%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET971+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 : n013.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 18:22:54 EDT 2022

% Result   : Theorem 0.21s 0.58s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  21 unt;   0 def)
%            Number of atoms       :   54 (  30 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   38 (  16   ~;   2   |;  15   &)
%                                         (   0 <=>;   5  =>;   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    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   58 (  42   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f49,plain,
    $false,
    inference(trivial_inequality_removal,[],[f48]) ).

fof(f48,plain,
    cartesian_product2(sK3,sK5) != cartesian_product2(sK3,sK5),
    inference(backward_demodulation,[],[f46,f47]) ).

fof(f47,plain,
    set_intersection2(sK4,sK3) = sK3,
    inference(forward_demodulation,[],[f42,f32]) ).

fof(f32,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(rectify,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f42,plain,
    set_intersection2(sK3,sK4) = sK3,
    inference(resolution,[],[f34,f36]) ).

fof(f36,plain,
    subset(sK3,sK4),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( set_intersection2(cartesian_product2(sK3,sK2),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5)
    & subset(sK5,sK2)
    & subset(sK3,sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f26,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2,X3] :
        ( cartesian_product2(X1,X3) != set_intersection2(cartesian_product2(X1,X0),cartesian_product2(X2,X3))
        & subset(X3,X0)
        & subset(X1,X2) )
   => ( set_intersection2(cartesian_product2(sK3,sK2),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5)
      & subset(sK5,sK2)
      & subset(sK3,sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f26,plain,
    ? [X0,X1,X2,X3] :
      ( cartesian_product2(X1,X3) != set_intersection2(cartesian_product2(X1,X0),cartesian_product2(X2,X3))
      & subset(X3,X0)
      & subset(X1,X2) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X3,X0,X2] :
      ( cartesian_product2(X3,X2) != set_intersection2(cartesian_product2(X3,X1),cartesian_product2(X0,X2))
      & subset(X2,X1)
      & subset(X3,X0) ),
    inference(flattening,[],[f16]) ).

fof(f16,plain,
    ? [X2,X0,X3,X1] :
      ( cartesian_product2(X3,X2) != set_intersection2(cartesian_product2(X3,X1),cartesian_product2(X0,X2))
      & subset(X2,X1)
      & subset(X3,X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ~ ! [X2,X0,X3,X1] :
        ( ( subset(X2,X1)
          & subset(X3,X0) )
       => cartesian_product2(X3,X2) = set_intersection2(cartesian_product2(X3,X1),cartesian_product2(X0,X2)) ),
    inference(rectify,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X3,X2,X0] :
        ( ( subset(X2,X3)
          & subset(X0,X1) )
       => cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X3,X2,X0] :
      ( ( subset(X2,X3)
        & subset(X0,X1) )
     => cartesian_product2(X0,X2) = set_intersection2(cartesian_product2(X0,X3),cartesian_product2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t124_zfmisc_1) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_intersection2(X0,X1) = X0 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,X1) = X0
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f46,plain,
    cartesian_product2(set_intersection2(sK4,sK3),sK5) != cartesian_product2(sK3,sK5),
    inference(backward_demodulation,[],[f41,f45]) ).

fof(f45,plain,
    sK5 = set_intersection2(sK2,sK5),
    inference(forward_demodulation,[],[f43,f32]) ).

fof(f43,plain,
    sK5 = set_intersection2(sK5,sK2),
    inference(resolution,[],[f34,f37]) ).

fof(f37,plain,
    subset(sK5,sK2),
    inference(cnf_transformation,[],[f28]) ).

fof(f41,plain,
    cartesian_product2(set_intersection2(sK4,sK3),set_intersection2(sK2,sK5)) != cartesian_product2(sK3,sK5),
    inference(forward_demodulation,[],[f40,f32]) ).

fof(f40,plain,
    cartesian_product2(set_intersection2(sK4,sK3),set_intersection2(sK5,sK2)) != cartesian_product2(sK3,sK5),
    inference(backward_demodulation,[],[f39,f35]) ).

fof(f35,plain,
    ! [X2,X3,X0,X1] : cartesian_product2(set_intersection2(X0,X3),set_intersection2(X2,X1)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X3,X1)),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X3),set_intersection2(X2,X1)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X3,X1)),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X1,X3,X0,X2] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X0,X3)) = set_intersection2(cartesian_product2(X1,X0),cartesian_product2(X2,X3)),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2,X0,X1,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).

fof(f39,plain,
    cartesian_product2(sK3,sK5) != set_intersection2(cartesian_product2(sK4,sK5),cartesian_product2(sK3,sK2)),
    inference(forward_demodulation,[],[f38,f32]) ).

fof(f38,plain,
    set_intersection2(cartesian_product2(sK3,sK2),cartesian_product2(sK4,sK5)) != cartesian_product2(sK3,sK5),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET971+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_uns --cores 0 -t %d %s
% 0.15/0.35  % Computer : n013.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Tue Aug 30 14:29:17 EDT 2022
% 0.15/0.35  % CPUTime    : 
% 0.21/0.56  % (30220)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.21/0.56  % (30199)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.21/0.57  % (30214)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.57  % (30205)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.57  % (30212)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.57  % (30205)First to succeed.
% 0.21/0.57  % (30195)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)
% 0.21/0.58  % (30214)Also succeeded, but the first one will report.
% 0.21/0.58  % (30197)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.58  % (30205)Refutation found. Thanks to Tanya!
% 0.21/0.58  % SZS status Theorem for theBenchmark
% 0.21/0.58  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.58  % (30205)------------------------------
% 0.21/0.58  % (30205)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.58  % (30205)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.58  % (30205)Termination reason: Refutation
% 0.21/0.58  
% 0.21/0.58  % (30205)Memory used [KB]: 5884
% 0.21/0.58  % (30205)Time elapsed: 0.080 s
% 0.21/0.58  % (30205)Instructions burned: 2 (million)
% 0.21/0.58  % (30205)------------------------------
% 0.21/0.58  % (30205)------------------------------
% 0.21/0.58  % (30189)Success in time 0.221 s
%------------------------------------------------------------------------------