%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET912+1 : 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_uns --cores 0 -t %d %s

% Computer : n012.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 18:22:43 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   32 (  13 unt;   0 def)
%            Number of atoms       :   77 (  25 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   73 (  28   ~;  17   |;  22   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   59 (  47   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f76,plain,
    $false,
    inference(subsumption_resolution,[],[f74,f44]) ).

fof(f44,plain,
    unordered_pair(sK1,sK2) != set_intersection2(sK0,unordered_pair(sK1,sK2)),
    inference(superposition,[],[f41,f32]) ).

fof(f32,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f41,plain,
    set_intersection2(unordered_pair(sK1,sK2),sK0) != unordered_pair(sK1,sK2),
    inference(backward_demodulation,[],[f36,f34]) ).

fof(f34,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f36,plain,
    unordered_pair(sK2,sK1) != set_intersection2(unordered_pair(sK2,sK1),sK0),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ( in(sK1,sK0)
    & unordered_pair(sK2,sK1) != set_intersection2(unordered_pair(sK2,sK1),sK0)
    & in(sK2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f23,f24]) ).

fof(f24,plain,
    ( ? [X0,X1,X2] :
        ( in(X1,X0)
        & set_intersection2(unordered_pair(X2,X1),X0) != unordered_pair(X2,X1)
        & in(X2,X0) )
   => ( in(sK1,sK0)
      & unordered_pair(sK2,sK1) != set_intersection2(unordered_pair(sK2,sK1),sK0)
      & in(sK2,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ? [X0,X1,X2] :
      ( in(X1,X0)
      & set_intersection2(unordered_pair(X2,X1),X0) != unordered_pair(X2,X1)
      & in(X2,X0) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X0,X2] :
      ( in(X0,X1)
      & set_intersection2(unordered_pair(X2,X0),X1) != unordered_pair(X2,X0)
      & in(X2,X1) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X2,X1,X0] :
      ( set_intersection2(unordered_pair(X2,X0),X1) != unordered_pair(X2,X0)
      & in(X2,X1)
      & in(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ~ ! [X2,X1,X0] :
        ( ( in(X2,X1)
          & in(X0,X1) )
       => set_intersection2(unordered_pair(X2,X0),X1) = unordered_pair(X2,X0) ),
    inference(rectify,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( ( in(X0,X1)
          & in(X2,X1) )
       => unordered_pair(X0,X2) = set_intersection2(unordered_pair(X0,X2),X1) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X2,X1,X0] :
      ( ( in(X0,X1)
        & in(X2,X1) )
     => unordered_pair(X0,X2) = set_intersection2(unordered_pair(X0,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_zfmisc_1) ).

fof(f74,plain,
    unordered_pair(sK1,sK2) = set_intersection2(sK0,unordered_pair(sK1,sK2)),
    inference(resolution,[],[f72,f35]) ).

fof(f35,plain,
    in(sK2,sK0),
    inference(cnf_transformation,[],[f25]) ).

fof(f72,plain,
    ! [X1] :
      ( ~ in(X1,sK0)
      | set_intersection2(sK0,unordered_pair(sK1,X1)) = unordered_pair(sK1,X1) ),
    inference(forward_demodulation,[],[f69,f32]) ).

fof(f69,plain,
    ! [X1] :
      ( ~ in(X1,sK0)
      | set_intersection2(unordered_pair(sK1,X1),sK0) = unordered_pair(sK1,X1) ),
    inference(resolution,[],[f65,f37]) ).

fof(f37,plain,
    in(sK1,sK0),
    inference(cnf_transformation,[],[f25]) ).

fof(f65,plain,
    ! [X8,X6,X7] :
      ( ~ in(X8,X7)
      | unordered_pair(X8,X6) = set_intersection2(unordered_pair(X8,X6),X7)
      | ~ in(X6,X7) ),
    inference(resolution,[],[f38,f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X1,X0),X2)
      | ~ in(X0,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X1,X0),X2) )
      & ( subset(unordered_pair(X1,X0),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,plain,
    ! [X1,X0,X2] :
      ( ( ( in(X0,X2)
          & in(X1,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) )
      & ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X0,X2)
        | ~ in(X1,X2) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X1,X0,X2] :
      ( ( ( in(X0,X2)
          & in(X1,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) )
      & ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X0,X2)
        | ~ in(X1,X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0,X2] :
      ( ( in(X0,X2)
        & in(X1,X2) )
    <=> subset(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t38_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET912+1 : TPTP v8.1.0. Released v3.2.0.
% 0.13/0.13  % 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 : n012.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 14:39:50 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.54  % (4456)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55  % (4442)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)
% 0.20/0.55  % (4442)First to succeed.
% 0.20/0.56  % (4450)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.56  % (4443)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.20/0.56  % (4443)Refutation not found, incomplete strategy% (4443)------------------------------
% 0.20/0.56  % (4443)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (4443)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (4443)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.56  
% 0.20/0.56  % (4443)Memory used [KB]: 1407
% 0.20/0.56  % (4443)Time elapsed: 0.143 s
% 0.20/0.56  % (4443)Instructions burned: 2 (million)
% 0.20/0.56  % (4443)------------------------------
% 0.20/0.56  % (4443)------------------------------
% 0.20/0.56  % (4442)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (4442)------------------------------
% 0.20/0.56  % (4442)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (4442)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (4442)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (4442)Memory used [KB]: 5884
% 0.20/0.56  % (4442)Time elapsed: 0.135 s
% 0.20/0.56  % (4442)Instructions burned: 3 (million)
% 0.20/0.56  % (4442)------------------------------
% 0.20/0.56  % (4442)------------------------------
% 0.20/0.56  % (4437)Success in time 0.208 s
%------------------------------------------------------------------------------