TSTP Solution File: DAT081_1 by SnakeForV-SAT---1.0

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : DAT081_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n029.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 : Wed Aug 31 16:04:50 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   35 (  10 unt;  17 typ;   0 def)
%            Number of atoms       :   30 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   24 (  12   ~;   6   |;   2   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   36 (   9 atm;   0 fun;  12 num;  15 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   25 (  14   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  14 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (  19   !;   2   ?;  21   :)

% 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,
    sK0: $int ).

tff(func_def_12,type,
    sK1: ( $int * list ) > list ).

tff(func_def_13,type,
    sK2: ( $int * list ) > $int ).

tff(func_def_14,type,
    sK3: ( $int * list ) > $int ).

tff(func_def_15,type,
    sK4: ( $int * list ) > list ).

tff(func_def_16,type,
    sK5: ( list * $int ) > $int ).

tff(func_def_17,type,
    sK6: ( list * $int ) > list ).

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

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

tff(f157,plain,
    $false,
    inference(resolution,[],[f156,f72]) ).

tff(f72,plain,
    in(sK0,nil),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,plain,
    in(sK0,nil),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f44,f49]) ).

tff(f49,plain,
    ( ? [X0: $int] : in(X0,nil)
   => in(sK0,nil) ),
    introduced(choice_axiom,[]) ).

tff(f44,plain,
    ? [X0: $int] : in(X0,nil),
    inference(ennf_transformation,[],[f36]) ).

tff(f36,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(f156,plain,
    ! [X0: $int] : ~ in(X0,nil),
    inference(evaluation,[],[f155]) ).

tff(f155,plain,
    ! [X0: $int] :
      ( $less(0,0)
      | ~ in(X0,nil) ),
    inference(superposition,[],[f91,f73]) ).

tff(f73,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(f91,plain,
    ! [X0: $int,X1: list] :
      ( $less(0,count(X0,X1))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f66]) ).

tff(f66,plain,
    ! [X0: $int,X1: list] :
      ( ( $less(0,count(X0,X1))
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | ~ $less(0,count(X0,X1)) ) ),
    inference(rectify,[],[f65]) ).

tff(f65,plain,
    ! [X1: $int,X0: list] :
      ( ( $less(0,count(X1,X0))
        | ~ in(X1,X0) )
      & ( in(X1,X0)
        | ~ $less(0,count(X1,X0)) ) ),
    inference(nnf_transformation,[],[f38]) ).

tff(f38,plain,
    ! [X1: $int,X0: list] :
      ( $less(0,count(X1,X0))
    <=> in(X1,X0) ),
    inference(rectify,[],[f18]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : DAT081=1 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34  % Computer : n029.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Mon Aug 29 20:30:56 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.50  % (4669)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50  % (4667)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.50  % (4681)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.51  % (4684)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.51  % (4673)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (4681)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.51  % (4689)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.51  % (4676)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.52  % (4673)First to succeed.
% 0.21/0.52  % (4681)Terminated due to inappropriate strategy.
% 0.21/0.52  % (4681)------------------------------
% 0.21/0.52  % (4681)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (4681)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (4681)Termination reason: Inappropriate
% 0.21/0.52  
% 0.21/0.52  % (4681)Memory used [KB]: 895
% 0.21/0.52  % (4681)Time elapsed: 0.004 s
% 0.21/0.52  % (4681)Instructions burned: 3 (million)
% 0.21/0.52  % (4681)------------------------------
% 0.21/0.52  % (4681)------------------------------
% 0.21/0.52  % (4688)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.52  % (4665)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.52  % (4669)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.52  % (4669)Terminated due to inappropriate strategy.
% 0.21/0.52  % (4669)------------------------------
% 0.21/0.52  % (4669)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (4669)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (4669)Termination reason: Inappropriate
% 0.21/0.52  
% 0.21/0.52  % (4669)Memory used [KB]: 895
% 0.21/0.52  % (4669)Time elapsed: 0.004 s
% 0.21/0.52  % (4669)Instructions burned: 3 (million)
% 0.21/0.52  % (4669)------------------------------
% 0.21/0.52  % (4669)------------------------------
% 0.21/0.52  % (4663)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.52  % (4673)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (4673)------------------------------
% 0.21/0.52  % (4673)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (4673)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (4673)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (4673)Memory used [KB]: 1023
% 0.21/0.52  % (4673)Time elapsed: 0.122 s
% 0.21/0.52  % (4673)Instructions burned: 6 (million)
% 0.21/0.52  % (4673)------------------------------
% 0.21/0.52  % (4673)------------------------------
% 0.21/0.52  % (4661)Success in time 0.169 s
%------------------------------------------------------------------------------