%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM906_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 : n008.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 18:02:50 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   33 (   2 unt;   2 typ;   0 def)
%            Number of atoms       :   92 (  20 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  103 (  42   ~;  43   |;  10   &)
%                                         (   6 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number arithmetic     :   66 (  46 atm;   0 fun;   0 num;  20 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    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   20 (  12   !;   8   ?;  20   :)

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

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

tff(f49,plain,
    $false,
    inference(avatar_sat_refutation,[],[f31,f37,f38,f41,f48]) ).

tff(f48,plain,
    ( ~ spl2_1
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f47]) ).

tff(f47,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_3 ),
    inference(subsumption_resolution,[],[f43,f36]) ).

tff(f36,plain,
    ( $less(sK0,sK1)
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f34]) ).

tff(f34,plain,
    ( spl2_3
  <=> $less(sK0,sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f43,plain,
    ( ~ $less(sK0,sK1)
    | ~ spl2_1 ),
    inference(unit_resulting_resolution,[],[f9,f26,f10]) ).

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

tff(f26,plain,
    ( $less(sK1,sK0)
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f24]) ).

tff(f24,plain,
    ( spl2_1
  <=> $less(sK1,sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

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

tff(f41,plain,
    ( ~ spl2_1
    | ~ spl2_2 ),
    inference(avatar_contradiction_clause,[],[f40]) ).

tff(f40,plain,
    ( $false
    | ~ spl2_1
    | ~ spl2_2 ),
    inference(subsumption_resolution,[],[f39,f9]) ).

tff(f39,plain,
    ( $less(sK0,sK0)
    | ~ spl2_1
    | ~ spl2_2 ),
    inference(forward_demodulation,[],[f26,f29]) ).

tff(f29,plain,
    ( ( sK1 = sK0 )
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f28]) ).

tff(f28,plain,
    ( spl2_2
  <=> ( sK1 = sK0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f38,plain,
    ( ~ spl2_3
    | spl2_1 ),
    inference(avatar_split_clause,[],[f21,f24,f34]) ).

tff(f21,plain,
    ( $less(sK1,sK0)
    | ~ $less(sK0,sK1) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ( $less(sK1,sK0)
      | ( ( sK1 != sK0 )
        & ~ $less(sK0,sK1) ) )
    & ( ~ $less(sK1,sK0)
      | ( sK1 = sK0 )
      | $less(sK0,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18]) ).

tff(f18,plain,
    ( ? [X0: $rat,X1: $rat] :
        ( ( $less(X1,X0)
          | ( ( X0 != X1 )
            & ~ $less(X0,X1) ) )
        & ( ~ $less(X1,X0)
          | ( X0 = X1 )
          | $less(X0,X1) ) )
   => ( ( $less(sK1,sK0)
        | ( ( sK1 != sK0 )
          & ~ $less(sK0,sK1) ) )
      & ( ~ $less(sK1,sK0)
        | ( sK1 = sK0 )
        | $less(sK0,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

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

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

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

tff(f1,conjecture,
    ! [X0: $rat,X1: $rat] :
      ( $lesseq(X0,X1)
    <=> ( ( X0 = X1 )
        | $less(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',rat_combined_problem_1) ).

tff(f37,plain,
    ( spl2_3
    | spl2_2 ),
    inference(avatar_split_clause,[],[f32,f28,f34]) ).

tff(f32,plain,
    ( ( sK1 = sK0 )
    | $less(sK0,sK1) ),
    inference(subsumption_resolution,[],[f20,f11]) ).

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

tff(f20,plain,
    ( $less(sK0,sK1)
    | ( sK1 = sK0 )
    | ~ $less(sK1,sK0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f31,plain,
    ( spl2_1
    | ~ spl2_2 ),
    inference(avatar_split_clause,[],[f22,f28,f24]) ).

tff(f22,plain,
    ( ( sK1 != sK0 )
    | $less(sK1,sK0) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : NUM906=1 : TPTP v8.1.0. Released v5.0.0.
% 0.03/0.13  % 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 : n008.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
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 18:39:40 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.19/0.49  % (19856)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=36:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/36Mi)
% 0.19/0.50  % (19855)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=32:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/32Mi)
% 0.19/0.50  % (19855)First to succeed.
% 0.19/0.51  % (19872)dis+32_1:1_bd=off:nm=4:sos=on:ss=included:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (19873)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 (2999ds/47Mi)
% 0.19/0.51  % (19871)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)
% 0.19/0.51  % (19865)lrs+10_1:1_ev=force:gve=cautious:tha=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51  % (19857)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 (2999ds/26Mi)
% 0.19/0.51  % (19864)dis+20_1:12_aac=none:acc=model:awrs=converge:fd=preordered:fsr=off:nicw=on:nwc=3.0:s2a=on:s2agt=16:spb=goal:to=lpo:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51  % (19864)Instruction limit reached!
% 0.19/0.51  % (19864)------------------------------
% 0.19/0.51  % (19864)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (19864)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (19864)Termination reason: Unknown
% 0.19/0.51  % (19864)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (19864)Memory used [KB]: 895
% 0.19/0.51  % (19864)Time elapsed: 0.005 s
% 0.19/0.51  % (19864)Instructions burned: 2 (million)
% 0.19/0.51  % (19864)------------------------------
% 0.19/0.51  % (19864)------------------------------
% 0.19/0.51  % (19855)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (19855)------------------------------
% 0.19/0.51  % (19855)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (19855)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (19855)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (19855)Memory used [KB]: 5500
% 0.19/0.51  % (19855)Time elapsed: 0.102 s
% 0.19/0.51  % (19855)Instructions burned: 2 (million)
% 0.19/0.51  % (19855)------------------------------
% 0.19/0.51  % (19855)------------------------------
% 0.19/0.51  % (19848)Success in time 0.169 s
%------------------------------------------------------------------------------