TSTP Solution File: SET588+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET588+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 : n012.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 18:21:31 EDT 2022

% Result   : Theorem 0.19s 0.56s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (   9 unt;   0 def)
%            Number of atoms       :  117 (   2 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  123 (  51   ~;  41   |;  21   &)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   81 (  69   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f231,plain,
    $false,
    inference(subsumption_resolution,[],[f230,f31]) ).

fof(f31,plain,
    ~ subset(sF4,sF5),
    inference(definition_folding,[],[f21,f30,f29]) ).

fof(f29,plain,
    sF4 = difference(sK0,sK1),
    introduced(function_definition,[]) ).

fof(f30,plain,
    sF5 = difference(sK2,sK1),
    introduced(function_definition,[]) ).

fof(f21,plain,
    ~ subset(difference(sK0,sK1),difference(sK2,sK1)),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ( subset(sK0,sK2)
    & ~ subset(difference(sK0,sK1),difference(sK2,sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f10,f11]) ).

fof(f11,plain,
    ( ? [X0,X1,X2] :
        ( subset(X0,X2)
        & ~ subset(difference(X0,X1),difference(X2,X1)) )
   => ( subset(sK0,sK2)
      & ~ subset(difference(sK0,sK1),difference(sK2,sK1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f10,plain,
    ? [X0,X1,X2] :
      ( subset(X0,X2)
      & ~ subset(difference(X0,X1),difference(X2,X1)) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ? [X2,X1,X0] :
      ( subset(X2,X0)
      & ~ subset(difference(X2,X1),difference(X0,X1)) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,plain,
    ~ ! [X1,X0,X2] :
        ( subset(X2,X0)
       => subset(difference(X2,X1),difference(X0,X1)) ),
    inference(rectify,[],[f5]) ).

fof(f5,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( subset(X0,X1)
       => subset(difference(X0,X2),difference(X1,X2)) ),
    inference(negated_conjecture,[],[f4]) ).

fof(f4,conjecture,
    ! [X1,X2,X0] :
      ( subset(X0,X1)
     => subset(difference(X0,X2),difference(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_subset1) ).

fof(f230,plain,
    subset(sF4,sF5),
    inference(forward_demodulation,[],[f229,f30]) ).

fof(f229,plain,
    subset(sF4,difference(sK2,sK1)),
    inference(subsumption_resolution,[],[f212,f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( member(sK3(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( member(sK3(X0,X1),X0)
          & ~ member(sK3(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f14,f15]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1) )
     => ( member(sK3(X0,X1),X0)
        & ~ member(sK3(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( member(X3,X0)
            & ~ member(X3,X1) ) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( member(X2,X0)
            & ~ member(X2,X1) ) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ member(X2,X0)
          | member(X2,X1) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

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

fof(f212,plain,
    ( ~ member(sK3(sF4,difference(sK2,sK1)),sF4)
    | subset(sF4,difference(sK2,sK1)) ),
    inference(resolution,[],[f204,f63]) ).

fof(f63,plain,
    ! [X0] :
      ( member(X0,sK2)
      | ~ member(X0,sF4) ),
    inference(resolution,[],[f62,f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ~ subset(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f62,plain,
    subset(sF4,sK2),
    inference(duplicate_literal_removal,[],[f61]) ).

fof(f61,plain,
    ( subset(sF4,sK2)
    | subset(sF4,sK2) ),
    inference(resolution,[],[f53,f24]) ).

fof(f53,plain,
    ! [X0] :
      ( ~ member(sK3(X0,sK2),sF4)
      | subset(X0,sK2) ),
    inference(resolution,[],[f43,f35]) ).

fof(f35,plain,
    ! [X0] :
      ( member(X0,sK0)
      | ~ member(X0,sF4) ),
    inference(superposition,[],[f26,f29]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,difference(X0,X2))
      | member(X1,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,difference(X0,X2))
        | member(X1,X2)
        | ~ member(X1,X0) )
      & ( ( ~ member(X1,X2)
          & member(X1,X0) )
        | ~ member(X1,difference(X0,X2)) ) ),
    inference(rectify,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,difference(X1,X2))
        | member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,difference(X1,X2)) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0,X2] :
      ( ( member(X0,difference(X1,X2))
        | member(X0,X2)
        | ~ member(X0,X1) )
      & ( ( ~ member(X0,X2)
          & member(X0,X1) )
        | ~ member(X0,difference(X1,X2)) ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,plain,
    ! [X1,X0,X2] :
      ( member(X0,difference(X1,X2))
    <=> ( ~ member(X0,X2)
        & member(X0,X1) ) ),
    inference(rectify,[],[f1]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( member(X2,difference(X0,X1))
    <=> ( member(X2,X0)
        & ~ member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).

fof(f43,plain,
    ! [X0] :
      ( ~ member(sK3(X0,sK2),sK0)
      | subset(X0,sK2) ),
    inference(resolution,[],[f41,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ~ member(sK3(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f41,plain,
    ! [X0] :
      ( member(X0,sK2)
      | ~ member(X0,sK0) ),
    inference(resolution,[],[f25,f22]) ).

fof(f22,plain,
    subset(sK0,sK2),
    inference(cnf_transformation,[],[f12]) ).

fof(f204,plain,
    ! [X15] :
      ( ~ member(sK3(sF4,difference(X15,sK1)),X15)
      | subset(sF4,difference(X15,sK1)) ),
    inference(duplicate_literal_removal,[],[f180]) ).

fof(f180,plain,
    ! [X15] :
      ( subset(sF4,difference(X15,sK1))
      | ~ member(sK3(sF4,difference(X15,sK1)),X15)
      | subset(sF4,difference(X15,sK1)) ),
    inference(resolution,[],[f46,f45]) ).

fof(f45,plain,
    ! [X0] :
      ( ~ member(sK3(sF4,X0),sK1)
      | subset(sF4,X0) ),
    inference(resolution,[],[f39,f24]) ).

fof(f39,plain,
    ! [X0] :
      ( ~ member(X0,sF4)
      | ~ member(X0,sK1) ),
    inference(superposition,[],[f27,f29]) ).

fof(f27,plain,
    ! [X2,X0,X1] :
      ( ~ member(X1,difference(X0,X2))
      | ~ member(X1,X2) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(sK3(X0,difference(X1,X2)),X2)
      | ~ member(sK3(X0,difference(X1,X2)),X1)
      | subset(X0,difference(X1,X2)) ),
    inference(resolution,[],[f28,f23]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( member(X1,difference(X0,X2))
      | ~ member(X1,X0)
      | member(X1,X2) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET588+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 30 14:02:05 EDT 2022
% 0.12/0.35  % CPUTime    : 
% 0.19/0.55  % (1115)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.19/0.55  % (1118)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.56  % (1140)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)
% 0.19/0.56  % (1139)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)
% 0.19/0.56  % (1138)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.56  % (1115)First to succeed.
% 0.19/0.56  % (1127)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.19/0.56  % (1127)Refutation not found, incomplete strategy% (1127)------------------------------
% 0.19/0.56  % (1127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (1115)Refutation found. Thanks to Tanya!
% 0.19/0.56  % SZS status Theorem for theBenchmark
% 0.19/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.56  % (1115)------------------------------
% 0.19/0.56  % (1115)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.56  % (1115)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.56  % (1115)Termination reason: Refutation
% 0.19/0.56  
% 0.19/0.56  % (1115)Memory used [KB]: 6012
% 0.19/0.56  % (1115)Time elapsed: 0.147 s
% 0.19/0.56  % (1115)Instructions burned: 7 (million)
% 0.19/0.56  % (1115)------------------------------
% 0.19/0.56  % (1115)------------------------------
% 0.19/0.56  % (1114)Success in time 0.209 s
%------------------------------------------------------------------------------