%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% 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 : n005.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 18:32:03 EDT 2022

% Result   : Theorem 0.19s 0.52s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   41 (  26 unt;   0 def)
%            Number of atoms       :   58 (  26 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   31 (  14   ~;   5   |;   5   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   56 (  50   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f426,plain,
    $false,
    inference(subsumption_resolution,[],[f425,f187]) ).

fof(f187,plain,
    sF10 != sK5,
    inference(definition_folding,[],[f157,f186]) ).

fof(f186,plain,
    sF10 = set_intersection2(sK5,sK6),
    introduced(function_definition,[]) ).

fof(f157,plain,
    set_intersection2(sK5,sK6) != sK5,
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ( set_intersection2(sK5,sK6) != sK5
    & subset(sK5,sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f102,f103]) ).

fof(f103,plain,
    ( ? [X0,X1] :
        ( set_intersection2(X0,X1) != X0
        & subset(X0,X1) )
   => ( set_intersection2(sK5,sK6) != sK5
      & subset(sK5,sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ? [X0,X1] :
      ( set_intersection2(X0,X1) != X0
      & subset(X0,X1) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ? [X1,X0] :
      ( set_intersection2(X1,X0) != X1
      & subset(X1,X0) ),
    inference(ennf_transformation,[],[f56]) ).

fof(f56,plain,
    ~ ! [X1,X0] :
        ( subset(X1,X0)
       => set_intersection2(X1,X0) = X1 ),
    inference(rectify,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X1,X0] :
        ( subset(X0,X1)
       => set_intersection2(X0,X1) = X0 ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X1,X0] :
      ( subset(X0,X1)
     => set_intersection2(X0,X1) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_xboole_1) ).

fof(f425,plain,
    sF10 = sK5,
    inference(backward_demodulation,[],[f320,f401]) ).

fof(f401,plain,
    set_union2(sK5,sF10) = sK5,
    inference(superposition,[],[f158,f235]) ).

fof(f235,plain,
    set_union2(sF10,sK5) = sK5,
    inference(resolution,[],[f220,f140]) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | set_union2(X0,X1) = X1 ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
     => set_union2(X0,X1) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).

fof(f220,plain,
    subset(sF10,sK5),
    inference(superposition,[],[f142,f186]) ).

fof(f142,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0,X1] : subset(set_intersection2(X0,X1),X0),
    inference(rectify,[],[f41]) ).

fof(f41,plain,
    ! [X1,X0] : subset(set_intersection2(X1,X0),X1),
    inference(rectify,[],[f23]) ).

fof(f23,axiom,
    ! [X1,X0] : subset(set_intersection2(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).

fof(f158,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/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

fof(f320,plain,
    set_union2(sK5,sF10) = sF10,
    inference(resolution,[],[f308,f140]) ).

fof(f308,plain,
    subset(sK5,sF10),
    inference(forward_demodulation,[],[f307,f186]) ).

fof(f307,plain,
    subset(sK5,set_intersection2(sK5,sK6)),
    inference(forward_demodulation,[],[f301,f141]) ).

fof(f141,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,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(f301,plain,
    subset(sK5,set_intersection2(sK6,sK5)),
    inference(superposition,[],[f243,f135]) ).

fof(f135,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(cnf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0] : set_intersection2(X0,X0) = X0,
    inference(rectify,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1] : set_intersection2(X0,X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).

fof(f243,plain,
    ! [X10] : subset(set_intersection2(sK5,X10),set_intersection2(sK6,X10)),
    inference(resolution,[],[f127,f156]) ).

fof(f156,plain,
    subset(sK5,sK6),
    inference(cnf_transformation,[],[f104]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X1,X0)
      | subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) ),
    inference(cnf_transformation,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ~ subset(X1,X0)
      | subset(set_intersection2(X1,X2),set_intersection2(X0,X2)) ),
    inference(rectify,[],[f65]) ).

fof(f65,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X2)
      | subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X2,X1] :
      ( subset(X0,X2)
     => subset(set_intersection2(X0,X1),set_intersection2(X2,X1)) ),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ! [X0,X2,X1] :
      ( subset(X0,X1)
     => subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_xboole_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU130+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n005.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 14:41:03 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (30713)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)
% 0.19/0.49  % (30695)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (30695)First to succeed.
% 0.19/0.51  % (30702)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)
% 0.19/0.52  % (30691)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.52  % (30705)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)
% 0.19/0.52  % (30720)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.52  % (30692)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52  % (30693)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52  % (30695)Refutation found. Thanks to Tanya!
% 0.19/0.52  % SZS status Theorem for theBenchmark
% 0.19/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.52  % (30695)------------------------------
% 0.19/0.52  % (30695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (30695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (30695)Termination reason: Refutation
% 0.19/0.52  
% 0.19/0.52  % (30695)Memory used [KB]: 5628
% 0.19/0.52  % (30695)Time elapsed: 0.111 s
% 0.19/0.52  % (30695)Instructions burned: 13 (million)
% 0.19/0.52  % (30695)------------------------------
% 0.19/0.52  % (30695)------------------------------
% 0.19/0.52  % (30690)Success in time 0.176 s
%------------------------------------------------------------------------------