%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : NUM894_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 : n003.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 18:02:48 EDT 2022

% Result   : Theorem 1.24s 0.53s
% Output   : Refutation 1.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   18 (   7 unt;   2 typ;   0 def)
%            Number of atoms       :   27 (   1 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   20 (   9   ~;   1   |;   5   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number arithmetic     :   73 (  25 atm;  16 fun;  14 num;  18 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   2 usr;   3 con; 0-2 aty)
%            Number of variables   :   18 (  12   !;   6   ?;  18   :)

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

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

tff(f29,plain,
    $false,
    inference(subsumption_resolution,[],[f28,f23]) ).

tff(f23,plain,
    $less(sK1,$sum(1,sK0)),
    inference(forward_demodulation,[],[f22,f4]) ).

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

tff(f22,plain,
    $less(sK1,$sum(sK0,1)),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ( $less(sK1,$sum(sK0,1))
    & $less(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19]) ).

tff(f19,plain,
    ( ? [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        & $less(X0,X1) )
   => ( $less(sK1,$sum(sK0,1))
      & $less(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ? [X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,1))
      & $less(X0,X1) ),
    inference(rectify,[],[f17]) ).

tff(f17,plain,
    ? [X1: $int,X0: $int] :
      ( $less(X0,$sum(X1,1))
      & $less(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

tff(f16,plain,
    ~ ! [X0: $int,X1: $int] :
        ( $less(X0,$sum(X1,1))
       => ~ $less(X1,X0) ),
    inference(rectify,[],[f3]) ).

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

tff(f2,negated_conjecture,
    ~ ! [X1: $int,X0: $int] :
        ( $less(X1,$sum(X0,1))
       => $lesseq(X1,X0) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X1: $int,X0: $int] :
      ( $less(X1,$sum(X0,1))
     => $lesseq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_successor) ).

tff(f28,plain,
    ~ $less(sK1,$sum(1,sK0)),
    inference(forward_demodulation,[],[f24,f4]) ).

tff(f24,plain,
    ~ $less(sK1,$sum(sK0,1)),
    inference(unit_resulting_resolution,[],[f21,f15]) ).

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

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem    : NUM894=1 : TPTP v8.1.0. Released v5.0.0.
% 0.08/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 09:13:52 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.24/0.52  % (28267)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=41:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/41Mi)
% 1.24/0.53  % (28249)lrs+10_1:1_ep=R:gve=force:plsq=on:plsqr=32,1:uwa=one_side_interpreted:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.24/0.53  % (28243)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)
% 1.24/0.53  % (28243)First to succeed.
% 1.24/0.53  % (28243)Refutation found. Thanks to Tanya!
% 1.24/0.53  % SZS status Theorem for theBenchmark
% 1.24/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.24/0.53  % (28243)------------------------------
% 1.24/0.53  % (28243)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.24/0.53  % (28243)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.24/0.53  % (28243)Termination reason: Refutation
% 1.24/0.53  
% 1.24/0.53  % (28243)Memory used [KB]: 5500
% 1.24/0.53  % (28243)Time elapsed: 0.128 s
% 1.24/0.53  % (28243)Instructions burned: 2 (million)
% 1.24/0.53  % (28243)------------------------------
% 1.24/0.53  % (28243)------------------------------
% 1.24/0.53  % (28235)Success in time 0.172 s
%------------------------------------------------------------------------------