%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET920+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_sat --cores 0 -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 : Wed Aug 31 18:26:06 EDT 2022

% Result   : Theorem 0.20s 0.53s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   23 (  10 unt;   0 def)
%            Number of atoms       :   46 (  21 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   34 (  11   ~;   9   |;   3   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   45 (  42   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f87,plain,
    $false,
    inference(resolution,[],[f85,f21]) ).

fof(f21,plain,
    ~ in(sK2,sK0),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ? [X0,X1,X2] :
      ( unordered_pair(X2,X1) = set_intersection2(unordered_pair(X2,X1),X0)
      & ~ in(X2,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X2,X0,X1] :
        ( unordered_pair(X2,X1) = set_intersection2(unordered_pair(X2,X1),X0)
       => in(X2,X0) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X2,X1,X0] :
        ( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
       => in(X0,X2) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X2,X1,X0] :
      ( unordered_pair(X0,X1) = set_intersection2(unordered_pair(X0,X1),X2)
     => in(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_zfmisc_1) ).

fof(f85,plain,
    in(sK2,sK0),
    inference(resolution,[],[f79,f52]) ).

fof(f52,plain,
    in(sK2,sF7),
    inference(superposition,[],[f40,f47]) ).

fof(f47,plain,
    sF7 = unordered_pair(sK2,sK1),
    introduced(function_definition,[]) ).

fof(f40,plain,
    ! [X2,X3] : in(X3,unordered_pair(X3,X2)),
    inference(equality_resolution,[],[f39]) ).

fof(f39,plain,
    ! [X2,X3,X1] :
      ( in(X3,X1)
      | unordered_pair(X3,X2) != X1 ),
    inference(equality_resolution,[],[f31]) ).

fof(f31,plain,
    ! [X2,X3,X0,X1] :
      ( X0 != X3
      | in(X3,X1)
      | unordered_pair(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X2) = X1
    <=> ! [X3] :
          ( in(X3,X1)
        <=> ( X0 = X3
            | X2 = X3 ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X2,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f79,plain,
    ! [X0] :
      ( ~ in(X0,sF7)
      | in(X0,sK0) ),
    inference(superposition,[],[f45,f50]) ).

fof(f50,plain,
    sF7 = set_intersection2(sF7,sK0),
    inference(forward_demodulation,[],[f48,f49]) ).

fof(f49,plain,
    sF8 = sF7,
    inference(definition_folding,[],[f22,f48,f47,f47]) ).

fof(f22,plain,
    unordered_pair(sK2,sK1) = set_intersection2(unordered_pair(sK2,sK1),sK0),
    inference(cnf_transformation,[],[f17]) ).

fof(f48,plain,
    sF8 = set_intersection2(sF7,sK0),
    introduced(function_definition,[]) ).

fof(f45,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,set_intersection2(X2,X0))
      | in(X3,X0) ),
    inference(equality_resolution,[],[f36]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | ~ in(X3,X1)
      | set_intersection2(X2,X0) != X1 ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1,X2] :
      ( set_intersection2(X2,X0) = X1
    <=> ! [X3] :
          ( in(X3,X1)
        <=> ( in(X3,X0)
            & in(X3,X2) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X2,X0] :
      ( set_intersection2(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( in(X3,X1)
            & in(X3,X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET920+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 14:41:51 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.52  % (24392)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53  % (24376)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)
% 0.20/0.53  % (24399)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53  % (24395)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53  % (24377)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (24376)First to succeed.
% 0.20/0.53  % (24396)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 (2999ds/467Mi)
% 0.20/0.53  % (24376)Refutation found. Thanks to Tanya!
% 0.20/0.53  % SZS status Theorem for theBenchmark
% 0.20/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.53  % (24376)------------------------------
% 0.20/0.53  % (24376)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53  % (24376)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53  % (24376)Termination reason: Refutation
% 0.20/0.53  
% 0.20/0.53  % (24376)Memory used [KB]: 5373
% 0.20/0.53  % (24376)Time elapsed: 0.118 s
% 0.20/0.53  % (24376)Instructions burned: 3 (million)
% 0.20/0.53  % (24376)------------------------------
% 0.20/0.53  % (24376)------------------------------
% 0.20/0.53  % (24372)Success in time 0.177 s
%------------------------------------------------------------------------------