%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM913_1 : TPTP v8.1.0. Released v5.0.0.
% 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 : n027.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 18:02:51 EDT 2022

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   35 (   2 unt;   2 typ;   0 def)
%            Number of atoms       :  101 (  22 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  115 (  47   ~;  48   |;  12   &)
%                                         (   6 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number arithmetic     :   75 (  51 atm;   0 fun;   2 num;  22 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   3 usr;   4 prp; 0-2 aty)
%            Number of functors    :    3 (   2 usr;   3 con; 0-0 aty)
%            Number of variables   :   22 (  12   !;  10   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_4,type,
    sK0: $real ).

tff(func_def_5,type,
    sK1: $real ).

tff(f52,plain,
    $false,
    inference(avatar_sat_refutation,[],[f32,f38,f39,f43,f51]) ).

tff(f51,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_contradiction_clause,[],[f50]) ).

tff(f50,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_2 ),
    inference(subsumption_resolution,[],[f45,f31]) ).

tff(f31,plain,
    ( $less(sK0,sK1)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f29]) ).

tff(f29,plain,
    ( spl2_2
  <=> $less(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f45,plain,
    ( ~ $less(sK0,sK1)
    | ~ spl2_1 ),
    inference(unit_resulting_resolution,[],[f9,f26,f10]) ).

tff(f10,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X0,X2)
      | ~ $less(X0,X1)
      | ~ $less(X1,X2) ),
    introduced(theory_axiom_148,[]) ).

tff(f26,plain,
    ( $less(sK1,sK0)
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f25]) ).

tff(f25,plain,
    ( spl2_1
  <=> $less(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

tff(f9,plain,
    ! [X0: $real] : ~ $less(X0,X0),
    introduced(theory_axiom_147,[]) ).

tff(f43,plain,
    ( ~ spl2_2
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f42]) ).

tff(f42,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(evaluation,[],[f41]) ).

tff(f41,plain,
    ( $less(0.0,0.0)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(cancellation,[],[f40]) ).

tff(f40,plain,
    ( $less(sK0,sK0)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f31,f37]) ).

tff(f37,plain,
    ( ( sK0 = sK1 )
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f35]) ).

tff(f35,plain,
    ( spl2_3
  <=> ( sK0 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f39,plain,
    ( spl2_2
    | ~ spl2_3 ),
    inference(avatar_split_clause,[],[f22,f35,f29]) ).

tff(f22,plain,
    ( ( sK0 != sK1 )
    | $less(sK0,sK1) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ( ( ( ~ $less(sK1,sK0)
        & ( sK0 != sK1 ) )
      | $less(sK0,sK1) )
    & ( $less(sK1,sK0)
      | ( sK0 = sK1 )
      | ~ $less(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).

tff(f19,plain,
    ( ? [X0: $real,X1: $real] :
        ( ( ( ~ $less(X1,X0)
            & ( X0 != X1 ) )
          | $less(X0,X1) )
        & ( $less(X1,X0)
          | ( X0 = X1 )
          | ~ $less(X0,X1) ) )
   => ( ( ( ~ $less(sK1,sK0)
          & ( sK0 != sK1 ) )
        | $less(sK0,sK1) )
      & ( $less(sK1,sK0)
        | ( sK0 = sK1 )
        | ~ $less(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ? [X0: $real,X1: $real] :
      ( ( ( ~ $less(X1,X0)
          & ( X0 != X1 ) )
        | $less(X0,X1) )
      & ( $less(X1,X0)
        | ( X0 = X1 )
        | ~ $less(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

tff(f17,plain,
    ? [X1: $real,X0: $real] :
      ( ( ( ~ $less(X0,X1)
          & ( X0 != X1 ) )
        | $less(X1,X0) )
      & ( $less(X0,X1)
        | ( X0 = X1 )
        | ~ $less(X1,X0) ) ),
    inference(flattening,[],[f16]) ).

tff(f16,plain,
    ? [X1: $real,X0: $real] :
      ( ( ( ~ $less(X0,X1)
          & ( X0 != X1 ) )
        | $less(X1,X0) )
      & ( $less(X0,X1)
        | ( X0 = X1 )
        | ~ $less(X1,X0) ) ),
    inference(nnf_transformation,[],[f15]) ).

tff(f15,plain,
    ? [X1: $real,X0: $real] :
      ( ~ $less(X1,X0)
    <~> ( $less(X0,X1)
        | ( X0 = X1 ) ) ),
    inference(ennf_transformation,[],[f3]) ).

tff(f3,plain,
    ~ ! [X0: $real,X1: $real] :
        ( ( $less(X0,X1)
          | ( X0 = X1 ) )
      <=> ~ $less(X1,X0) ),
    inference(theory_normalization,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X0: $real,X1: $real] :
        ( $lesseq(X0,X1)
      <=> ( $less(X0,X1)
          | ( X0 = X1 ) ) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X0: $real,X1: $real] :
      ( $lesseq(X0,X1)
    <=> ( $less(X0,X1)
        | ( X0 = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_combined_problem_1) ).

tff(f38,plain,
    ( spl2_1
    | spl2_3 ),
    inference(avatar_split_clause,[],[f33,f35,f25]) ).

tff(f33,plain,
    ( ( sK0 = sK1 )
    | $less(sK1,sK0) ),
    inference(subsumption_resolution,[],[f21,f11]) ).

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

tff(f21,plain,
    ( ( sK0 = sK1 )
    | ~ $less(sK0,sK1)
    | $less(sK1,sK0) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f32,plain,
    ( ~ spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f23,f29,f25]) ).

tff(f23,plain,
    ( $less(sK0,sK1)
    | ~ $less(sK1,sK0) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : NUM913=1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.12  % 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 : n027.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   : Tue Aug 30 09:30:16 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.49  % (1802)lrs+1_1:10_av=off:drc=off:nwc=2.0:sp=reverse_frequency:thsq=on:thsqc=64:thsql=off:i=47:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/47Mi)
% 0.18/0.49  % (1794)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.18/0.49  % (1784)lrs+1010_1:1_ep=RST:s2a=on:s2at=5.0:sos=all:i=26:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/26Mi)
% 0.18/0.50  % (1786)lrs+10_1:8_ep=R:erd=off:fs=off:fsr=off:gve=force:nwc=2.0:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.18/0.50  % (1804)lrs+1002_1:1_br=off:canc=force:drc=off:s2a=on:sos=on:sp=reverse_frequency:urr=on:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/42Mi)
% 0.18/0.50  % (1804)First to succeed.
% 0.18/0.50  % (1791)dis+10_1:64_nwc=1.4:tha=off:i=21:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/21Mi)
% 0.18/0.50  % (1791)Refutation not found, incomplete strategy% (1791)------------------------------
% 0.18/0.50  % (1791)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (1791)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (1791)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.50  
% 0.18/0.50  % (1791)Memory used [KB]: 5373
% 0.18/0.50  % (1791)Time elapsed: 0.110 s
% 0.18/0.50  % (1791)Instructions burned: 2 (million)
% 0.18/0.50  % (1791)------------------------------
% 0.18/0.50  % (1791)------------------------------
% 0.18/0.50  % (1795)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 (3000ds/49Mi)
% 0.18/0.50  % (1804)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (1804)------------------------------
% 0.18/0.50  % (1804)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (1804)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (1804)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (1804)Memory used [KB]: 5500
% 0.18/0.50  % (1804)Time elapsed: 0.110 s
% 0.18/0.50  % (1804)Instructions burned: 2 (million)
% 0.18/0.50  % (1804)------------------------------
% 0.18/0.50  % (1804)------------------------------
% 0.18/0.50  % (1774)Success in time 0.157 s
%------------------------------------------------------------------------------