%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : ARI592_1 : TPTP v8.1.0. Released v5.1.0.
% 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 : n006.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 15:48:39 EDT 2022

% Result   : Theorem 1.44s 0.52s
% Output   : Refutation 1.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   33 (  11 unt;   2 typ;   0 def)
%            Number of atoms       :   76 (  30 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   71 (  26   ~;  33   |;   9   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :  144 (  45 atm;   9 fun;  60 num;  30 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   2 usr;   6 con; 0-2 aty)
%            Number of variables   :   30 (  22   !;   8   ?;  30   :)

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

tff(func_def_6,type,
    sK1: $int ).

tff(f230,plain,
    $false,
    inference(evaluation,[],[f223]) ).

tff(f223,plain,
    ~ $less(1,3),
    inference(backward_demodulation,[],[f191,f195]) ).

tff(f195,plain,
    3 = sK0,
    inference(evaluation,[],[f194]) ).

tff(f194,plain,
    ( ( 3 = sK0 )
    | ( 2 = 3 ) ),
    inference(forward_demodulation,[],[f179,f180]) ).

tff(f180,plain,
    2 = sK1,
    inference(evaluation,[],[f177]) ).

tff(f177,plain,
    ( ( 2 = 0 )
    | ( 2 = sK1 )
    | $less(2,0) ),
    inference(resolution,[],[f77,f19]) ).

tff(f19,plain,
    $less(2,sK0),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ( ! [X2: $int] :
        ( ( sK1 = X2 )
        | ~ $less(0,X2)
        | ~ $less(X2,sK0) )
    & $less(2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f17]) ).

tff(f17,plain,
    ( ? [X0: $int,X1: $int] :
        ( ! [X2: $int] :
            ( ( X1 = X2 )
            | ~ $less(0,X2)
            | ~ $less(X2,X0) )
        & $less(2,X0) )
   => ( ! [X2: $int] :
          ( ( sK1 = X2 )
          | ~ $less(0,X2)
          | ~ $less(X2,sK0) )
      & $less(2,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ? [X0: $int,X1: $int] :
      ( ! [X2: $int] :
          ( ( X1 = X2 )
          | ~ $less(0,X2)
          | ~ $less(X2,X0) )
      & $less(2,X0) ),
    inference(rectify,[],[f15]) ).

tff(f15,plain,
    ? [X1: $int,X0: $int] :
      ( ! [X2: $int] :
          ( ( X0 = X2 )
          | ~ $less(0,X2)
          | ~ $less(X2,X1) )
      & $less(2,X1) ),
    inference(ennf_transformation,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X1: $int,X0: $int] :
        ( $less(2,X1)
       => ? [X2: $int] :
            ( ( X0 != X2 )
            & $less(0,X2)
            & $less(X2,X1) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X1: $int,X0: $int] :
      ( $less(2,X1)
     => ? [X2: $int] :
          ( ( X0 != X2 )
          & $less(0,X2)
          & $less(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_X_0_Z_noteq_Y) ).

tff(f77,plain,
    ! [X0: $int] :
      ( ~ $less(X0,sK0)
      | ( 0 = X0 )
      | ( sK1 = X0 )
      | $less(X0,0) ),
    inference(resolution,[],[f10,f20]) ).

tff(f20,plain,
    ! [X2: $int] :
      ( ~ $less(0,X2)
      | ~ $less(X2,sK0)
      | ( sK1 = X2 ) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f10,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_149,[]) ).

tff(f179,plain,
    ( ( 3 = sK1 )
    | ( 3 = sK0 ) ),
    inference(evaluation,[],[f178]) ).

tff(f178,plain,
    ( ( 3 = sK0 )
    | ( 0 = 3 )
    | ( 3 = sK1 )
    | $less(3,0) ),
    inference(resolution,[],[f77,f85]) ).

tff(f85,plain,
    ( $less(3,sK0)
    | ( 3 = sK0 ) ),
    inference(resolution,[],[f10,f48]) ).

tff(f48,plain,
    ~ $less(sK0,3),
    inference(evaluation,[],[f46]) ).

tff(f46,plain,
    ~ $less(sK0,$sum(2,1)),
    inference(resolution,[],[f14,f19]) ).

tff(f14,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_166,[]) ).

tff(f191,plain,
    ~ $less(1,sK0),
    inference(evaluation,[],[f184]) ).

tff(f184,plain,
    ( ~ $less(1,sK0)
    | ( 2 = 1 ) ),
    inference(backward_demodulation,[],[f53,f180]) ).

tff(f53,plain,
    ( ~ $less(1,sK0)
    | ( 1 = sK1 ) ),
    inference(evaluation,[],[f52]) ).

tff(f52,plain,
    ( ( 1 = sK1 )
    | ~ $less(1,sK0)
    | $less(0,0) ),
    inference(superposition,[],[f39,f31]) ).

tff(f31,plain,
    ! [X0: $int] : ( $sum(0,X0) = X0 ),
    inference(superposition,[],[f5,f3]) ).

tff(f3,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_140,[]) ).

tff(f5,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_142,[]) ).

tff(f39,plain,
    ! [X0: $int] :
      ( ~ $less($sum(X0,1),sK0)
      | ( sK1 = $sum(X0,1) )
      | $less(X0,0) ),
    inference(resolution,[],[f12,f20]) ).

tff(f12,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      | $less(X0,X1) ),
    introduced(theory_axiom_152,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : ARI592=1 : TPTP v8.1.0. Released v5.1.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n006.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Mon Aug 29 15:49:10 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.50  % (11413)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 0.19/0.50  % (11421)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)
% 0.19/0.51  % (11407)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)
% 0.19/0.51  % (11421)First to succeed.
% 0.19/0.51  % (11413)Instruction limit reached!
% 0.19/0.51  % (11413)------------------------------
% 0.19/0.51  % (11413)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (11429)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.19/0.51  % (11434)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/439Mi)
% 1.44/0.52  % (11410)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 1.44/0.52  % (11413)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.52  % (11413)Termination reason: Unknown
% 1.44/0.52  % (11413)Termination phase: Saturation
% 1.44/0.52  
% 1.44/0.52  % (11413)Memory used [KB]: 5500
% 1.44/0.52  % (11413)Time elapsed: 0.125 s
% 1.44/0.52  % (11413)Instructions burned: 8 (million)
% 1.44/0.52  % (11413)------------------------------
% 1.44/0.52  % (11413)------------------------------
% 1.44/0.52  % (11423)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 1.44/0.52  % (11423)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 1.44/0.52  % (11423)Terminated due to inappropriate strategy.
% 1.44/0.52  % (11423)------------------------------
% 1.44/0.52  % (11423)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.52  % (11423)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.52  % (11423)Termination reason: Inappropriate
% 1.44/0.52  
% 1.44/0.52  % (11423)Memory used [KB]: 895
% 1.44/0.52  % (11423)Time elapsed: 0.003 s
% 1.44/0.52  % (11423)------------------------------
% 1.44/0.52  % (11423)------------------------------
% 1.44/0.52  % (11408)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 (3000ds/37Mi)
% 1.44/0.52  % (11415)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 (3000ds/51Mi)
% 1.44/0.52  % (11421)Refutation found. Thanks to Tanya!
% 1.44/0.52  % SZS status Theorem for theBenchmark
% 1.44/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.44/0.52  % (11421)------------------------------
% 1.44/0.52  % (11421)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.44/0.52  % (11421)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.44/0.52  % (11421)Termination reason: Refutation
% 1.44/0.52  
% 1.44/0.52  % (11421)Memory used [KB]: 1023
% 1.44/0.52  % (11421)Time elapsed: 0.120 s
% 1.44/0.52  % (11421)Instructions burned: 11 (million)
% 1.44/0.52  % (11421)------------------------------
% 1.44/0.52  % (11421)------------------------------
% 1.44/0.52  % (11405)Success in time 0.183 s
%------------------------------------------------------------------------------