TSTP Solution File: DAT081_1 by Vampire-SAT---4.8

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT081_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 : n013.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 11:04:00 EDT 2024

% Result   : Theorem 0.13s 0.38s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   36 (  10 unt;  19 typ;   0 def)
%            Number of atoms       :   26 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   19 (  10   ~;   4   |;   1   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   31 (   7 atm;   0 fun;  10 num;  14 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 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :   19 (  17   !;   2   ?;  19   :)

% 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 ).

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

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

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

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

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

tff(func_def_17,type,
    sK8: ( $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(f141,plain,
    $false,
    inference(resolution,[],[f140,f64]) ).

tff(f64,plain,
    in(sK2,nil),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,plain,
    in(sK2,nil),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f41,f48]) ).

tff(f48,plain,
    ( ? [X0: $int] : in(X0,nil)
   => in(sK2,nil) ),
    introduced(choice_axiom,[]) ).

tff(f41,plain,
    ? [X0: $int] : in(X0,nil),
    inference(ennf_transformation,[],[f31]) ).

tff(f31,plain,
    ~ ! [X0: $int] : ~ in(X0,nil),
    inference(rectify,[],[f16]) ).

tff(f16,negated_conjecture,
    ~ ! [X7: $int] : ~ in(X7,nil),
    inference(negated_conjecture,[],[f15]) ).

tff(f15,conjecture,
    ! [X7: $int] : ~ in(X7,nil),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',c) ).

tff(f140,plain,
    ! [X0: $int] : ~ in(X0,nil),
    inference(evaluation,[],[f139]) ).

tff(f139,plain,
    ! [X0: $int] :
      ( $less(0,0)
      | ~ in(X0,nil) ),
    inference(superposition,[],[f81,f66]) ).

tff(f66,plain,
    ! [X0: $int] : ( 0 = count(X0,nil) ),
    inference(cnf_transformation,[],[f9]) ).

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

tff(f81,plain,
    ! [X0: $int,X1: list] :
      ( $less(0,count(X0,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,plain,
    ! [X0: $int,X1: list] :
      ( ( in(X0,X1)
        | ~ $less(0,count(X0,X1)) )
      & ( $less(0,count(X0,X1))
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

tff(f36,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/sandbox/benchmark/theBenchmark.p',a_8) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : DAT081_1 : TPTP v8.1.2. Released v6.1.0.
% 0.11/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36  % Computer : n013.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit   : 300
% 0.13/0.36  % WCLimit    : 300
% 0.13/0.36  % DateTime   : Mon Apr 29 22:08:19 EDT 2024
% 0.13/0.36  % CPUTime    : 
% 0.13/0.36  % (7299)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38  % (7302)WARNING: value z3 for option sas not known
% 0.13/0.38  % (7303)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38  % (7306)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)
% 0.13/0.38  % (7304)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)
% 0.13/0.38  % (7301)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38  % (7305)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)
% 0.13/0.38  % (7302)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)
% 0.13/0.38  % (7300)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38  % (7301)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (7303)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (7303)Terminated due to inappropriate strategy.
% 0.13/0.38  % (7303)------------------------------
% 0.13/0.38  % (7303)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (7301)Terminated due to inappropriate strategy.
% 0.13/0.38  % (7301)------------------------------
% 0.13/0.38  % (7301)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (7301)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (7301)Memory used [KB]: 803
% 0.13/0.38  % (7301)Time elapsed: 0.003 s
% 0.13/0.38  % (7301)Instructions burned: 3 (million)
% 0.13/0.38  % (7301)------------------------------
% 0.13/0.38  % (7301)------------------------------
% 0.13/0.38  % (7303)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (7303)Memory used [KB]: 803
% 0.13/0.38  % (7303)Time elapsed: 0.003 s
% 0.13/0.38  % (7303)Instructions burned: 3 (million)
% 0.13/0.38  % (7303)------------------------------
% 0.13/0.38  % (7303)------------------------------
% 0.13/0.38  % (7300)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38  % (7300)Terminated due to inappropriate strategy.
% 0.13/0.38  % (7300)------------------------------
% 0.13/0.38  % (7300)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (7300)Termination reason: Inappropriate
% 0.13/0.38  
% 0.13/0.38  % (7300)Memory used [KB]: 803
% 0.13/0.38  % (7300)Time elapsed: 0.003 s
% 0.13/0.38  % (7300)Instructions burned: 3 (million)
% 0.13/0.38  % (7300)------------------------------
% 0.13/0.38  % (7300)------------------------------
% 0.13/0.38  % (7305)First to succeed.
% 0.13/0.38  % (7304)Also succeeded, but the first one will report.
% 0.13/0.38  % (7305)Refutation found. Thanks to Tanya!
% 0.13/0.38  % SZS status Theorem for theBenchmark
% 0.13/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.38  % (7305)------------------------------
% 0.13/0.38  % (7305)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38  % (7305)Termination reason: Refutation
% 0.13/0.38  
% 0.13/0.38  % (7305)Memory used [KB]: 842
% 0.13/0.38  % (7305)Time elapsed: 0.006 s
% 0.13/0.38  % (7305)Instructions burned: 7 (million)
% 0.13/0.38  % (7305)------------------------------
% 0.13/0.38  % (7305)------------------------------
% 0.13/0.38  % (7299)Success in time 0.019 s
%------------------------------------------------------------------------------