%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 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 : n015.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 17:28:42 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   15 (   5 unt;   0 def)
%            Number of atoms       :   29 (   7 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   26 (  12   ~;   3   |;   6   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   26 (  17   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f55,plain,
    $false,
    inference(subsumption_resolution,[],[f53,f34]) ).

fof(f34,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f53,plain,
    addition(addition(sK1,sK2),addition(sK1,sK2)) != addition(sK1,sK2),
    inference(resolution,[],[f41,f36]) ).

fof(f36,plain,
    ~ leq(addition(sK1,sK2),addition(sK1,sK2)),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ( leq(sK1,sK0)
    & ~ leq(addition(sK1,sK2),addition(sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f25]) ).

fof(f25,plain,
    ( ? [X0,X1,X2] :
        ( leq(X1,X0)
        & ~ leq(addition(X1,X2),addition(X1,X2)) )
   => ( leq(sK1,sK0)
      & ~ leq(addition(sK1,sK2),addition(sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f24,plain,
    ? [X0,X1,X2] :
      ( leq(X1,X0)
      & ~ leq(addition(X1,X2),addition(X1,X2)) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ? [X0,X2,X1] :
      ( leq(X2,X0)
      & ~ leq(addition(X2,X1),addition(X2,X1)) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X0,X1,X2] :
        ( leq(X2,X0)
       => leq(addition(X2,X1),addition(X2,X1)) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X4,X5,X3] :
        ( leq(X3,X4)
       => leq(addition(X3,X5),addition(X3,X5)) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X4,X5,X3] :
      ( leq(X3,X4)
     => leq(addition(X3,X5),addition(X3,X5)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(f41,plain,
    ! [X0,X1] :
      ( leq(X0,X1)
      | addition(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ( leq(X0,X1)
        | addition(X0,X1) != X1 )
      & ( addition(X0,X1) = X1
        | ~ leq(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n015.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 00:32:50 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.46  % (3790)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.48  % (3803)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.48  % (3790)First to succeed.
% 0.20/0.48  % (3811)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.49  % (3790)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (3790)------------------------------
% 0.20/0.49  % (3790)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (3790)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (3790)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (3790)Memory used [KB]: 5373
% 0.20/0.49  % (3790)Time elapsed: 0.094 s
% 0.20/0.49  % (3790)Instructions burned: 2 (million)
% 0.20/0.49  % (3790)------------------------------
% 0.20/0.49  % (3790)------------------------------
% 0.20/0.49  % (3784)Success in time 0.131 s
%------------------------------------------------------------------------------