TSTP Solution File: SET930+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET930+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 : n020.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 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   38 (  13 unt;   0 def)
%            Number of atoms       :  125 (  60 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  154 (  67   ~;  41   |;  40   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   72 (  66   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f748,plain,
    $false,
    inference(subsumption_resolution,[],[f747,f31]) ).

fof(f31,plain,
    set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3)
    & set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2)
    & set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1)
    & empty_set != set_difference(unordered_pair(sK1,sK2),sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f11,f15]) ).

fof(f15,plain,
    ( ? [X0,X1,X2] :
        ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
        & empty_set != set_difference(unordered_pair(X0,X1),X2) )
   => ( unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3)
      & set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK2)
      & set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1)
      & empty_set != set_difference(unordered_pair(sK1,sK2),sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1,X2] :
      ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
      & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
      & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      & empty_set != set_difference(unordered_pair(X0,X1),X2) ),
    inference(ennf_transformation,[],[f10]) ).

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

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ~ ( unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X1)
        & set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
        & empty_set != set_difference(unordered_pair(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_zfmisc_1) ).

fof(f747,plain,
    set_difference(unordered_pair(sK1,sK2),sK3) = singleton(sK2),
    inference(forward_demodulation,[],[f742,f34]) ).

fof(f34,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f742,plain,
    singleton(sK2) = set_difference(unordered_pair(sK2,sK1),sK3),
    inference(unit_resulting_resolution,[],[f689,f44]) ).

fof(f44,plain,
    ! [X2,X0,X1] :
      ( ~ sP0(X1,X0,X2)
      | set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
        | ~ sP0(X1,X0,X2) )
      & ( sP0(X1,X0,X2)
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <=> sP0(X1,X0,X2) ),
    inference(definition_folding,[],[f4,f13]) ).

fof(f13,plain,
    ! [X1,X0,X2] :
      ( sP0(X1,X0,X2)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f4,axiom,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).

fof(f689,plain,
    sP0(sK1,sK2,sK3),
    inference(unit_resulting_resolution,[],[f618,f622,f41]) ).

fof(f41,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | sP0(X0,X1,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( X0 != X1
          & ~ in(X0,X2) )
        | in(X1,X2) )
      & ( ( ( X0 = X1
            | in(X0,X2) )
          & ~ in(X1,X2) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ! [X1,X0,X2] :
      ( ( sP0(X1,X0,X2)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | ~ sP0(X1,X0,X2) ) ),
    inference(nnf_transformation,[],[f13]) ).

fof(f622,plain,
    ~ in(sK2,sK3),
    inference(unit_resulting_resolution,[],[f29,f618,f38]) ).

fof(f38,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | empty_set = set_difference(unordered_pair(X0,X1),X2)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1,X2] :
      ( ( empty_set = set_difference(unordered_pair(X0,X1),X2)
        | ~ in(X1,X2)
        | ~ in(X0,X2) )
      & ( ( in(X1,X2)
          & in(X0,X2) )
        | empty_set != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [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(f29,plain,
    empty_set != set_difference(unordered_pair(sK1,sK2),sK3),
    inference(cnf_transformation,[],[f16]) ).

fof(f618,plain,
    in(sK1,sK3),
    inference(subsumption_resolution,[],[f611,f32]) ).

fof(f32,plain,
    unordered_pair(sK1,sK2) != set_difference(unordered_pair(sK1,sK2),sK3),
    inference(cnf_transformation,[],[f16]) ).

fof(f611,plain,
    ( in(sK1,sK3)
    | unordered_pair(sK1,sK2) = set_difference(unordered_pair(sK1,sK2),sK3) ),
    inference(factoring,[],[f334]) ).

fof(f334,plain,
    ! [X0] :
      ( in(X0,sK3)
      | in(sK1,sK3)
      | unordered_pair(X0,sK2) = set_difference(unordered_pair(X0,sK2),sK3) ),
    inference(resolution,[],[f77,f60]) ).

fof(f60,plain,
    ~ sP0(sK2,sK1,sK3),
    inference(unit_resulting_resolution,[],[f30,f44]) ).

fof(f30,plain,
    set_difference(unordered_pair(sK1,sK2),sK3) != singleton(sK1),
    inference(cnf_transformation,[],[f16]) ).

fof(f77,plain,
    ! [X2,X3,X0,X1] :
      ( sP0(X0,X3,X1)
      | unordered_pair(X2,X0) = set_difference(unordered_pair(X2,X0),X1)
      | in(X2,X1)
      | in(X3,X1) ),
    inference(resolution,[],[f47,f41]) ).

fof(f47,plain,
    ! [X2,X0,X1] :
      ( in(X1,X2)
      | in(X0,X2)
      | unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
        | in(X1,X2)
        | in(X0,X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(flattening,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
        | in(X1,X2)
        | in(X0,X2) )
      & ( ( ~ in(X1,X2)
          & ~ in(X0,X2) )
        | unordered_pair(X0,X1) != set_difference(unordered_pair(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( unordered_pair(X0,X1) = set_difference(unordered_pair(X0,X1),X2)
    <=> ( ~ in(X1,X2)
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t72_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15  % Problem    : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.17  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit   : 300
% 0.15/0.37  % WCLimit    : 300
% 0.15/0.37  % DateTime   : Tue Apr 30 01:06:02 EDT 2024
% 0.15/0.37  % CPUTime    : 
% 0.15/0.37  % (20203)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.39  % (20206)WARNING: value z3 for option sas not known
% 0.15/0.39  % (20206)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)
% 0.15/0.39  % (20208)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)
% 0.15/0.39  % (20207)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (20205)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (20210)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)
% 0.15/0.39  % (20209)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (20204)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  TRYING [3]
% 0.15/0.40  TRYING [4]
% 0.15/0.40  TRYING [1]
% 0.15/0.40  TRYING [2]
% 0.19/0.41  TRYING [3]
% 0.19/0.41  TRYING [5]
% 0.19/0.42  % (20210)First to succeed.
% 0.19/0.42  % (20210)Refutation found. Thanks to Tanya!
% 0.19/0.42  % SZS status Theorem for theBenchmark
% 0.19/0.42  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.42  % (20210)------------------------------
% 0.19/0.42  % (20210)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.42  % (20210)Termination reason: Refutation
% 0.19/0.42  
% 0.19/0.42  % (20210)Memory used [KB]: 931
% 0.19/0.42  % (20210)Time elapsed: 0.030 s
% 0.19/0.42  % (20210)Instructions burned: 59 (million)
% 0.19/0.42  % (20210)------------------------------
% 0.19/0.42  % (20210)------------------------------
% 0.19/0.42  % (20203)Success in time 0.044 s
%------------------------------------------------------------------------------