TSTP Solution File: SET175+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n024.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 18:19:39 EDT 2022

% Result   : Theorem 0.17s 0.49s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   39 (  13 unt;   0 def)
%            Number of atoms       :  128 (  19 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  145 (  56   ~;  57   |;  24   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   75 (  66   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f100,plain,
    $false,
    inference(subsumption_resolution,[],[f98,f86]) ).

fof(f86,plain,
    ~ member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1),
    inference(subsumption_resolution,[],[f84,f48]) ).

fof(f48,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f28]) ).

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

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

fof(f26,plain,
    ! [X1,X0,X2] :
      ( ( member(X2,X0)
        | member(X2,X1)
        | ~ member(X2,union(X1,X0)) )
      & ( member(X2,union(X1,X0))
        | ( ~ member(X2,X0)
          & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X1,X0,X2] :
      ( ( member(X2,X0)
        | member(X2,X1) )
    <=> member(X2,union(X1,X0)) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X1,X0,X2] :
      ( ( member(X2,X1)
        | member(X2,X0) )
    <=> member(X2,union(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).

fof(f84,plain,
    ( ~ member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1)
    | ~ member(sK0(union(sK1,intersection(sK1,sK2)),sK1),union(sK1,intersection(sK1,sK2))) ),
    inference(resolution,[],[f61,f66]) ).

fof(f66,plain,
    ~ sQ4_eqProxy(union(sK1,intersection(sK1,sK2)),sK1),
    inference(equality_proxy_replacement,[],[f52,f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

fof(f52,plain,
    union(sK1,intersection(sK1,sK2)) != sK1,
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    union(sK1,intersection(sK1,sK2)) != sK1,
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] : union(X0,intersection(X0,X1)) != X0
   => union(sK1,intersection(sK1,sK2)) != sK1 ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1] : union(X0,intersection(X0,X1)) != X0,
    inference(rectify,[],[f16]) ).

fof(f16,plain,
    ? [X1,X0] : union(X1,intersection(X1,X0)) != X1,
    inference(ennf_transformation,[],[f14]) ).

fof(f14,plain,
    ~ ! [X0,X1] : union(X1,intersection(X1,X0)) = X1,
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X0] : union(X0,intersection(X0,X1)) = X0,
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X0] : union(X0,intersection(X0,X1)) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_union) ).

fof(f61,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | ~ member(sK0(X0,X1),X1)
      | ~ member(sK0(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f37,f60]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK0(X0,X1),X0)
      | ~ member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ( ( ~ member(sK0(X0,X1),X0)
            | ~ member(sK0(X0,X1),X1) )
          & ( member(sK0(X0,X1),X0)
            | member(sK0(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( ~ member(X3,X0)
            | ~ member(X3,X1) )
          & ( member(X3,X0)
            | member(X3,X1) ) )
     => ( ( ~ member(sK0(X0,X1),X0)
          | ~ member(sK0(X0,X1),X1) )
        & ( member(sK0(X0,X1),X0)
          | member(sK0(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X0)
              | ~ member(X2,X1) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ? [X3] :
            ( ( ~ member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X0)
              | member(X3,X1) ) ) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 )
      & ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f98,plain,
    member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1),
    inference(resolution,[],[f96,f42]) ).

fof(f42,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,intersection(X2,X0))
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( ( member(X1,X0)
          & member(X1,X2) )
        | ~ member(X1,intersection(X2,X0)) )
      & ( member(X1,intersection(X2,X0))
        | ~ member(X1,X0)
        | ~ member(X1,X2) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,plain,
    ! [X1,X2,X0] :
      ( ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) )
      & ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) ) ),
    inference(flattening,[],[f21]) ).

fof(f21,plain,
    ! [X1,X2,X0] :
      ( ( ( member(X2,X1)
          & member(X2,X0) )
        | ~ member(X2,intersection(X0,X1)) )
      & ( member(X2,intersection(X0,X1))
        | ~ member(X2,X1)
        | ~ member(X2,X0) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X2,X0] :
      ( ( member(X2,X1)
        & member(X2,X0) )
    <=> member(X2,intersection(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

fof(f96,plain,
    member(sK0(union(sK1,intersection(sK1,sK2)),sK1),intersection(sK1,sK2)),
    inference(subsumption_resolution,[],[f94,f86]) ).

fof(f94,plain,
    ( member(sK0(union(sK1,intersection(sK1,sK2)),sK1),intersection(sK1,sK2))
    | member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1) ),
    inference(resolution,[],[f93,f50]) ).

fof(f50,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f93,plain,
    member(sK0(union(sK1,intersection(sK1,sK2)),sK1),union(sK1,intersection(sK1,sK2))),
    inference(subsumption_resolution,[],[f91,f86]) ).

fof(f91,plain,
    ( member(sK0(union(sK1,intersection(sK1,sK2)),sK1),union(sK1,intersection(sK1,sK2)))
    | member(sK0(union(sK1,intersection(sK1,sK2)),sK1),sK1) ),
    inference(resolution,[],[f62,f66]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | member(sK0(X0,X1),X1)
      | member(sK0(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f36,f60]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK0(X0,X1),X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem    : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n024.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 13:36:34 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.17/0.47  % (14254)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)
% 0.17/0.48  % (14255)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.17/0.48  % (14263)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.49  % (14255)Refutation not found, incomplete strategy% (14255)------------------------------
% 0.17/0.49  % (14255)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.49  % (14263)Refutation not found, incomplete strategy% (14263)------------------------------
% 0.17/0.49  % (14263)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.49  % (14262)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)
% 0.17/0.49  % (14271)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.49  % (14254)Refutation not found, incomplete strategy% (14254)------------------------------
% 0.17/0.49  % (14254)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.49  % (14254)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.49  % (14254)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.49  
% 0.17/0.49  % (14254)Memory used [KB]: 5884
% 0.17/0.49  % (14254)Time elapsed: 0.104 s
% 0.17/0.49  % (14254)Instructions burned: 2 (million)
% 0.17/0.49  % (14254)------------------------------
% 0.17/0.49  % (14254)------------------------------
% 0.17/0.49  % (14271)First to succeed.
% 0.17/0.49  % (14255)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.49  % (14255)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.49  
% 0.17/0.49  % (14255)Memory used [KB]: 5884
% 0.17/0.49  % (14255)Time elapsed: 0.102 s
% 0.17/0.49  % (14255)Instructions burned: 2 (million)
% 0.17/0.49  % (14255)------------------------------
% 0.17/0.49  % (14255)------------------------------
% 0.17/0.49  % (14263)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.49  % (14263)Termination reason: Refutation not found, incomplete strategy
% 0.17/0.49  
% 0.17/0.49  % (14263)Memory used [KB]: 6012
% 0.17/0.49  % (14263)Time elapsed: 0.109 s
% 0.17/0.49  % (14263)Instructions burned: 2 (million)
% 0.17/0.49  % (14263)------------------------------
% 0.17/0.49  % (14263)------------------------------
% 0.17/0.49  % (14270)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)
% 0.17/0.49  % (14271)Refutation found. Thanks to Tanya!
% 0.17/0.49  % SZS status Theorem for theBenchmark
% 0.17/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.50  % (14271)------------------------------
% 0.17/0.50  % (14271)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.50  % (14271)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.50  % (14271)Termination reason: Refutation
% 0.17/0.50  
% 0.17/0.50  % (14271)Memory used [KB]: 5884
% 0.17/0.50  % (14271)Time elapsed: 0.107 s
% 0.17/0.50  % (14271)Instructions burned: 3 (million)
% 0.17/0.50  % (14271)------------------------------
% 0.17/0.50  % (14271)------------------------------
% 0.17/0.50  % (14246)Success in time 0.163 s
%------------------------------------------------------------------------------