%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ARI735_1 : TPTP v8.1.0. Released v6.4.0.
% 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 : n018.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 15:49:07 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (  14 unt;   4 typ;   0 def)
%            Number of atoms       :   70 (  30 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   79 (  37   ~;  13   |;  17   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :  159 (  36 atm;  32 fun;  62 num;  29 var)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   1 usr;   4 con; 0-2 aty)
%            Number of variables   :   29 (  22   !;   7   ?;  29   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_5,type,
    sK0: $int ).

tff(pred_def_3,type,
    sQ1_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_4,type,
    sQ2_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_5,type,
    sQ3_eqProxy: ( $real * $real ) > $o ).

tff(f145,plain,
    $false,
    inference(subsumption_resolution,[],[f144,f31]) ).

tff(f31,plain,
    0 != sK0,
    inference(literal_reordering,[],[f21]) ).

tff(f21,plain,
    0 != sK0,
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ( ~ $less(sK0,0)
    & ! [X1: $int] :
        ( $less(X1,0)
        | ( $sum(sK0,$uminus(1)) != X1 ) )
    & ( 0 != sK0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).

tff(f19,plain,
    ( ? [X0: $int] :
        ( ~ $less(X0,0)
        & ! [X1: $int] :
            ( $less(X1,0)
            | ( $sum(X0,$uminus(1)) != X1 ) )
        & ( 0 != X0 ) )
   => ( ~ $less(sK0,0)
      & ! [X1: $int] :
          ( $less(X1,0)
          | ( $sum(sK0,$uminus(1)) != X1 ) )
      & ( 0 != sK0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ? [X0: $int] :
      ( ~ $less(X0,0)
      & ! [X1: $int] :
          ( $less(X1,0)
          | ( $sum(X0,$uminus(1)) != X1 ) )
      & ( 0 != X0 ) ),
    inference(flattening,[],[f17]) ).

tff(f17,plain,
    ? [X0: $int] :
      ( ! [X1: $int] :
          ( $less(X1,0)
          | ( $sum(X0,$uminus(1)) != X1 ) )
      & ( 0 != X0 )
      & ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ~ ! [X0: $int] :
        ( ~ $less(X0,0)
       => ( ( 0 != X0 )
         => ? [X1: $int] :
              ( ( $sum(X0,$uminus(1)) = X1 )
              & ~ $less(X1,0) ) ) ),
    inference(true_and_false_elimination,[],[f3]) ).

tff(f3,plain,
    ~ ! [X0: $int] :
        ( ~ $less(X0,0)
       => ( ( ( 0 = X0 )
           => $true )
          & ( ( 0 != X0 )
           => ? [X1: $int] :
                ( ( $sum(X0,$uminus(1)) = X1 )
                & ~ $less(X1,0) ) ) ) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X0: $int] :
        ( $greatereq(X0,0)
       => ( ( ( 0 = X0 )
           => $true )
          & ( ( 0 != X0 )
           => ? [X1: $int] :
                ( ( $difference(X0,1) = X1 )
                & $greatereq(X1,0) ) ) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X0: $int] :
      ( $greatereq(X0,0)
     => ( ( ( 0 = X0 )
         => $true )
        & ( ( 0 != X0 )
         => ? [X1: $int] :
              ( ( $difference(X0,1) = X1 )
              & $greatereq(X1,0) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula) ).

tff(f144,plain,
    0 = sK0,
    inference(subsumption_resolution,[],[f140,f39]) ).

tff(f39,plain,
    ~ $less(sK0,0),
    inference(literal_reordering,[],[f23]) ).

tff(f23,plain,
    ~ $less(sK0,0),
    inference(cnf_transformation,[],[f20]) ).

tff(f140,plain,
    ( $less(sK0,0)
    | ( 0 = sK0 ) ),
    inference(resolution,[],[f83,f34]) ).

tff(f34,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    inference(literal_reordering,[],[f11]) ).

tff(f11,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f83,plain,
    ~ $less(0,sK0),
    inference(evaluation,[],[f82]) ).

tff(f82,plain,
    ~ $less(0,$sum($sum(-1,sK0),1)),
    inference(resolution,[],[f28,f76]) ).

tff(f76,plain,
    $less($sum(-1,sK0),0),
    inference(backward_demodulation,[],[f72,f33]) ).

tff(f33,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    inference(literal_reordering,[],[f4]) ).

tff(f4,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_140,[]) ).

tff(f72,plain,
    $less($sum(sK0,-1),0),
    inference(evaluation,[],[f38]) ).

tff(f38,plain,
    $less($sum(sK0,$uminus(1)),0),
    inference(literal_reordering,[],[f24]) ).

tff(f24,plain,
    $less($sum(sK0,$uminus(1)),0),
    inference(equality_resolution,[],[f22]) ).

tff(f22,plain,
    ! [X1: $int] :
      ( $less(X1,0)
      | ( $sum(sK0,$uminus(1)) != X1 ) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f28,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    inference(literal_reordering,[],[f15]) ).

tff(f15,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_166,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : ARI735=1 : TPTP v8.1.0. Released v6.4.0.
% 0.12/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n018.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 16:26:39 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.51  % (8355)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.20/0.52  % (8355)First to succeed.
% 0.20/0.52  % (8356)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.20/0.52  % (8345)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.52  % (8345)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.52  % (8345)Terminated due to inappropriate strategy.
% 0.20/0.52  % (8345)------------------------------
% 0.20/0.52  % (8345)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (8345)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (8345)Termination reason: Inappropriate
% 0.20/0.52  
% 0.20/0.52  % (8345)Memory used [KB]: 895
% 0.20/0.52  % (8345)Time elapsed: 0.001 s
% 0.20/0.52  % (8345)------------------------------
% 0.20/0.52  % (8345)------------------------------
% 0.20/0.52  % (8342)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.52  % (8353)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 0.20/0.52  % (8339)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.20/0.52  % (8355)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (8355)------------------------------
% 0.20/0.52  % (8355)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (8355)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (8355)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (8355)Memory used [KB]: 5756
% 0.20/0.52  % (8355)Time elapsed: 0.008 s
% 0.20/0.52  % (8355)Instructions burned: 6 (million)
% 0.20/0.52  % (8355)------------------------------
% 0.20/0.52  % (8355)------------------------------
% 0.20/0.52  % (8335)Success in time 0.17 s
%------------------------------------------------------------------------------