TSTP Solution File: DAT104_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT104_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 05:06:03 EDT 2024

% Result   : Theorem 1.62s 0.60s
% Output   : Refutation 1.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   52 (  17 unt;   9 typ;   0 def)
%            Number of atoms       :  140 (  33 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  149 (  52   ~;  48   |;  39   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  156 (  41 atm;  18 fun;  47 num;  50 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   12 (   7   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   90 (  74   !;  16   ?;  90   :)

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

tff(func_def_0,type,
    nil: list ).

tff(func_def_1,type,
    cons: ( $int * list ) > list ).

tff(func_def_2,type,
    head: list > $int ).

tff(func_def_3,type,
    tail: list > list ).

tff(func_def_9,type,
    sK1: ( $int * list ) > $int ).

tff(func_def_10,type,
    sK2: ( $int * list ) > list ).

tff(pred_def_1,type,
    inRange: ( $int * list ) > $o ).

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

tff(f15940,plain,
    $false,
    inference(subsumption_resolution,[],[f15932,f15933]) ).

tff(f15933,plain,
    ~ $less(sK1(0,cons(0,nil)),0),
    inference(unit_resulting_resolution,[],[f36,f15386,f40]) ).

tff(f40,plain,
    ! [X0: $int,X1: list] :
      ( ~ sP0(X0,X1)
      | ( nil = X1 )
      | ~ $less(sK1(X0,X1),0) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ( inRange(X0,sK2(X0,X1))
          & $less(sK1(X0,X1),X0)
          & ~ $less(sK1(X0,X1),0)
          & ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f30,f31]) ).

tff(f31,plain,
    ! [X0: $int,X1: list] :
      ( ? [X4: $int,X5: list] :
          ( inRange(X0,X5)
          & $less(X4,X0)
          & ~ $less(X4,0)
          & ( cons(X4,X5) = X1 ) )
     => ( inRange(X0,sK2(X0,X1))
        & $less(sK1(X0,X1),X0)
        & ~ $less(sK1(X0,X1),0)
        & ( cons(sK1(X0,X1),sK2(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X4: $int,X5: list] :
            ( inRange(X0,X5)
            & $less(X4,X0)
            & ~ $less(X4,0)
            & ( cons(X4,X5) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(flattening,[],[f28]) ).

tff(f28,plain,
    ! [X0: $int,X1: list] :
      ( ( sP0(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ inRange(X0,X3)
              | ~ $less(X2,X0)
              | $less(X2,0)
              | ( cons(X2,X3) != X1 ) )
          & ( nil != X1 ) ) )
      & ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 )
        | ~ sP0(X0,X1) ) ),
    inference(nnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f15386,plain,
    sP0(0,cons(0,nil)),
    inference(unit_resulting_resolution,[],[f15384,f45]) ).

tff(f45,plain,
    ! [X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | sP0(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: list] :
      ( ( inRange(X0,X1)
        | ~ sP0(X0,X1) )
      & ( sP0(X0,X1)
        | ~ inRange(X0,X1) ) ),
    inference(nnf_transformation,[],[f27]) ).

tff(f27,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> sP0(X0,X1) ),
    inference(definition_folding,[],[f24,f26]) ).

tff(f24,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( inRange(X0,X3)
            & $less(X2,X0)
            & ~ $less(X2,0)
            & ( cons(X2,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(rectify,[],[f9]) ).

tff(f9,plain,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & ~ $less(X0,0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    inference(theory_normalization,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
    <=> ( ? [X0: $int,X3: list] :
            ( inRange(X2,X3)
            & $less(X0,X2)
            & $lesseq(0,X0)
            & ( cons(X0,X3) = X1 ) )
        | ( nil = X1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).

tff(f15384,plain,
    inRange(0,cons(0,nil)),
    inference(evaluation,[],[f15378]) ).

tff(f15378,plain,
    inRange($sum(1,-1),cons(0,nil)),
    inference(unit_resulting_resolution,[],[f15333,f49]) ).

tff(f49,plain,
    ! [X0: $int,X1: list] :
      ( ~ inRange(X0,X1)
      | inRange($sum(X0,-1),X1) ),
    inference(evaluation,[],[f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: list] :
      ( inRange($sum(X0,$uminus(1)),X1)
      | ~ inRange(X0,X1) ),
    inference(cnf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0: $int,X1: list] :
      ( inRange($sum(X0,$uminus(1)),X1)
      | ~ inRange(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: $int,X1: list] :
      ( inRange(X0,X1)
     => inRange($sum(X0,$uminus(1)),X1) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ! [X2: $int,X1: list] :
      ( inRange(X2,X1)
     => inRange($sum(X2,$uminus(1)),X1) ),
    inference(theory_normalization,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ~ ! [X2: $int,X1: list] :
          ( inRange(X2,X1)
         => inRange($difference(X2,1),X1) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ~ ! [X2: $int,X1: list] :
        ( inRange(X2,X1)
       => inRange($difference(X2,1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).

tff(f15333,plain,
    inRange(1,cons(0,nil)),
    inference(unit_resulting_resolution,[],[f13581,f46]) ).

tff(f46,plain,
    ! [X0: $int,X1: list] :
      ( ~ sP0(X0,X1)
      | inRange(X0,X1) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f13581,plain,
    sP0(1,cons(0,nil)),
    inference(evaluation,[],[f11817]) ).

tff(f11817,plain,
    sP0($sum(1,0),cons(0,nil)),
    inference(unit_resulting_resolution,[],[f51,f75,f15,f47]) ).

tff(f47,plain,
    ! [X2: $int,X3: list,X0: $int] :
      ( ~ inRange(X0,X3)
      | sP0(X0,cons(X2,X3))
      | ~ $less(X2,X0)
      | $less(X2,0) ),
    inference(equality_resolution,[],[f44]) ).

tff(f44,plain,
    ! [X2: $int,X3: list,X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ~ inRange(X0,X3)
      | ~ $less(X2,X0)
      | $less(X2,0)
      | ( cons(X2,X3) != X1 ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f15,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f75,plain,
    ! [X0: $int] : $less(X0,$sum(1,X0)),
    inference(superposition,[],[f69,f10]) ).

tff(f10,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f69,plain,
    ! [X0: $int] : $less(X0,$sum(X0,1)),
    inference(unit_resulting_resolution,[],[f15,f19]) ).

tff(f19,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_147,[]) ).

tff(f51,plain,
    ! [X0: $int] : inRange(X0,nil),
    inference(unit_resulting_resolution,[],[f48,f46]) ).

tff(f48,plain,
    ! [X0: $int] : sP0(X0,nil),
    inference(equality_resolution,[],[f43]) ).

tff(f43,plain,
    ! [X0: $int,X1: list] :
      ( sP0(X0,X1)
      | ( nil != X1 ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f36,plain,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    inference(cnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0: $int,X1: list] : ( cons(X0,X1) != nil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).

tff(f15932,plain,
    $less(sK1(0,cons(0,nil)),0),
    inference(unit_resulting_resolution,[],[f36,f15386,f41]) ).

tff(f41,plain,
    ! [X0: $int,X1: list] :
      ( ~ sP0(X0,X1)
      | ( nil = X1 )
      | $less(sK1(X0,X1),X0) ),
    inference(cnf_transformation,[],[f32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : DAT104_1 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36  % Computer : n026.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Fri May  3 13:17:21 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.37  % (32573)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (32574)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (32574)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (32574)Terminated due to inappropriate strategy.
% 0.14/0.38  % (32574)------------------------------
% 0.14/0.38  % (32574)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38  % (32574)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (32574)Memory used [KB]: 729
% 0.14/0.38  % (32574)Time elapsed: 0.002 s
% 0.14/0.38  % (32574)Instructions burned: 2 (million)
% 0.14/0.39  % (32574)------------------------------
% 0.14/0.39  % (32574)------------------------------
% 0.14/0.39  % (32577)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (32580)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)
% 0.14/0.39  % (32577)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (32577)Terminated due to inappropriate strategy.
% 0.14/0.39  % (32577)------------------------------
% 0.14/0.39  % (32577)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (32577)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (32577)Memory used [KB]: 729
% 0.14/0.39  % (32577)Time elapsed: 0.002 s
% 0.14/0.39  % (32577)Instructions burned: 2 (million)
% 0.14/0.39  % (32577)------------------------------
% 0.14/0.39  % (32577)------------------------------
% 0.14/0.39  % (32579)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)
% 0.14/0.39  % (32576)WARNING: value z3 for option sas not known
% 0.14/0.39  % (32575)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (32576)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)
% 0.14/0.39  % (32578)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)
% 0.14/0.39  % (32575)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (32575)Terminated due to inappropriate strategy.
% 0.14/0.39  % (32575)------------------------------
% 0.14/0.39  % (32575)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39  % (32575)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (32575)Memory used [KB]: 730
% 0.14/0.39  % (32575)Time elapsed: 0.003 s
% 0.14/0.39  % (32575)Instructions burned: 2 (million)
% 0.14/0.39  % (32575)------------------------------
% 0.14/0.39  % (32575)------------------------------
% 0.14/0.40  % (32581)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.14/0.40  % (32581)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.40  % (32581)Terminated due to inappropriate strategy.
% 0.14/0.40  % (32581)------------------------------
% 0.14/0.40  % (32581)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40  % (32581)Termination reason: Inappropriate
% 0.14/0.40  
% 0.14/0.40  % (32581)Memory used [KB]: 729
% 0.14/0.40  % (32581)Time elapsed: 0.003 s
% 0.14/0.40  % (32581)Instructions burned: 2 (million)
% 0.14/0.40  % (32581)------------------------------
% 0.14/0.40  % (32581)------------------------------
% 0.14/0.41  % (32582)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)
% 0.14/0.41  % (32583)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)
% 0.14/0.42  % (32584)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)
% 1.62/0.60  % (32582)First to succeed.
% 1.62/0.60  % (32582)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-32573"
% 1.62/0.60  % (32582)Refutation found. Thanks to Tanya!
% 1.62/0.60  % SZS status Theorem for theBenchmark
% 1.62/0.60  % SZS output start Proof for theBenchmark
% See solution above
% 1.62/0.60  % (32582)------------------------------
% 1.62/0.60  % (32582)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.62/0.60  % (32582)Termination reason: Refutation
% 1.62/0.60  
% 1.62/0.60  % (32582)Memory used [KB]: 2962
% 1.62/0.60  % (32582)Time elapsed: 0.195 s
% 1.62/0.60  % (32582)Instructions burned: 440 (million)
% 1.62/0.60  % (32573)Success in time 0.231 s
%------------------------------------------------------------------------------