TSTP Solution File: DAT088_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT088_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 : 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 : Tue Apr 30 11:04:02 EDT 2024

% Result   : Theorem 0.22s 0.38s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   57 (  13 unt;  18 typ;   0 def)
%            Number of atoms       :  115 (  63 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  116 (  40   ~;  35   |;  28   &)
%                                         (   7 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   83 (   9 atm;   0 fun;  12 num;  62 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    :   14 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :  121 (  93   !;  28   ?; 121   :)

% 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(f193,plain,
    $false,
    inference(evaluation,[],[f190]) ).

tff(f190,plain,
    $less(0,0),
    inference(superposition,[],[f183,f65]) ).

tff(f65,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(f183,plain,
    ! [X0: $int,X1: list] : $less(0,count(X0,X1)),
    inference(superposition,[],[f142,f181]) ).

tff(f181,plain,
    ! [X2: $int,X0: $int,X1: list] : ( count(X2,cons(X0,X1)) = count(X2,X1) ),
    inference(subsumption_resolution,[],[f179,f68]) ).

tff(f68,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(f179,plain,
    ! [X2: $int,X0: $int,X1: list] :
      ( ( count(X2,cons(X0,X1)) = count(X2,X1) )
      | ( cons(X0,X1) = nil ) ),
    inference(superposition,[],[f63,f70]) ).

tff(f70,plain,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: $int,X1: list] : ( tail(cons(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).

tff(f63,plain,
    ! [X0: $int,X1: list] :
      ( ( count(X0,X1) = count(X0,tail(X1)) )
      | ( nil = X1 ) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: $int,X1: list] :
      ( ( count(X0,X1) = count(X0,tail(X1)) )
      | ( nil = X1 ) ),
    inference(ennf_transformation,[],[f32]) ).

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

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

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

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

tff(f142,plain,
    ! [X0: $int,X1: list] : $less(0,count(X0,cons(X0,X1))),
    inference(resolution,[],[f80,f102]) ).

tff(f102,plain,
    ! [X0: $int,X1: list] : in(X0,cons(X0,X1)),
    inference(resolution,[],[f89,f97]) ).

tff(f97,plain,
    ! [X4: $int,X5: list] : sP1(X4,cons(X4,X5)),
    inference(equality_resolution,[],[f96]) ).

tff(f96,plain,
    ! [X1: list,X4: $int,X5: list] :
      ( sP1(X4,X1)
      | ( cons(X4,X5) != X1 ) ),
    inference(equality_resolution,[],[f86]) ).

tff(f86,plain,
    ! [X0: $int,X1: list,X4: $int,X5: list] :
      ( sP1(X0,X1)
      | ( X0 != X4 )
      | ( cons(X4,X5) != X1 ) ),
    inference(cnf_transformation,[],[f61]) ).

tff(f61,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])],[f58,f60,f59]) ).

tff(f59,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(f60,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(f58,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,[],[f57]) ).

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 ) ) ) )
      & ( ? [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,[],[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(nnf_transformation,[],[f47]) ).

tff(f47,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(f89,plain,
    ! [X0: $int,X1: list] :
      ( ~ sP1(X0,X1)
      | in(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

tff(f62,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ sP1(X0,X1) )
      & ( sP1(X0,X1)
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f48]) ).

tff(f48,plain,
    ! [X0: $int,X1: list] :
      ( in(X0,X1)
    <=> sP1(X0,X1) ),
    inference(definition_folding,[],[f38,f47]) ).

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(f80,plain,
    ! [X0: $int,X1: list] :
      ( ~ in(X0,X1)
      | $less(0,count(X0,X1)) ),
    inference(cnf_transformation,[],[f55]) ).

tff(f55,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
% 0.07/0.12  % Problem    : DAT088_1 : TPTP v8.1.2. Released v6.1.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35  % Computer : n003.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Mon Apr 29 22:22:18 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.15/0.36  % (12525)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37  % (12528)WARNING: value z3 for option sas not known
% 0.15/0.38  % (12529)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38  % (12526)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38  % (12527)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38  % (12528)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)
% 0.15/0.38  % (12530)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)
% 0.15/0.38  % (12531)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)
% 0.15/0.38  % (12532)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)
% 0.15/0.38  % (12529)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (12527)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (12526)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.15/0.38  % (12527)Terminated due to inappropriate strategy.
% 0.15/0.38  % (12527)------------------------------
% 0.15/0.38  % (12527)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (12527)Termination reason: Inappropriate
% 0.15/0.38  
% 0.15/0.38  % (12526)Terminated due to inappropriate strategy.
% 0.15/0.38  % (12526)------------------------------
% 0.15/0.38  % (12526)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (12527)Memory used [KB]: 803
% 0.15/0.38  % (12526)Termination reason: Inappropriate
% 0.15/0.38  % (12527)Time elapsed: 0.003 s
% 0.15/0.38  
% 0.15/0.38  % (12527)Instructions burned: 3 (million)
% 0.15/0.38  % (12526)Memory used [KB]: 803
% 0.15/0.38  % (12527)------------------------------
% 0.15/0.38  % (12527)------------------------------
% 0.15/0.38  % (12526)Time elapsed: 0.003 s
% 0.15/0.38  % (12526)Instructions burned: 3 (million)
% 0.15/0.38  % (12526)------------------------------
% 0.15/0.38  % (12526)------------------------------
% 0.15/0.38  % (12529)Terminated due to inappropriate strategy.
% 0.15/0.38  % (12529)------------------------------
% 0.15/0.38  % (12529)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38  % (12529)Termination reason: Inappropriate
% 0.15/0.38  
% 0.15/0.38  % (12529)Memory used [KB]: 803
% 0.15/0.38  % (12529)Time elapsed: 0.003 s
% 0.15/0.38  % (12529)Instructions burned: 3 (million)
% 0.15/0.38  % (12529)------------------------------
% 0.15/0.38  % (12529)------------------------------
% 0.15/0.38  % (12528)First to succeed.
% 0.22/0.38  % (12528)Refutation found. Thanks to Tanya!
% 0.22/0.38  % SZS status Theorem for theBenchmark
% 0.22/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38  % (12528)------------------------------
% 0.22/0.38  % (12528)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.38  % (12528)Termination reason: Refutation
% 0.22/0.38  
% 0.22/0.38  % (12528)Memory used [KB]: 878
% 0.22/0.38  % (12528)Time elapsed: 0.009 s
% 0.22/0.38  % (12528)Instructions burned: 10 (million)
% 0.22/0.38  % (12528)------------------------------
% 0.22/0.38  % (12528)------------------------------
% 0.22/0.38  % (12525)Success in time 0.014 s
%------------------------------------------------------------------------------