%------------------------------------------------------------------------------
% File     : SnakeForV---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_uns --cores 0 -t %d %s

% Computer : n019.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 15:46:33 EDT 2022

% Result   : Theorem 0.19s 0.57s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   25 (   8 unt;   2 typ;   0 def)
%            Number of atoms       :   60 (  15 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   65 (  28   ~;  23   |;  10   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :  121 (  44 atm;   7 fun;  39 num;  31 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    :    6 (   2 usr;   5 con; 0-2 aty)
%            Number of variables   :   31 (  24   !;   7   ?;  31   :)

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

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

tff(f72,plain,
    $false,
    inference(unit_resulting_resolution,[],[f20,f8,f70,f9]) ).

tff(f9,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | ~ $less(X0,X1) ),
    introduced(theory_axiom_148,[]) ).

tff(f70,plain,
    $less(sK0,2),
    inference(evaluation,[],[f69]) ).

tff(f69,plain,
    $less(sK0,$sum(1,1)),
    inference(resolution,[],[f68,f12]) ).

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

tff(f68,plain,
    ~ $less(1,sK0),
    inference(evaluation,[],[f62]) ).

tff(f62,plain,
    ( ~ $less(0,1)
    | ~ $less(1,sK0)
    | ( 2 = 1 ) ),
    inference(resolution,[],[f14,f51]) ).

tff(f51,plain,
    ! [X0: $int] :
      ( $less(sK0,$sum(1,X0))
      | ( 2 = X0 )
      | ~ $less(0,X0) ),
    inference(superposition,[],[f44,f3]) ).

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

tff(f44,plain,
    ! [X0: $int] :
      ( $less(sK0,$sum(X0,1))
      | ~ $less(0,X0)
      | ( 2 = X0 ) ),
    inference(resolution,[],[f12,f23]) ).

tff(f23,plain,
    ! [X2: $int] :
      ( ~ $less(X2,sK0)
      | ~ $less(0,X2)
      | ( 2 = X2 ) ),
    inference(backward_demodulation,[],[f19,f22]) ).

tff(f22,plain,
    2 = sK1,
    inference(evaluation,[],[f21]) ).

tff(f21,plain,
    ( ~ $less(0,2)
    | ( 2 = sK1 ) ),
    inference(resolution,[],[f19,f20]) ).

tff(f19,plain,
    ! [X2: $int] :
      ( ~ $less(X2,sK0)
      | ( sK1 = X2 )
      | ~ $less(0,X2) ),
    inference(cnf_transformation,[],[f18]) ).

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

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

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

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

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

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

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

tff(f8,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_147,[]) ).

tff(f20,plain,
    $less(2,sK0),
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ARI592=1 : TPTP v8.1.0. Released v5.1.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon Aug 29 15:53:35 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.53  % (26675)lrs+10_1:1_canc=force:tha=some:to=lpo:i=35:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/35Mi)
% 0.19/0.53  % (26676)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=4:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.54  % (26665)dis+1010_1:4_aac=none:abs=on:atotf=0.5:avsq=on:avsqc=2:avsqr=215,247:awrs=converge:awrsf=128:bsd=on:erd=off:fde=none:gve=cautious:newcnf=on:nwc=5.0:rnwc=on:sac=on:sas=z3:sp=const_min:tgt=ground:thsq=on:thsqc=64:thsqr=1,4:i=59848:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59848Mi)
% 0.19/0.54  % (26670)lrs+10_1:32_s2a=on:s2agt=10:sgt=8:ss=axioms:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.54  % (26682)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.19/0.54  % (26676)Instruction limit reached!
% 0.19/0.54  % (26676)------------------------------
% 0.19/0.54  % (26676)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.54  % (26676)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.55  % (26676)Termination reason: Unknown
% 0.19/0.55  % (26676)Termination phase: Saturation
% 0.19/0.55  
% 0.19/0.55  % (26676)Memory used [KB]: 5500
% 0.19/0.55  % (26676)Time elapsed: 0.139 s
% 0.19/0.55  % (26676)Instructions burned: 4 (million)
% 0.19/0.55  % (26676)------------------------------
% 0.19/0.55  % (26676)------------------------------
% 0.19/0.55  % (26669)ott+1011_1:2_br=off:bs=unit_only:bsr=unit_only:nwc=5.0:s2a=on:s2agt=32:urr=on:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.56  % (26681)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.56  % (26681)Refutation not found, incomplete strategy% (26681)------------------------------
% 0.19/0.56  % (26681)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (26681)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (26681)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.56  
% 0.19/0.56  % (26681)Memory used [KB]: 5373
% 0.19/0.56  % (26681)Time elapsed: 0.147 s
% 0.19/0.56  % (26681)Instructions burned: 1 (million)
% 0.19/0.56  % (26678)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/21Mi)
% 0.19/0.56  % (26681)------------------------------
% 0.19/0.56  % (26681)------------------------------
% 0.19/0.57  % (26682)First to succeed.
% 0.19/0.57  % (26687)dis+2_1:1_av=off:bsr=on:erd=off:s2pl=on:sgt=16:sos=on:sp=frequency:ss=axioms:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.19/0.57  % (26682)Refutation found. Thanks to Tanya!
% 0.19/0.57  % SZS status Theorem for theBenchmark
% 0.19/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.57  % (26682)------------------------------
% 0.19/0.57  % (26682)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.57  % (26682)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.57  % (26682)Termination reason: Refutation
% 0.19/0.57  
% 0.19/0.57  % (26682)Memory used [KB]: 5500
% 0.19/0.57  % (26682)Time elapsed: 0.150 s
% 0.19/0.57  % (26682)Instructions burned: 3 (million)
% 0.19/0.57  % (26682)------------------------------
% 0.19/0.57  % (26682)------------------------------
% 0.19/0.57  % (26664)Success in time 0.226 s
%------------------------------------------------------------------------------