TSTP Solution File: SET637+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET637+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 : 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 18:25:11 EDT 2022

% Result   : Theorem 0.18s 0.57s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   60 (  12 unt;   0 def)
%            Number of atoms       :  197 (  36 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  210 (  73   ~;  87   |;  34   &)
%                                         (  12 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  111 (  97   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f195,plain,
    $false,
    inference(subsumption_resolution,[],[f194,f176]) ).

fof(f176,plain,
    member(sK0(sK3,sK2),sK2),
    inference(resolution,[],[f172,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ intersect(X1,X0)
      | member(sK0(X0,X1),X1) ),
    inference(cnf_transformation,[],[f20]) ).

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

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

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

fof(f17,plain,
    ! [X0,X1] :
      ( ( intersect(X1,X0)
        | ! [X2] :
            ( ~ member(X2,X0)
            | ~ member(X2,X1) ) )
      & ( ? [X2] :
            ( member(X2,X0)
            & member(X2,X1) )
        | ~ intersect(X1,X0) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( intersect(X1,X0)
    <=> ? [X2] :
          ( member(X2,X0)
          & member(X2,X1) ) ),
    inference(rectify,[],[f2]) ).

fof(f2,axiom,
    ! [X1,X0] :
      ( intersect(X0,X1)
    <=> ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).

fof(f172,plain,
    intersect(sK2,sK3),
    inference(subsumption_resolution,[],[f165,f52]) ).

fof(f52,plain,
    ! [X1] : ~ not_equal(X1,X1),
    inference(equality_resolution,[],[f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( X0 != X1
      | ~ not_equal(X1,X0) ),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ! [X0,X1] :
      ( ( X0 != X1
        | ~ not_equal(X1,X0) )
      & ( not_equal(X1,X0)
        | X0 = X1 ) ),
    inference(nnf_transformation,[],[f12]) ).

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

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

fof(f165,plain,
    ( intersect(sK2,sK3)
    | not_equal(intersection(sK2,sK3),intersection(sK2,sK3)) ),
    inference(backward_demodulation,[],[f46,f164]) ).

fof(f164,plain,
    empty_set = intersection(sK2,sK3),
    inference(duplicate_literal_removal,[],[f159]) ).

fof(f159,plain,
    ( empty_set = intersection(sK2,sK3)
    | empty_set = intersection(sK2,sK3) ),
    inference(resolution,[],[f148,f49]) ).

fof(f49,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f148,plain,
    ! [X0] :
      ( member(sK1(intersection(sK2,sK3),X0),X0)
      | empty_set = intersection(sK2,sK3)
      | intersection(sK2,sK3) = X0 ),
    inference(forward_demodulation,[],[f147,f36]) ).

fof(f36,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

fof(f147,plain,
    ! [X0] :
      ( intersection(sK2,sK3) = X0
      | member(sK1(intersection(sK3,sK2),X0),X0)
      | empty_set = intersection(sK2,sK3) ),
    inference(forward_demodulation,[],[f145,f36]) ).

fof(f145,plain,
    ! [X0] :
      ( empty_set = intersection(sK2,sK3)
      | intersection(sK3,sK2) = X0
      | member(sK1(intersection(sK3,sK2),X0),X0) ),
    inference(duplicate_literal_removal,[],[f139]) ).

fof(f139,plain,
    ! [X0] :
      ( member(sK1(intersection(sK3,sK2),X0),X0)
      | intersection(sK3,sK2) = X0
      | intersection(sK3,sK2) = X0
      | member(sK1(intersection(sK3,sK2),X0),X0)
      | empty_set = intersection(sK2,sK3) ),
    inference(resolution,[],[f131,f69]) ).

fof(f69,plain,
    ! [X2,X3,X1] :
      ( member(sK1(intersection(X1,X2),X3),X2)
      | member(sK1(intersection(X1,X2),X3),X3)
      | intersection(X1,X2) = X3 ),
    inference(resolution,[],[f39,f43]) ).

fof(f43,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,intersection(X0,X1))
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

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

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

fof(f25,plain,
    ! [X2,X0,X1] :
      ( ( ( member(X1,X0)
          & member(X1,X2) )
        | ~ member(X1,intersection(X2,X0)) )
      & ( member(X1,intersection(X2,X0))
        | ~ member(X1,X0)
        | ~ member(X1,X2) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X2,X0,X1] :
      ( ( member(X1,X0)
        & member(X1,X2) )
    <=> member(X1,intersection(X2,X0)) ),
    inference(rectify,[],[f1]) ).

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

fof(f39,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | member(sK1(X0,X1),X1)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK1(X0,X1),X0)
            | ~ member(sK1(X0,X1),X1) )
          & ( member(sK1(X0,X1),X0)
            | member(sK1(X0,X1),X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X0)
            | ~ member(X2,X1) )
          & ( member(X2,X0)
            | member(X2,X1) ) )
     => ( ( ~ member(sK1(X0,X1),X0)
          | ~ member(sK1(X0,X1),X1) )
        & ( member(sK1(X0,X1),X0)
          | member(sK1(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X0)
              | member(X2,X1) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X1)
              | ~ member(X3,X0) )
            & ( member(X3,X0)
              | ~ member(X3,X1) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X1,X0] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X1,X0] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) )
    <=> X0 = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ~ member(sK1(intersection(sK3,X0),X1),sK2)
      | member(sK1(intersection(sK3,X0),X1),X1)
      | empty_set = intersection(sK2,sK3)
      | intersection(sK3,X0) = X1 ),
    inference(superposition,[],[f114,f36]) ).

fof(f114,plain,
    ! [X19,X20] :
      ( ~ member(sK1(intersection(X19,sK3),X20),sK2)
      | intersection(X19,sK3) = X20
      | empty_set = intersection(sK2,sK3)
      | member(sK1(intersection(X19,sK3),X20),X20) ),
    inference(resolution,[],[f69,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | empty_set = intersection(sK2,sK3)
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f35,f54]) ).

fof(f54,plain,
    ( ~ intersect(sK2,sK3)
    | empty_set = intersection(sK2,sK3) ),
    inference(resolution,[],[f44,f47]) ).

fof(f47,plain,
    ( ~ not_equal(intersection(sK2,sK3),empty_set)
    | ~ intersect(sK2,sK3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ( ( ~ not_equal(intersection(sK2,sK3),empty_set)
      | ~ intersect(sK2,sK3) )
    & ( not_equal(intersection(sK2,sK3),empty_set)
      | intersect(sK2,sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f29,f30]) ).

fof(f30,plain,
    ( ? [X0,X1] :
        ( ( ~ not_equal(intersection(X0,X1),empty_set)
          | ~ intersect(X0,X1) )
        & ( not_equal(intersection(X0,X1),empty_set)
          | intersect(X0,X1) ) )
   => ( ( ~ not_equal(intersection(sK2,sK3),empty_set)
        | ~ intersect(sK2,sK3) )
      & ( not_equal(intersection(sK2,sK3),empty_set)
        | intersect(sK2,sK3) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f29,plain,
    ? [X0,X1] :
      ( ( ~ not_equal(intersection(X0,X1),empty_set)
        | ~ intersect(X0,X1) )
      & ( not_equal(intersection(X0,X1),empty_set)
        | intersect(X0,X1) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ? [X0,X1] :
      ( intersect(X0,X1)
    <~> not_equal(intersection(X0,X1),empty_set) ),
    inference(ennf_transformation,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X1,X0] :
      ( intersect(X0,X1)
    <=> not_equal(intersection(X0,X1),empty_set) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th119) ).

fof(f44,plain,
    ! [X0,X1] :
      ( not_equal(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f28]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( intersect(X1,X0)
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f46,plain,
    ( not_equal(intersection(sK2,sK3),empty_set)
    | intersect(sK2,sK3) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f194,plain,
    ~ member(sK0(sK3,sK2),sK2),
    inference(resolution,[],[f178,f175]) ).

fof(f175,plain,
    member(sK0(sK3,sK2),sK3),
    inference(resolution,[],[f172,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ intersect(X1,X0)
      | member(sK0(X0,X1),X0) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f178,plain,
    ! [X0] :
      ( ~ member(X0,sK3)
      | ~ member(X0,sK2) ),
    inference(resolution,[],[f167,f41]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( member(X2,intersection(X0,X1))
      | ~ member(X2,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f167,plain,
    ! [X0] : ~ member(X0,intersection(sK2,sK3)),
    inference(backward_demodulation,[],[f49,f164]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SET637+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_sat --cores 0 -t %d %s
% 0.12/0.34  % Computer : n005.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 14:08:48 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 0.18/0.51  % (23090)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 (3000ds/191324Mi)
% 0.18/0.52  TRYING [1]
% 0.18/0.53  % (23113)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 (3000ds/467Mi)
% 0.18/0.53  TRYING [2]
% 0.18/0.53  TRYING [3]
% 0.18/0.54  % (23105)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.18/0.54  TRYING [4]
% 0.18/0.54  TRYING [5]
% 0.18/0.55  % (23091)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.18/0.55  % (23098)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 0.18/0.55  % (23112)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 (3000ds/498Mi)
% 0.18/0.55  % (23107)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 0.18/0.56  % (23098)Instruction limit reached!
% 0.18/0.56  % (23098)------------------------------
% 0.18/0.56  % (23098)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56  % (23098)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (23098)Termination reason: Unknown
% 0.18/0.56  % (23098)Termination phase: Saturation
% 0.18/0.56  
% 0.18/0.56  % (23098)Memory used [KB]: 5373
% 0.18/0.56  % (23098)Time elapsed: 0.006 s
% 0.18/0.56  % (23098)Instructions burned: 2 (million)
% 0.18/0.56  % (23098)------------------------------
% 0.18/0.56  % (23098)------------------------------
% 0.18/0.56  % (23091)Refutation not found, incomplete strategy% (23091)------------------------------
% 0.18/0.56  % (23091)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.56  % (23091)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.56  % (23091)Termination reason: Refutation not found, incomplete strategy
% 0.18/0.56  
% 0.18/0.56  % (23091)Memory used [KB]: 5373
% 0.18/0.56  % (23091)Time elapsed: 0.111 s
% 0.18/0.56  % (23091)Instructions burned: 2 (million)
% 0.18/0.56  % (23091)------------------------------
% 0.18/0.56  % (23091)------------------------------
% 0.18/0.56  % (23100)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.18/0.56  % (23115)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/500Mi)
% 0.18/0.57  TRYING [1]
% 0.18/0.57  % (23112)First to succeed.
% 0.18/0.57  % (23092)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 (3000ds/37Mi)
% 0.18/0.57  % (23112)Refutation found. Thanks to Tanya!
% 0.18/0.57  % SZS status Theorem for theBenchmark
% 0.18/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.57  % (23112)------------------------------
% 0.18/0.57  % (23112)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.57  % (23112)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.57  % (23112)Termination reason: Refutation
% 0.18/0.57  
% 0.18/0.57  % (23112)Memory used [KB]: 1023
% 0.18/0.57  % (23112)Time elapsed: 0.147 s
% 0.18/0.57  % (23112)Instructions burned: 9 (million)
% 0.18/0.57  % (23112)------------------------------
% 0.18/0.57  % (23112)------------------------------
% 0.18/0.57  % (23089)Success in time 0.227 s
%------------------------------------------------------------------------------