TSTP Solution File: SET929+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n026.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 : Tue Apr 30 15:14:02 EDT 2024

% Result   : Theorem 0.10s 0.27s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   32 (   6 unt;   0 def)
%            Number of atoms       :  100 (  30 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  111 (  43   ~;  43   |;  19   &)
%                                         (   4 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (  36   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f95,plain,
    $false,
    inference(resolution,[],[f86,f84]) ).

fof(f84,plain,
    in(sK0,sK2),
    inference(resolution,[],[f82,f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X0,X1),X2)
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( subset(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | ~ subset(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0,X1,X2] :
      ( subset(unordered_pair(X0,X1),X2)
    <=> ( in(X1,X2)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).

fof(f82,plain,
    subset(unordered_pair(sK0,sK1),sK2),
    inference(trivial_inequality_removal,[],[f81]) ).

fof(f81,plain,
    ( empty_set != empty_set
    | subset(unordered_pair(sK0,sK1),sK2) ),
    inference(superposition,[],[f32,f77]) ).

fof(f77,plain,
    empty_set = set_difference(unordered_pair(sK0,sK1),sK2),
    inference(duplicate_literal_removal,[],[f76]) ).

fof(f76,plain,
    ( empty_set = set_difference(unordered_pair(sK0,sK1),sK2)
    | empty_set = set_difference(unordered_pair(sK0,sK1),sK2)
    | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ),
    inference(resolution,[],[f66,f26]) ).

fof(f26,plain,
    ( in(sK1,sK2)
    | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ( ( ~ in(sK1,sK2)
      | ~ in(sK0,sK2)
      | empty_set != set_difference(unordered_pair(sK0,sK1),sK2) )
    & ( ( in(sK1,sK2)
        & in(sK0,sK2) )
      | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f15,f16]) ).

fof(f16,plain,
    ( ? [X0,X1,X2] :
        ( ( ~ in(X1,X2)
          | ~ in(X0,X2)
          | empty_set != set_difference(unordered_pair(X0,X1),X2) )
        & ( ( in(X1,X2)
            & in(X0,X2) )
          | empty_set = set_difference(unordered_pair(X0,X1),X2) ) )
   => ( ( ~ in(sK1,sK2)
        | ~ in(sK0,sK2)
        | empty_set != set_difference(unordered_pair(sK0,sK1),sK2) )
      & ( ( in(sK1,sK2)
          & in(sK0,sK2) )
        | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X1,X2)
        | ~ in(X0,X2)
        | empty_set != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f14]) ).

fof(f14,plain,
    ? [X0,X1,X2] :
      ( ( ~ in(X1,X2)
        | ~ in(X0,X2)
        | empty_set != set_difference(unordered_pair(X0,X1),X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set = set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ? [X0,X1,X2] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
    <~> ( in(X1,X2)
        & in(X0,X2) ) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( empty_set = set_difference(unordered_pair(X0,X1),X2)
      <=> ( in(X1,X2)
          & in(X0,X2) ) ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ( empty_set = set_difference(unordered_pair(X0,X1),X2)
    <=> ( in(X1,X2)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t73_zfmisc_1) ).

fof(f66,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | empty_set = set_difference(unordered_pair(sK0,X0),sK2)
      | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ),
    inference(resolution,[],[f63,f25]) ).

fof(f25,plain,
    ( in(sK0,sK2)
    | empty_set = set_difference(unordered_pair(sK0,sK1),sK2) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f63,plain,
    ! [X2,X0,X1] :
      ( ~ in(X2,X1)
      | ~ in(X0,X1)
      | empty_set = set_difference(unordered_pair(X2,X0),X1) ),
    inference(resolution,[],[f36,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | empty_set = set_difference(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(f36,plain,
    ! [X2,X0,X1] :
      ( subset(unordered_pair(X0,X1),X2)
      | ~ in(X1,X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( empty_set != set_difference(X0,X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f86,plain,
    ~ in(sK0,sK2),
    inference(resolution,[],[f83,f80]) ).

fof(f80,plain,
    ( ~ in(sK1,sK2)
    | ~ in(sK0,sK2) ),
    inference(trivial_inequality_removal,[],[f79]) ).

fof(f79,plain,
    ( empty_set != empty_set
    | ~ in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(backward_demodulation,[],[f27,f77]) ).

fof(f27,plain,
    ( empty_set != set_difference(unordered_pair(sK0,sK1),sK2)
    | ~ in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f83,plain,
    in(sK1,sK2),
    inference(resolution,[],[f82,f35]) ).

fof(f35,plain,
    ! [X2,X0,X1] :
      ( ~ subset(unordered_pair(X0,X1),X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06  % Problem    : SET929+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.07/0.26  % Computer : n026.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit   : 300
% 0.07/0.26  % WCLimit    : 300
% 0.07/0.26  % DateTime   : Tue Apr 30 01:27:49 EDT 2024
% 0.07/0.26  % CPUTime    : 
% 0.07/0.26  % (6836)Running in auto input_syntax mode. Trying TPTP
% 0.07/0.27  % (6840)WARNING: value z3 for option sas not known
% 0.07/0.27  % (6841)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.07/0.27  % (6839)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.07/0.27  % (6838)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.07/0.27  % (6842)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.07/0.27  % (6840)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.07/0.27  % (6843)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.07/0.27  % (6844)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.07/0.27  TRYING [1]
% 0.07/0.27  TRYING [1]
% 0.07/0.27  TRYING [2]
% 0.07/0.27  TRYING [2]
% 0.07/0.27  TRYING [3]
% 0.07/0.27  TRYING [3]
% 0.10/0.27  TRYING [4]
% 0.10/0.27  TRYING [4]
% 0.10/0.27  % (6843)First to succeed.
% 0.10/0.27  % (6842)Also succeeded, but the first one will report.
% 0.10/0.27  TRYING [1]
% 0.10/0.27  TRYING [2]
% 0.10/0.27  % (6840)Also succeeded, but the first one will report.
% 0.10/0.27  TRYING [3]
% 0.10/0.27  % (6843)Refutation found. Thanks to Tanya!
% 0.10/0.27  % SZS status Theorem for theBenchmark
% 0.10/0.27  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.27  % (6843)------------------------------
% 0.10/0.27  % (6843)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.27  % (6843)Termination reason: Refutation
% 0.10/0.27  
% 0.10/0.27  % (6843)Memory used [KB]: 838
% 0.10/0.27  % (6843)Time elapsed: 0.004 s
% 0.10/0.27  % (6843)Instructions burned: 7 (million)
% 0.10/0.27  % (6843)------------------------------
% 0.10/0.27  % (6843)------------------------------
% 0.10/0.27  % (6836)Success in time 0.012 s
%------------------------------------------------------------------------------