0.37  % (11849)Time elapsed: 0.002 s
% 0.13/0.37  % (11849)Instructions burned: 3 (million)
% 0.13/0.37  % (11846)Terminated due to inappropriate strategy.
% 0.13/0.37  % (11846)------------------------------
% 0.13/0.37  % (11846)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (11846)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11846)Memory used [KB]: 749
% 0.13/0.37  % (11846)Time elapsed: 0.003 s
% 0.13/0.37  % (11846)Instructions burned: 3 (million)
% 0.13/0.37  % (11847)Termination reason: Inappropriate
% 0.13/0.37  
% 0.13/0.37  % (11847)Memory used [KB]: 749
% 0.13/0.37  % (11847)Time elapsed: 0.003 s
% 0.13/0.37  % (11847)Instructions burned: 3 (million)
% 0.13/0.37  % (11849)------------------------------
% 0.13/0.37  % (11849)------------------------------
% 0.13/0.37  % (11846)------------------------------
% 0.13/0.37  % (11846)------------------------------
% 0.13/0.37  % (11847)------------------------------
% 0.13/0.37  % (11847)------------------------------
% 0.20/0.38  % (11853)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.38  % (11854)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)
% 0.20/0.38  % (11855)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)
% 0.20/0.38  % (11853)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.38  % (11853)Terminated due to inappropriate strategy.
% 0.20/0.38  % (11853)------------------------------
% 0.20/0.38  % (11853)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.38  % (11853)Termination reason: Inappropriate
% 0.20/0.38  
% 0.20/0.38  % (11853)Memory used [KB]: 747
% 0.20/0.38  % (11853)Time elapsed: 0.002 s
% 0.20/0.38  % (11853)Instructions burned: 3 (million)
% 0.20/0.38  % (11853)------------------------------
% 0.20/0.38  % (11853)------------------------------
% 0.20/0.40  % (11855)First to succeed.
% 0.20/0.40  % (11855)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-11845"
% 0.20/0.40  % (11855)Refutation found. Thanks to Tanya!
% 0.20/0.40  % SZS status Theorem for theBenchmark
% 0.20/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40  % (11855)------------------------------
% 0.20/0.40  % (11855)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40  % (11855)Termination reason: Refutation
% 0.20/0.40  
% 0.20/0.40  % (11855)Memory used [KB]: 959
% 0.20/0.40  % (11855)Time elapsed: 0.039 s
% 0.20/0.40  % (11855)Instructions burned: 25 (million)
% 0.20/0.40  % (11845)Success in time 0.039 s
%------------------------------------------------------------------------------