TSTP Solution File: SET891+1 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -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 : Sat Sep  2 00:03:27 EDT 2023

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   62 (  33 unt;   0 def)
%            Number of atoms       :   97 (  31 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   70 (  35   ~;  19   |;   0   &)
%                                         (  11 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   14 (  12 usr;  12 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   61 (;  53   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f100,plain,
    $false,
    inference(avatar_sat_refutation,[],[f36,f41,f46,f50,f54,f58,f64,f68,f76,f83,f96,f99]) ).

fof(f99,plain,
    ( ~ spl4_10
    | spl4_11 ),
    inference(avatar_contradiction_clause,[],[f98]) ).

fof(f98,plain,
    ( $false
    | ~ spl4_10
    | spl4_11 ),
    inference(trivial_inequality_removal,[],[f97]) ).

fof(f97,plain,
    ( unordered_pair(sK0,sK1) != unordered_pair(sK0,sK1)
    | ~ spl4_10
    | spl4_11 ),
    inference(superposition,[],[f95,f82]) ).

fof(f82,plain,
    ( ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1))
    | ~ spl4_10 ),
    inference(avatar_component_clause,[],[f81]) ).

fof(f81,plain,
    ( spl4_10
  <=> ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f95,plain,
    ( unordered_pair(sK0,sK1) != set_union2(singleton(sK0),singleton(sK1))
    | spl4_11 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f93,plain,
    ( spl4_11
  <=> unordered_pair(sK0,sK1) = set_union2(singleton(sK0),singleton(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f96,plain,
    ( ~ spl4_11
    | spl4_3
    | ~ spl4_9 ),
    inference(avatar_split_clause,[],[f79,f74,f43,f93]) ).

fof(f43,plain,
    ( spl4_3
  <=> unordered_pair(sK0,sK1) = union(unordered_pair(singleton(sK0),singleton(sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f74,plain,
    ( spl4_9
  <=> ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f79,plain,
    ( unordered_pair(sK0,sK1) != set_union2(singleton(sK0),singleton(sK1))
    | spl4_3
    | ~ spl4_9 ),
    inference(superposition,[],[f45,f75]) ).

fof(f75,plain,
    ( ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1))
    | ~ spl4_9 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f45,plain,
    ( unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1)))
    | spl4_3 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f83,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f27,f81]) ).

fof(f27,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    inference(cnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = set_union2(singleton(X0),singleton(X1)),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',t41_enumset1) ).

fof(f76,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f26,f74]) ).

fof(f26,plain,
    ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : set_union2(X0,X1) = union(unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',l52_zfmisc_1) ).

fof(f68,plain,
    spl4_8,
    inference(avatar_split_clause,[],[f25,f66]) ).

fof(f66,plain,
    ( spl4_8
  <=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f25,plain,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',commutativity_k2_xboole_0) ).

fof(f64,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f24,f62]) ).

fof(f62,plain,
    ( spl4_7
  <=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f24,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',commutativity_k2_tarski) ).

fof(f58,plain,
    spl4_6,
    inference(avatar_split_clause,[],[f29,f56]) ).

fof(f56,plain,
    ( spl4_6
  <=> ! [X0,X1] :
        ( ~ empty(set_union2(X0,X1))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f29,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X0,X1))
      | empty(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X0,X1))
      | empty(X0) ),
    inference(ennf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ~ empty(X0)
     => ~ empty(set_union2(X0,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',fc2_xboole_0) ).

fof(f54,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f28,f52]) ).

fof(f52,plain,
    ( spl4_5
  <=> ! [X0,X1] :
        ( ~ empty(set_union2(X1,X0))
        | empty(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X1,X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ~ empty(set_union2(X1,X0))
      | empty(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ~ empty(X0)
     => ~ empty(set_union2(X1,X0)) ),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',fc3_xboole_0) ).

fof(f50,plain,
    spl4_4,
    inference(avatar_split_clause,[],[f23,f48]) ).

fof(f48,plain,
    ( spl4_4
  <=> ! [X0] : set_union2(X0,X0) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f23,plain,
    ! [X0] : set_union2(X0,X0) = X0,
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0] : set_union2(X0,X0) = X0,
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] : set_union2(X0,X0) = X0,
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',idempotence_k2_xboole_0) ).

fof(f46,plain,
    ~ spl4_3,
    inference(avatar_split_clause,[],[f22,f43]) ).

fof(f22,plain,
    unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).

fof(f16,plain,
    ( ? [X0,X1] : unordered_pair(X0,X1) != union(unordered_pair(singleton(X0),singleton(X1)))
   => unordered_pair(sK0,sK1) != union(unordered_pair(singleton(sK0),singleton(sK1))) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] : unordered_pair(X0,X1) != union(unordered_pair(singleton(X0),singleton(X1))),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] : unordered_pair(X0,X1) = union(unordered_pair(singleton(X0),singleton(X1))),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] : unordered_pair(X0,X1) = union(unordered_pair(singleton(X0),singleton(X1))),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',t32_zfmisc_1) ).

fof(f41,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f31,f38]) ).

fof(f38,plain,
    ( spl4_2
  <=> empty(sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f31,plain,
    empty(sK3),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    empty(sK3),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f7,f20]) ).

fof(f20,plain,
    ( ? [X0] : empty(X0)
   => empty(sK3) ),
    introduced(choice_axiom,[]) ).

fof(f7,axiom,
    ? [X0] : empty(X0),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',rc1_xboole_0) ).

fof(f36,plain,
    ~ spl4_1,
    inference(avatar_split_clause,[],[f30,f33]) ).

fof(f33,plain,
    ( spl4_1
  <=> empty(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f30,plain,
    ~ empty(sK2),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ empty(sK2),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f8,f18]) ).

fof(f18,plain,
    ( ? [X0] : ~ empty(X0)
   => ~ empty(sK2) ),
    introduced(choice_axiom,[]) ).

fof(f8,axiom,
    ? [X0] : ~ empty(X0),
    file('/export/starexec/sandbox/tmp/tmp.HNtXslnbzq/Vampire---4.8_2715',rc2_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SET891+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.35  % Computer : n015.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Wed Aug 30 16:02:12 EDT 2023
% 0.16/0.35  % CPUTime    : 
% 0.21/0.41  % (2932)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (2947)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.21/0.41  % (2939)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.41  % (2941)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.41  % (2942)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.21/0.41  % (2946)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.41  % (2949)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.21/0.41  % (2950)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.21/0.41  % (2947)First to succeed.
% 0.21/0.41  TRYING [1]
% 0.21/0.41  TRYING [2]
% 0.21/0.41  % (2947)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for Vampire---4
% 0.21/0.41  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.41  % (2947)------------------------------
% 0.21/0.41  % (2947)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.41  % (2947)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.41  % (2947)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (2947)Memory used [KB]: 5373
% 0.21/0.41  % (2947)Time elapsed: 0.003 s
% 0.21/0.41  % (2947)------------------------------
% 0.21/0.41  % (2947)------------------------------
% 0.21/0.41  % (2932)Success in time 0.06 s
% 0.21/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------