TSTP Solution File: SET974+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET974+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 : n019.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 18:26:14 EDT 2022

% Result   : Theorem 0.16s 0.49s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   49 (  13 unt;   0 def)
%            Number of atoms       :  117 (  10 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  111 (  43   ~;  29   |;  29   &)
%                                         (   2 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-5 aty)
%            Number of variables   :  113 (  91   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f99,plain,
    $false,
    inference(avatar_sat_refutation,[],[f67,f87,f98]) ).

fof(f98,plain,
    ~ spl9_1,
    inference(avatar_contradiction_clause,[],[f97]) ).

fof(f97,plain,
    ( $false
    | ~ spl9_1 ),
    inference(subsumption_resolution,[],[f96,f88]) ).

fof(f88,plain,
    ~ disjoint(sK2,sK4),
    inference(resolution,[],[f75,f55]) ).

fof(f55,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,set_intersection2(X1,X0))
      | ~ disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X1,X0)
        | ! [X2] : ~ in(X2,set_intersection2(X1,X0)) )
      & ( in(sK8(X0,X1),set_intersection2(X1,X0))
        | disjoint(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f22,f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ? [X3] : in(X3,set_intersection2(X1,X0))
     => in(sK8(X0,X1),set_intersection2(X1,X0)) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( ~ disjoint(X1,X0)
        | ! [X2] : ~ in(X2,set_intersection2(X1,X0)) )
      & ( ? [X3] : in(X3,set_intersection2(X1,X0))
        | disjoint(X1,X0) ) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ~ ( ~ disjoint(X1,X0)
          & ! [X3] : ~ in(X3,set_intersection2(X1,X0)) )
      & ~ ( disjoint(X1,X0)
          & ? [X2] : in(X2,set_intersection2(X1,X0)) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X1,X0] :
      ( ~ ( ? [X2] : in(X2,set_intersection2(X0,X1))
          & disjoint(X0,X1) )
      & ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
          & ~ disjoint(X0,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).

fof(f75,plain,
    in(sK6(sK2,sK1,sK3,sK4,sK8(cartesian_product2(sK3,sK2),cartesian_product2(sK1,sK4))),set_intersection2(sK2,sK4)),
    inference(forward_demodulation,[],[f72,f53]) ).

fof(f53,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,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(f72,plain,
    in(sK6(sK2,sK1,sK3,sK4,sK8(cartesian_product2(sK3,sK2),cartesian_product2(sK1,sK4))),set_intersection2(sK4,sK2)),
    inference(resolution,[],[f70,f47]) ).

fof(f47,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X0)))
      | in(sK6(X0,X1,X2,X3,X4),set_intersection2(X3,X0)) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( in(sK6(X0,X1,X2,X3,X4),set_intersection2(X3,X0))
        & ordered_pair(sK5(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) = X4
        & in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X2)) )
      | ~ in(X4,set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f32,f33]) ).

fof(f33,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X3,X0))
          & ordered_pair(X5,X6) = X4
          & in(X5,set_intersection2(X1,X2)) )
     => ( in(sK6(X0,X1,X2,X3,X4),set_intersection2(X3,X0))
        & ordered_pair(sK5(X0,X1,X2,X3,X4),sK6(X0,X1,X2,X3,X4)) = X4
        & in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f32,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X3,X0))
          & ordered_pair(X5,X6) = X4
          & in(X5,set_intersection2(X1,X2)) )
      | ~ in(X4,set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X0))) ),
    inference(rectify,[],[f24]) ).

fof(f24,plain,
    ! [X3,X2,X4,X1,X0] :
      ( ? [X5,X6] :
          ( in(X6,set_intersection2(X1,X3))
          & ordered_pair(X5,X6) = X0
          & in(X5,set_intersection2(X2,X4)) )
      | ~ in(X0,set_intersection2(cartesian_product2(X2,X1),cartesian_product2(X4,X3))) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X4,X1,X2,X3,X0] :
      ~ ( in(X0,set_intersection2(cartesian_product2(X2,X1),cartesian_product2(X4,X3)))
        & ! [X6,X5] :
            ~ ( in(X6,set_intersection2(X1,X3))
              & ordered_pair(X5,X6) = X0
              & in(X5,set_intersection2(X2,X4)) ) ),
    inference(rectify,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X2,X1,X4,X3] :
      ~ ( in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
        & ! [X5,X6] :
            ~ ( in(X6,set_intersection2(X2,X4))
              & ordered_pair(X5,X6) = X0
              & in(X5,set_intersection2(X1,X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).

fof(f70,plain,
    in(sK8(cartesian_product2(sK3,sK2),cartesian_product2(sK1,sK4)),set_intersection2(cartesian_product2(sK1,sK4),cartesian_product2(sK3,sK2))),
    inference(resolution,[],[f54,f44]) ).

fof(f44,plain,
    ~ disjoint(cartesian_product2(sK1,sK4),cartesian_product2(sK3,sK2)),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ~ disjoint(cartesian_product2(sK1,sK4),cartesian_product2(sK3,sK2))
    & ( disjoint(sK4,sK2)
      | disjoint(sK1,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1,X2,X3] :
        ( ~ disjoint(cartesian_product2(X0,X3),cartesian_product2(X2,X1))
        & ( disjoint(X3,X1)
          | disjoint(X0,X2) ) )
   => ( ~ disjoint(cartesian_product2(sK1,sK4),cartesian_product2(sK3,sK2))
      & ( disjoint(sK4,sK2)
        | disjoint(sK1,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1,X2,X3] :
      ( ~ disjoint(cartesian_product2(X0,X3),cartesian_product2(X2,X1))
      & ( disjoint(X3,X1)
        | disjoint(X0,X2) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ? [X1,X0,X3,X2] :
      ( ~ disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X0))
      & ( disjoint(X2,X0)
        | disjoint(X1,X3) ) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X1,X0,X3,X2] :
        ( ( disjoint(X2,X0)
          | disjoint(X1,X3) )
       => disjoint(cartesian_product2(X1,X2),cartesian_product2(X3,X0)) ),
    inference(rectify,[],[f12]) ).

fof(f12,negated_conjecture,
    ~ ! [X3,X0,X2,X1] :
        ( ( disjoint(X2,X3)
          | disjoint(X0,X1) )
       => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    inference(negated_conjecture,[],[f11]) ).

fof(f11,conjecture,
    ! [X3,X0,X2,X1] :
      ( ( disjoint(X2,X3)
        | disjoint(X0,X1) )
     => disjoint(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t127_zfmisc_1) ).

fof(f54,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | in(sK8(X0,X1),set_intersection2(X1,X0)) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f96,plain,
    ( disjoint(sK2,sK4)
    | ~ spl9_1 ),
    inference(resolution,[],[f62,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | disjoint(X1,X0) ),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1] :
      ( disjoint(X1,X0)
      | ~ disjoint(X0,X1) ),
    inference(rectify,[],[f23]) ).

fof(f23,plain,
    ! [X1,X0] :
      ( disjoint(X0,X1)
      | ~ disjoint(X1,X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X0] :
      ( disjoint(X1,X0)
     => disjoint(X0,X1) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X0] :
      ( disjoint(X0,X1)
     => disjoint(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).

fof(f62,plain,
    ( disjoint(sK4,sK2)
    | ~ spl9_1 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f60,plain,
    ( spl9_1
  <=> disjoint(sK4,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).

fof(f87,plain,
    ~ spl9_2,
    inference(avatar_contradiction_clause,[],[f86]) ).

fof(f86,plain,
    ( $false
    | ~ spl9_2 ),
    inference(subsumption_resolution,[],[f85,f66]) ).

fof(f66,plain,
    ( disjoint(sK1,sK3)
    | ~ spl9_2 ),
    inference(avatar_component_clause,[],[f64]) ).

fof(f64,plain,
    ( spl9_2
  <=> disjoint(sK1,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).

fof(f85,plain,
    ~ disjoint(sK1,sK3),
    inference(resolution,[],[f73,f55]) ).

fof(f73,plain,
    in(sK5(sK2,sK1,sK3,sK4,sK8(cartesian_product2(sK3,sK2),cartesian_product2(sK1,sK4))),set_intersection2(sK1,sK3)),
    inference(resolution,[],[f70,f45]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ in(X4,set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X0)))
      | in(sK5(X0,X1,X2,X3,X4),set_intersection2(X1,X2)) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f67,plain,
    ( spl9_1
    | spl9_2 ),
    inference(avatar_split_clause,[],[f43,f64,f60]) ).

fof(f43,plain,
    ( disjoint(sK1,sK3)
    | disjoint(sK4,sK2) ),
    inference(cnf_transformation,[],[f31]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10  % Problem    : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.11  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.10/0.31  % Computer : n019.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Tue Aug 30 14:36:05 EDT 2022
% 0.10/0.32  % CPUTime    : 
% 0.16/0.46  % (17698)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 (2999ds/75Mi)
% 0.16/0.47  % (17690)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.47  % (17694)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)
% 0.16/0.47  % (17689)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.16/0.47  % (17697)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)
% 0.16/0.48  % (17706)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)
% 0.16/0.48  % (17702)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)
% 0.16/0.48  % (17710)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.16/0.48  % (17690)Instruction limit reached!
% 0.16/0.48  % (17690)------------------------------
% 0.16/0.48  % (17690)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.48  % (17705)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)
% 0.16/0.48  % (17706)First to succeed.
% 0.16/0.49  % (17706)Refutation found. Thanks to Tanya!
% 0.16/0.49  % SZS status Theorem for theBenchmark
% 0.16/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.49  % (17706)------------------------------
% 0.16/0.49  % (17706)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.16/0.49  % (17706)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.16/0.49  % (17706)Termination reason: Refutation
% 0.16/0.49  
% 0.16/0.49  % (17706)Memory used [KB]: 5500
% 0.16/0.49  % (17706)Time elapsed: 0.121 s
% 0.16/0.49  % (17706)Instructions burned: 3 (million)
% 0.16/0.49  % (17706)------------------------------
% 0.16/0.49  % (17706)------------------------------
% 0.16/0.49  % (17682)Success in time 0.169 s
%------------------------------------------------------------------------------