%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 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 : n021.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 18:23:00 EDT 2022

% Result   : Unsatisfiable 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   30 (   8 unt;   0 def)
%            Number of atoms       :   59 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   49 (  20   ~;  26   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   4 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   19 (  19   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f65,plain,
    $false,
    inference(avatar_sat_refutation,[],[f45,f58,f60,f64]) ).

fof(f64,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f61]) ).

fof(f61,plain,
    ( $false
    | ~ spl0_4 ),
    inference(resolution,[],[f57,f14]) ).

fof(f14,axiom,
    ~ equal_sets(aUa,a),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_aUa) ).

fof(f57,plain,
    ( equal_sets(aUa,a)
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f55,plain,
    ( spl0_4
  <=> equal_sets(aUa,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f60,plain,
    spl0_3,
    inference(avatar_contradiction_clause,[],[f59]) ).

fof(f59,plain,
    ( $false
    | spl0_3 ),
    inference(resolution,[],[f53,f25]) ).

fof(f25,plain,
    subset(a,aUa),
    inference(duplicate_literal_removal,[],[f24]) ).

fof(f24,plain,
    ( subset(a,aUa)
    | subset(a,aUa) ),
    inference(resolution,[],[f23,f3]) ).

fof(f3,axiom,
    ! [X2,X1] :
      ( ~ member(member_of_1_not_of_2(X1,X2),X2)
      | subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom2) ).

fof(f23,plain,
    ! [X0] :
      ( member(member_of_1_not_of_2(a,X0),aUa)
      | subset(a,X0) ),
    inference(resolution,[],[f22,f2]) ).

fof(f2,axiom,
    ! [X2,X1] :
      ( member(member_of_1_not_of_2(X1,X2),X1)
      | subset(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_axiom1) ).

fof(f22,plain,
    ! [X0] :
      ( ~ member(X0,a)
      | member(X0,aUa) ),
    inference(resolution,[],[f8,f13]) ).

fof(f13,axiom,
    union(a,a,aUa),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).

fof(f8,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ union(X3,X4,X5)
      | ~ member(X0,X3)
      | member(X0,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_set1_is_member_of_union) ).

fof(f53,plain,
    ( ~ subset(a,aUa)
    | spl0_3 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f51,plain,
    ( spl0_3
  <=> subset(a,aUa) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f58,plain,
    ( ~ spl0_3
    | spl0_4
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f48,f33,f55,f51]) ).

fof(f33,plain,
    ( spl0_2
  <=> subset(aUa,a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f48,plain,
    ( equal_sets(aUa,a)
    | ~ subset(a,aUa)
    | ~ spl0_2 ),
    inference(resolution,[],[f34,f6]) ).

fof(f6,axiom,
    ! [X3,X4] :
      ( ~ subset(X4,X3)
      | equal_sets(X4,X3)
      | ~ subset(X3,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsets_are_set_equal_sets) ).

fof(f34,plain,
    ( subset(aUa,a)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f33]) ).

fof(f45,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f44,f33]) ).

fof(f44,plain,
    subset(aUa,a),
    inference(duplicate_literal_removal,[],[f42]) ).

fof(f42,plain,
    ( subset(aUa,a)
    | subset(aUa,a) ),
    inference(resolution,[],[f41,f3]) ).

fof(f41,plain,
    ! [X1] :
      ( member(member_of_1_not_of_2(aUa,X1),a)
      | subset(aUa,X1) ),
    inference(resolution,[],[f39,f2]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ member(X0,aUa)
      | member(X0,a) ),
    inference(duplicate_literal_removal,[],[f38]) ).

fof(f38,plain,
    ! [X0] :
      ( member(X0,a)
      | member(X0,a)
      | ~ member(X0,aUa) ),
    inference(resolution,[],[f7,f13]) ).

fof(f7,axiom,
    ! [X3,X0,X4,X5] :
      ( ~ union(X3,X4,X5)
      | member(X0,X3)
      | ~ member(X0,X5)
      | member(X0,X4) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_union_is_member_of_one_set) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 12:46:26 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.49  % (6902)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.49  % (6894)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (6904)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50  % (6902)First to succeed.
% 0.20/0.50  % (6902)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (6902)------------------------------
% 0.20/0.50  % (6902)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (6902)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (6902)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (6902)Memory used [KB]: 5373
% 0.20/0.50  % (6902)Time elapsed: 0.104 s
% 0.20/0.50  % (6902)Instructions burned: 2 (million)
% 0.20/0.50  % (6902)------------------------------
% 0.20/0.50  % (6902)------------------------------
% 0.20/0.50  % (6885)Success in time 0.158 s
%------------------------------------------------------------------------------