TSTP Solution File: SET762+4 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 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 : n017.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 18:22:09 EDT 2022

% Result   : Theorem 1.61s 0.57s
% Output   : Refutation 1.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   36 (   9 unt;   0 def)
%            Number of atoms       :   93 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   91 (  34   ~;  21   |;  22   &)
%                                         (   4 <=>;  10  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-3 aty)
%            Number of variables   :   86 (  69   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f82,plain,
    $false,
    inference(resolution,[],[f81,f64]) ).

fof(f64,plain,
    ~ equal_set(image2(sK3,empty_set),empty_set),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,plain,
    ( ~ equal_set(image2(sK3,empty_set),empty_set)
    & maps(sK3,sK4,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f50,f51]) ).

fof(f51,plain,
    ( ? [X0,X1,X2] :
        ( ~ equal_set(image2(X1,empty_set),empty_set)
        & maps(X1,X2,X0) )
   => ( ~ equal_set(image2(sK3,empty_set),empty_set)
      & maps(sK3,sK4,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f50,plain,
    ? [X0,X1,X2] :
      ( ~ equal_set(image2(X1,empty_set),empty_set)
      & maps(X1,X2,X0) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ? [X1,X0,X2] :
      ( ~ equal_set(image2(X0,empty_set),empty_set)
      & maps(X0,X2,X1) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,plain,
    ~ ! [X1,X2,X0] :
        ( maps(X0,X2,X1)
       => equal_set(image2(X0,empty_set),empty_set) ),
    inference(rectify,[],[f30]) ).

fof(f30,negated_conjecture,
    ~ ! [X5,X1,X0] :
        ( maps(X5,X0,X1)
       => equal_set(image2(X5,empty_set),empty_set) ),
    inference(negated_conjecture,[],[f29]) ).

fof(f29,conjecture,
    ! [X5,X1,X0] :
      ( maps(X5,X0,X1)
     => equal_set(image2(X5,empty_set),empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIIa12) ).

fof(f81,plain,
    ! [X2] : equal_set(image2(X2,empty_set),empty_set),
    inference(resolution,[],[f78,f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | equal_set(X0,empty_set) ),
    inference(resolution,[],[f57,f70]) ).

fof(f70,plain,
    ! [X1] : subset(empty_set,X1),
    inference(resolution,[],[f59,f65]) ).

fof(f65,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f33]) ).

fof(f33,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X2] : ~ member(X2,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).

fof(f59,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ( member(sK0(X0,X1),X1)
        & ~ member(sK0(X0,X1),X0) )
      | subset(X1,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f44,f45]) ).

fof(f45,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & ~ member(X2,X0) )
     => ( member(sK0(X0,X1),X1)
        & ~ member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( member(X2,X1)
          & ~ member(X2,X0) )
      | subset(X1,X0) ),
    inference(rectify,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0] :
      ( ? [X2] :
          ( member(X2,X0)
          & ~ member(X2,X1) )
      | subset(X0,X1) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) )
     => subset(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f1]) ).

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

fof(f57,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | equal_set(X0,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | equal_set(X0,X1)
      | ~ subset(X0,X1) ),
    inference(flattening,[],[f42]) ).

fof(f42,plain,
    ! [X1,X0] :
      ( equal_set(X0,X1)
      | ~ subset(X1,X0)
      | ~ subset(X0,X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        & subset(X0,X1) )
     => equal_set(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f2]) ).

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

fof(f78,plain,
    ! [X0,X1] : subset(image2(X0,empty_set),X1),
    inference(resolution,[],[f77,f59]) ).

fof(f77,plain,
    ! [X0,X1] : ~ member(X0,image2(X1,empty_set)),
    inference(resolution,[],[f66,f65]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( member(sK5(X0,X1,X2),X2)
      | ~ member(X1,image2(X0,X2)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,image2(X0,X2))
        | ! [X3] :
            ( ~ apply(X0,X3,X1)
            | ~ member(X3,X2) ) )
      & ( ( apply(X0,sK5(X0,X1,X2),X1)
          & member(sK5(X0,X1,X2),X2) )
        | ~ member(X1,image2(X0,X2)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f54,f55]) ).

fof(f55,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( apply(X0,X4,X1)
          & member(X4,X2) )
     => ( apply(X0,sK5(X0,X1,X2),X1)
        & member(sK5(X0,X1,X2),X2) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,image2(X0,X2))
        | ! [X3] :
            ( ~ apply(X0,X3,X1)
            | ~ member(X3,X2) ) )
      & ( ? [X4] :
            ( apply(X0,X4,X1)
            & member(X4,X2) )
        | ~ member(X1,image2(X0,X2)) ) ),
    inference(rectify,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2] :
      ( ( member(X1,image2(X0,X2))
        | ! [X3] :
            ( ~ apply(X0,X3,X1)
            | ~ member(X3,X2) ) )
      & ( ? [X3] :
            ( apply(X0,X3,X1)
            & member(X3,X2) )
        | ~ member(X1,image2(X0,X2)) ) ),
    inference(nnf_transformation,[],[f32]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( member(X1,image2(X0,X2))
    <=> ? [X3] :
          ( apply(X0,X3,X1)
          & member(X3,X2) ) ),
    inference(rectify,[],[f22]) ).

fof(f22,axiom,
    ! [X5,X4,X0] :
      ( ? [X2] :
          ( apply(X5,X2,X4)
          & member(X2,X0) )
    <=> member(X4,image2(X5,X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET762+4 : TPTP v8.1.0. Bugfixed v2.2.1.
% 0.07/0.13  % 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 : n017.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 13:43:20 EDT 2022
% 0.12/0.34  % CPUTime    : 
% 1.28/0.55  % (15630)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)
% 1.28/0.55  % (15628)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.28/0.56  % (15646)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)
% 1.28/0.56  % (15638)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)
% 1.28/0.56  % (15628)First to succeed.
% 1.28/0.56  % (15638)Also succeeded, but the first one will report.
% 1.28/0.57  % (15636)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.61/0.57  % (15644)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)
% 1.61/0.57  % (15628)Refutation found. Thanks to Tanya!
% 1.61/0.57  % SZS status Theorem for theBenchmark
% 1.61/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 1.61/0.57  % (15628)------------------------------
% 1.61/0.57  % (15628)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.61/0.57  % (15628)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.61/0.57  % (15628)Termination reason: Refutation
% 1.61/0.57  
% 1.61/0.57  % (15628)Memory used [KB]: 6012
% 1.61/0.57  % (15628)Time elapsed: 0.129 s
% 1.61/0.57  % (15628)Instructions burned: 2 (million)
% 1.61/0.57  % (15628)------------------------------
% 1.61/0.57  % (15628)------------------------------
% 1.61/0.57  % (15621)Success in time 0.215 s
%------------------------------------------------------------------------------