TSTP Solution File: DAT087_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT087_1 : TPTP v8.2.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.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 19:51:23 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   50 (  11 unt;  18 typ;   0 def)
%            Number of atoms       :  103 (  49 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  109 (  38   ~;  34   |;  28   &)
%                                         (   7 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   82 (   8 atm;   0 fun;  20 num;  54 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   29 (  16   >;  13   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  13 usr;   3 con; 0-2 aty)
%            Number of variables   :  104 (  76   !;  28   ?; 104   :)

% 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_5,type,
    length: list > $int ).

tff(func_def_8,type,
    count: ( $int * list ) > $int ).

tff(func_def_9,type,
    append: ( list * list ) > list ).

tff(func_def_11,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_12,type,
    sK3: ( $int * list ) > list ).

tff(func_def_13,type,
    sK4: ( $int * list ) > $int ).

tff(func_def_14,type,
    sK5: ( $int * list ) > list ).

tff(func_def_15,type,
    sK6: ( $int * list ) > $int ).

tff(func_def_16,type,
    sK7: ( $int * list ) > list ).

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

tff(pred_def_2,type,
    inRange: ( $int * list ) > $o ).

tff(pred_def_6,type,
    sP0: ( $int * list ) > $o ).

tff(pred_def_7,type,
    sP1: ( $int * list ) > $o ).

tff(f151,plain,
    $false,
    inference(resolution,[],[f148,f96]) ).

tff(f96,plain,
    ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
    inference(equality_resolution,[],[f95]) ).

tff(f95,plain,
    ! [X1: list,X4: $int,X5: list] :
      ( sP1(X4,X1)
      | ( cons(X4,X5) != X1 ) ),
    inference(equality_resolution,[],[f85]) ).

tff(f85,plain,
    ! [X0: $int,X1: list,X4: $int,X5: list] :
      ( sP1(X0,X1)
      | ( X0 != X4 )
      | ( cons(X4,X5) != X1 ) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f60,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ( in(X0,sK5(X0,X1))
          & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) )
        | ( ( sK6(X0,X1) = X0 )
          & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f57,f59,f58]) ).

tff(f58,plain,
    ! [X0: $int,X1: list] :
      ( ? [X6: $int,X7: list] :
          ( in(X0,X7)
          & ( cons(X6,X7) = X1 ) )
     => ( in(X0,sK5(X0,X1))
        & ( cons(sK4(X0,X1),sK5(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f59,plain,
    ! [X0: $int,X1: list] :
      ( ? [X8: $int,X9: list] :
          ( ( X0 = X8 )
          & ( cons(X8,X9) = X1 ) )
     => ( ( sK6(X0,X1) = X0 )
        & ( cons(sK6(X0,X1),sK7(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f57,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X6: $int,X7: list] :
            ( in(X0,X7)
            & ( cons(X6,X7) = X1 ) )
        | ? [X8: $int,X9: list] :
            ( ( X0 = X8 )
            & ( cons(X8,X9) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f56]) ).

tff(f56,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(flattening,[],[f55]) ).

tff(f55,plain,
    ! [X0: $int,X1: list] :
      ( ( sP1(X0,X1)
        | ( ! [X2: $int,X3: list] :
              ( ~ in(X0,X3)
              | ( cons(X2,X3) != X1 ) )
          & ! [X4: $int,X5: list] :
              ( ( X0 != X4 )
              | ( cons(X4,X5) != X1 ) ) ) )
      & ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) )
        | ~ sP1(X0,X1) ) ),
    inference(nnf_transformation,[],[f46]) ).

tff(f46,plain,
    ! [X0: $int,X1: list] :
      ( sP1(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f148,plain,
    ! [X0: $int] : ~ sP1(X0,cons(1,nil)),
    inference(resolution,[],[f146,f88]) ).

tff(f88,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

tff(f61,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f47]) ).

tff(f47,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f38,f46]) ).

tff(f38,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> ( ? [X2: $int,X3: list] :
            ( in(X0,X3)
            & ( cons(X2,X3) = X1 ) )
        | ? [X4: $int,X5: list] :
            ( ( X0 = X4 )
            & ( cons(X4,X5) = X1 ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X2: $int,X1: list] :
      ( in(X2,X1)
    <=> ( ? [X3: $int,X4: list] :
            ( in(X2,X4)
            & ( cons(X3,X4) = X1 ) )
        | ? [X3: $int,X4: list] :
            ( ( X2 = X3 )
            & ( cons(X3,X4) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).

tff(f146,plain,
    ! [X0: $int] : ~ in(X0,cons(1,nil)),
    inference(evaluation,[],[f144]) ).

tff(f144,plain,
    ! [X0: $int] :
      ( $less(0,0)
      | ~ in(X0,cons(1,nil)) ),
    inference(superposition,[],[f138,f64]) ).

tff(f64,plain,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).

tff(f138,plain,
    ! [X0: $int,X1: list] :
      ( $less(0,count(X0,X1))
      | ~ in(X0,cons(1,X1)) ),
    inference(superposition,[],[f79,f62]) ).

tff(f62,plain,
    ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
    inference(flattening,[],[f31]) ).

tff(f31,plain,
    ~ ~ ! [X0: $int,X1: list] : ( count(X0,X1) = count(X0,cons(1,X1)) ),
    inference(rectify,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ~ ! [X5: $int,X1: list] : ( count(X5,X1) = count(X5,cons(1,X1)) ),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ~ ! [X5: $int,X1: list] : ( count(X5,X1) = count(X5,cons(1,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).

tff(f79,plain,
    ! [X0: $int,X1: list] :
      ( $less(0,count(X0,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ $less(0,count(X0,X1)) )
      & ( $less(0,count(X0,X1))
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f37]) ).

tff(f37,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> $less(0,count(X0,X1)) ),
    inference(rectify,[],[f18]) ).

tff(f18,plain,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $less(0,count(X5,X1)) ),
    inference(theory_normalization,[],[f14]) ).

tff(f14,axiom,
    ! [X5: $int,X1: list] :
      ( in(X5,X1)
    <=> $greater(count(X5,X1),0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : DAT087_1 : TPTP v8.2.0. Released v6.1.0.
% 0.08/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n012.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Sun May 19 23:05:38 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (30893)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (30896)WARNING: value z3 for option sas not known
% 0.15/0.39  % (30894)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (30895)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (30897)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (30896)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)
% 0.15/0.39  % (30899)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)
% 0.15/0.39  % (30898)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)
% 0.15/0.39  % (30900)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)
% 0.15/0.39  % (30895)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39  % (30897)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39  % (30894)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.39  % (30895)Terminated due to inappropriate strategy.
% 0.15/0.39  % (30895)------------------------------
% 0.15/0.39  % (30895)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (30897)Terminated due to inappropriate strategy.
% 0.15/0.39  % (30897)------------------------------
% 0.15/0.39  % (30897)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (30894)Terminated due to inappropriate strategy.
% 0.15/0.39  % (30894)------------------------------
% 0.15/0.39  % (30894)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.39  % (30895)Termination reason: Inappropriate
% 0.15/0.39  % (30897)Termination reason: Inappropriate
% 0.15/0.39  
% 0.15/0.39  % (30894)Termination reason: Inappropriate
% 0.15/0.39  
% 0.15/0.39  
% 0.15/0.39  % (30895)Memory used [KB]: 803
% 0.15/0.39  % (30897)Memory used [KB]: 803
% 0.15/0.39  % (30894)Memory used [KB]: 803
% 0.15/0.39  % (30895)Time elapsed: 0.003 s
% 0.15/0.39  % (30897)Time elapsed: 0.003 s
% 0.15/0.39  % (30894)Time elapsed: 0.003 s
% 0.15/0.39  % (30895)Instructions burned: 3 (million)
% 0.15/0.39  % (30897)Instructions burned: 3 (million)
% 0.15/0.39  % (30894)Instructions burned: 3 (million)
% 0.15/0.39  % (30894)------------------------------
% 0.15/0.39  % (30894)------------------------------
% 0.15/0.39  % (30895)------------------------------
% 0.15/0.39  % (30895)------------------------------
% 0.15/0.39  % (30897)------------------------------
% 0.15/0.39  % (30897)------------------------------
% 0.15/0.39  % (30899)First to succeed.
% 0.15/0.39  % (30896)Also succeeded, but the first one will report.
% 0.15/0.39  % (30899)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-30893"
% 0.15/0.40  % (30899)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (30899)------------------------------
% 0.15/0.40  % (30899)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40  % (30899)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (30899)Memory used [KB]: 845
% 0.15/0.40  % (30899)Time elapsed: 0.007 s
% 0.15/0.40  % (30899)Instructions burned: 9 (million)
% 0.15/0.40  % (30893)Success in time 0.022 s
%------------------------------------------------------------------------------