%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 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 : n018.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 18:56:00 EDT 2022

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   12 (  10 unt;   0 def)
%            Number of atoms       :   15 (   8 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    9 (   6   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   14 (  14   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f12,plain,
    $false,
    inference(trivial_inequality_removal,[],[f11]) ).

fof(f11,plain,
    c_emptyset != c_emptyset,
    inference(superposition,[],[f10,f9]) ).

fof(f9,plain,
    ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(v_nat,X0,tc_nat),
    inference(resolution,[],[f8,f7]) ).

fof(f7,plain,
    ! [X5] : c_lessequals(X5,v_nat,tc_nat),
    inference(definition_unfolding,[],[f4,f5]) ).

fof(f5,axiom,
    ! [X5] : v_x(X5) = v_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f4,axiom,
    ! [X5] : c_lessequals(X5,v_x(X5),tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ~ c_lessequals(X1,X0,tc_nat)
      | c_emptyset = c_SetInterval_OatLeastLessThan(X0,X1,tc_nat) ),
    inference(resolution,[],[f6,f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Orderings_Oorder(X0)
      | c_SetInterval_OatLeastLessThan(X2,X1,X0) = c_emptyset
      | ~ c_lessequals(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).

fof(f6,axiom,
    class_Orderings_Oorder(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).

fof(f10,plain,
    ! [X0] : c_emptyset != c_SetInterval_OatLeastLessThan(X0,c_Suc(X0),tc_nat),
    inference(superposition,[],[f3,f2]) ).

fof(f2,axiom,
    ! [X2] : c_SetInterval_OatLeastLessThan(X2,c_Suc(X2),tc_nat) = c_insert(X2,c_emptyset,tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).

fof(f3,axiom,
    ! [X3,X0,X4] : c_emptyset != c_insert(X3,X4,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem    : SWV254-2 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n018.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 19:13:25 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.45  % (7752)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.19/0.45  % (7752)First to succeed.
% 0.19/0.45  % (7744)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.19/0.46  % (7744)Also succeeded, but the first one will report.
% 0.19/0.46  % (7752)Refutation found. Thanks to Tanya!
% 0.19/0.46  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46  % (7752)------------------------------
% 0.19/0.46  % (7752)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.46  % (7752)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.46  % (7752)Termination reason: Refutation
% 0.19/0.46  
% 0.19/0.46  % (7752)Memory used [KB]: 5373
% 0.19/0.46  % (7752)Time elapsed: 0.055 s
% 0.19/0.46  % (7752)Instructions burned: 2 (million)
% 0.19/0.46  % (7752)------------------------------
% 0.19/0.46  % (7752)------------------------------
% 0.19/0.46  % (7728)Success in time 0.12 s
%------------------------------------------------------------------------------