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

% Computer : n013.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 17:27:31 EDT 2022

% Result   : Theorem 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   17 (   5 unt;   0 def)
%            Number of atoms       :   33 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   28 (  12   ~;   4   |;   6   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   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   :   30 (  21   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f36,plain,
    $false,
    inference(resolution,[],[f35,f31]) ).

fof(f31,plain,
    ~ leq(addition(sK0,sK2),addition(sK0,sK2)),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ( ~ leq(addition(sK0,sK2),addition(sK0,sK2))
    & leq(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f22,f23]) ).

fof(f23,plain,
    ( ? [X0,X1,X2] :
        ( ~ leq(addition(X0,X2),addition(X0,X2))
        & leq(X0,X1) )
   => ( ~ leq(addition(sK0,sK2),addition(sK0,sK2))
      & leq(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ? [X0,X1,X2] :
      ( ~ leq(addition(X0,X2),addition(X0,X2))
      & leq(X0,X1) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ? [X1,X0,X2] :
      ( ~ leq(addition(X1,X2),addition(X1,X2))
      & leq(X1,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X2,X1,X0] :
        ( leq(X1,X0)
       => leq(addition(X1,X2),addition(X1,X2)) ),
    inference(rectify,[],[f14]) ).

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

fof(f13,conjecture,
    ! [X4,X3,X5] :
      ( leq(X3,X4)
     => leq(addition(X3,X5),addition(X3,X5)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(f35,plain,
    ! [X0] : leq(X0,X0),
    inference(trivial_inequality_removal,[],[f32]) ).

fof(f32,plain,
    ! [X0] :
      ( leq(X0,X0)
      | X0 != X0 ),
    inference(superposition,[],[f28,f26]) ).

fof(f26,plain,
    ! [X0] : addition(X0,X0) = X0,
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0] : addition(X0,X0) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).

fof(f28,plain,
    ! [X0,X1] :
      ( addition(X1,X0) != X0
      | leq(X1,X0) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( addition(X1,X0) = X0
        | ~ leq(X1,X0) )
      & ( leq(X1,X0)
        | addition(X1,X0) != X0 ) ),
    inference(nnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( addition(X1,X0) = X0
    <=> leq(X1,X0) ),
    inference(rectify,[],[f12]) ).

fof(f12,axiom,
    ! [X1,X0] :
      ( leq(X0,X1)
    <=> addition(X0,X1) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : KLE001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n013.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % 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 00:17:32 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.51  % (2996)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.21/0.51  % (2978)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.21/0.51  % (2978)First to succeed.
% 0.21/0.51  % (2980)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.51  % (2978)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Theorem for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51  % (2978)------------------------------
% 0.21/0.51  % (2978)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (2978)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (2978)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (2978)Memory used [KB]: 5884
% 0.21/0.51  % (2978)Time elapsed: 0.104 s
% 0.21/0.51  % (2978)Instructions burned: 2 (million)
% 0.21/0.51  % (2978)------------------------------
% 0.21/0.51  % (2978)------------------------------
% 0.21/0.51  % (2973)Success in time 0.157 s
%------------------------------------------------------------------------------