TSTP Solution File: SET600+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET600+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_sat --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 18:25:02 EDT 2022

% Result   : Theorem 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   75 (   5 unt;   0 def)
%            Number of atoms       :  239 (  83 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  272 ( 108   ~; 110   |;  37   &)
%                                         (  12 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   93 (  80   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f147,plain,
    $false,
    inference(avatar_sat_refutation,[],[f72,f77,f78,f121,f134,f146]) ).

fof(f146,plain,
    ( ~ spl5_1
    | spl5_3 ),
    inference(avatar_contradiction_clause,[],[f145]) ).

fof(f145,plain,
    ( $false
    | ~ spl5_1
    | spl5_3 ),
    inference(subsumption_resolution,[],[f144,f75]) ).

fof(f75,plain,
    ( empty_set != sK3
    | spl5_3 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f74,plain,
    ( spl5_3
  <=> empty_set = sK3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f144,plain,
    ( empty_set = sK3
    | ~ spl5_1 ),
    inference(resolution,[],[f141,f99]) ).

fof(f99,plain,
    ! [X1] :
      ( ~ subset(X1,empty_set)
      | empty_set = X1 ),
    inference(resolution,[],[f38,f96]) ).

fof(f96,plain,
    ! [X1] : subset(empty_set,X1),
    inference(resolution,[],[f49,f51]) ).

fof(f51,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f49,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ member(X2,X0)
            | member(X2,X1) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( member(sK1(X0,X1),X0)
          & ~ member(sK1(X0,X1),X1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f29,f30]) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X0)
          & ~ member(X3,X1) )
     => ( member(sK1(X0,X1),X0)
        & ~ member(sK1(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,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,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ( ! [X2] :
            ( ~ member(X2,X1)
            | member(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( member(X2,X1)
            & ~ member(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ~ member(X2,X1)
          | member(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( member(X2,X1)
         => member(X2,X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

fof(f38,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X1,X0] :
      ( ( ( subset(X0,X1)
          & subset(X1,X0) )
        | X0 != X1 )
      & ( X0 = X1
        | ~ subset(X0,X1)
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        & subset(X1,X0) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).

fof(f141,plain,
    ( ! [X0] : subset(sK3,X0)
    | ~ spl5_1 ),
    inference(resolution,[],[f136,f49]) ).

fof(f136,plain,
    ( ! [X0] : ~ member(X0,sK3)
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f135,f51]) ).

fof(f135,plain,
    ( ! [X0] :
        ( ~ member(X0,sK3)
        | member(X0,empty_set) )
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f83,f67]) ).

fof(f67,plain,
    ( empty_set = sF4
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f65,plain,
    ( spl5_1
  <=> empty_set = sF4 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | member(X0,sF4) ),
    inference(superposition,[],[f45,f60]) ).

fof(f60,plain,
    union(sK2,sK3) = sF4,
    introduced(function_definition,[]) ).

fof(f45,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

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

fof(f26,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X0,X2)) )
      & ( member(X1,union(X0,X2))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,X0)
        | member(X1,X2)
        | ~ member(X1,union(X0,X2)) )
      & ( member(X1,union(X0,X2))
        | ( ~ member(X1,X0)
          & ~ member(X1,X2) ) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,X0)
        | member(X1,X2) )
    <=> member(X1,union(X0,X2)) ),
    inference(rectify,[],[f1]) ).

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

fof(f134,plain,
    ( spl5_2
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f129,f65,f69]) ).

fof(f69,plain,
    ( spl5_2
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f129,plain,
    ( empty_set = sK2
    | ~ spl5_1 ),
    inference(resolution,[],[f126,f99]) ).

fof(f126,plain,
    ( ! [X0] : subset(sK2,X0)
    | ~ spl5_1 ),
    inference(resolution,[],[f125,f49]) ).

fof(f125,plain,
    ( ! [X0] : ~ member(X0,sK2)
    | ~ spl5_1 ),
    inference(subsumption_resolution,[],[f124,f51]) ).

fof(f124,plain,
    ( ! [X0] :
        ( member(X0,empty_set)
        | ~ member(X0,sK2) )
    | ~ spl5_1 ),
    inference(forward_demodulation,[],[f88,f67]) ).

fof(f88,plain,
    ! [X0] :
      ( member(X0,sF4)
      | ~ member(X0,sK2) ),
    inference(superposition,[],[f46,f60]) ).

fof(f46,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X1,X0))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f121,plain,
    ( spl5_1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(avatar_contradiction_clause,[],[f120]) ).

fof(f120,plain,
    ( $false
    | spl5_1
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f119,f66]) ).

fof(f66,plain,
    ( empty_set != sF4
    | spl5_1 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f119,plain,
    ( empty_set = sF4
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f116,f99]) ).

fof(f116,plain,
    ( ! [X0] : subset(sF4,X0)
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(resolution,[],[f115,f49]) ).

fof(f115,plain,
    ( ! [X0] : ~ member(X0,sF4)
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(subsumption_resolution,[],[f114,f51]) ).

fof(f114,plain,
    ( ! [X0] :
        ( member(X0,empty_set)
        | ~ member(X0,sF4) )
    | ~ spl5_2
    | ~ spl5_3 ),
    inference(forward_demodulation,[],[f113,f76]) ).

fof(f76,plain,
    ( empty_set = sK3
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f74]) ).

fof(f113,plain,
    ( ! [X0] :
        ( member(X0,sK3)
        | ~ member(X0,sF4) )
    | ~ spl5_2 ),
    inference(subsumption_resolution,[],[f112,f51]) ).

fof(f112,plain,
    ( ! [X0] :
        ( member(X0,empty_set)
        | ~ member(X0,sF4)
        | member(X0,sK3) )
    | ~ spl5_2 ),
    inference(forward_demodulation,[],[f107,f71]) ).

fof(f71,plain,
    ( empty_set = sK2
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f69]) ).

fof(f107,plain,
    ! [X0] :
      ( member(X0,sK2)
      | member(X0,sK3)
      | ~ member(X0,sF4) ),
    inference(superposition,[],[f47,f60]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X1,X0))
      | member(X2,X1)
      | member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f78,plain,
    ( ~ spl5_3
    | ~ spl5_2
    | ~ spl5_1 ),
    inference(avatar_split_clause,[],[f61,f65,f69,f74]) ).

fof(f61,plain,
    ( empty_set != sF4
    | empty_set != sK2
    | empty_set != sK3 ),
    inference(definition_folding,[],[f54,f60]) ).

fof(f54,plain,
    ( empty_set != union(sK2,sK3)
    | empty_set != sK3
    | empty_set != sK2 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ( ( empty_set != union(sK2,sK3)
      | empty_set != sK3
      | empty_set != sK2 )
    & ( empty_set = union(sK2,sK3)
      | ( empty_set = sK3
        & empty_set = sK2 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f34,f35]) ).

fof(f35,plain,
    ( ? [X0,X1] :
        ( ( union(X0,X1) != empty_set
          | empty_set != X1
          | empty_set != X0 )
        & ( union(X0,X1) = empty_set
          | ( empty_set = X1
            & empty_set = X0 ) ) )
   => ( ( empty_set != union(sK2,sK3)
        | empty_set != sK3
        | empty_set != sK2 )
      & ( empty_set = union(sK2,sK3)
        | ( empty_set = sK3
          & empty_set = sK2 ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f34,plain,
    ? [X0,X1] :
      ( ( union(X0,X1) != empty_set
        | empty_set != X1
        | empty_set != X0 )
      & ( union(X0,X1) = empty_set
        | ( empty_set = X1
          & empty_set = X0 ) ) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ? [X1,X0] :
      ( ( empty_set != union(X1,X0)
        | empty_set != X0
        | empty_set != X1 )
      & ( empty_set = union(X1,X0)
        | ( empty_set = X0
          & empty_set = X1 ) ) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ? [X1,X0] :
      ( ( empty_set != union(X1,X0)
        | empty_set != X0
        | empty_set != X1 )
      & ( empty_set = union(X1,X0)
        | ( empty_set = X0
          & empty_set = X1 ) ) ),
    inference(nnf_transformation,[],[f17]) ).

fof(f17,plain,
    ? [X1,X0] :
      ( ( empty_set = X0
        & empty_set = X1 )
    <~> empty_set = union(X1,X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ~ ! [X1,X0] :
        ( empty_set = union(X1,X0)
      <=> ( empty_set = X0
          & empty_set = X1 ) ),
    inference(rectify,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X1,X0] :
        ( ( empty_set = X1
          & empty_set = X0 )
      <=> union(X0,X1) = empty_set ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X1,X0] :
      ( ( empty_set = X1
        & empty_set = X0 )
    <=> union(X0,X1) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th59) ).

fof(f77,plain,
    ( spl5_3
    | spl5_1 ),
    inference(avatar_split_clause,[],[f62,f65,f74]) ).

fof(f62,plain,
    ( empty_set = sF4
    | empty_set = sK3 ),
    inference(definition_folding,[],[f53,f60]) ).

fof(f53,plain,
    ( empty_set = union(sK2,sK3)
    | empty_set = sK3 ),
    inference(cnf_transformation,[],[f36]) ).

fof(f72,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f63,f69,f65]) ).

fof(f63,plain,
    ( empty_set = sK2
    | empty_set = sF4 ),
    inference(definition_folding,[],[f52,f60]) ).

fof(f52,plain,
    ( empty_set = union(sK2,sK3)
    | empty_set = sK2 ),
    inference(cnf_transformation,[],[f36]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 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
% 0.14/0.34  % Computer : n024.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 14:06:19 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.20/0.47  % (7808)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)
% 0.20/0.48  TRYING [1]
% 0.20/0.49  TRYING [2]
% 0.20/0.49  TRYING [3]
% 0.20/0.49  TRYING [4]
% 0.20/0.49  TRYING [5]
% 0.20/0.50  % (7832)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.50  % (7824)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50  % (7821)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.50  % (7812)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (7821)First to succeed.
% 0.20/0.50  % (7816)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.50  % (7820)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51  % (7816)Instruction limit reached!
% 0.20/0.51  % (7816)------------------------------
% 0.20/0.51  % (7816)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (7816)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (7816)Termination reason: Unknown
% 0.20/0.51  % (7816)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (7816)Memory used [KB]: 5373
% 0.20/0.51  % (7816)Time elapsed: 0.123 s
% 0.20/0.51  % (7816)Instructions burned: 3 (million)
% 0.20/0.51  % (7816)------------------------------
% 0.20/0.51  % (7816)------------------------------
% 0.20/0.51  % (7830)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)
% 0.20/0.51  % (7831)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)
% 0.20/0.51  % (7814)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)
% 0.20/0.51  TRYING [6]
% 0.20/0.52  % (7821)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Theorem for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (7821)------------------------------
% 0.20/0.52  % (7821)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (7821)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (7821)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (7821)Memory used [KB]: 5500
% 0.20/0.52  % (7821)Time elapsed: 0.097 s
% 0.20/0.52  % (7821)Instructions burned: 4 (million)
% 0.20/0.52  % (7821)------------------------------
% 0.20/0.52  % (7821)------------------------------
% 0.20/0.52  % (7807)Success in time 0.165 s
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