TSTP Solution File: SET927+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET927+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 : n025.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 15:14:01 EDT 2024

% Result   : Theorem 0.10s 0.36s
% Output   : Refutation 0.10s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   43 (   5 unt;   0 def)
%            Number of atoms       :  149 (  83 equ)
%            Maximal formula atoms :   16 (   3 avg)
%            Number of connectives :  168 (  62   ~;  76   |;  25   &)
%                                         (   3 <=>;   1  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   42 (  30   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f116,plain,
    $false,
    inference(resolution,[],[f115,f55]) ).

fof(f55,plain,
    ~ in(sK0,sK2),
    inference(trivial_inequality_removal,[],[f54]) ).

fof(f54,plain,
    ( singleton(sK0) != singleton(sK0)
    | ~ in(sK0,sK2) ),
    inference(superposition,[],[f26,f51]) ).

fof(f51,plain,
    singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2),
    inference(duplicate_literal_removal,[],[f50]) ).

fof(f50,plain,
    ( singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2)
    | singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
    inference(resolution,[],[f48,f32]) ).

fof(f32,plain,
    ! [X2,X1] :
      ( in(X1,X2)
      | set_difference(unordered_pair(X1,X1),X2) = singleton(X1) ),
    inference(equality_resolution,[],[f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | X0 != X1
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f15]) ).

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

fof(f14,plain,
    ! [X0,X1,X2] :
      ( ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
        | ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_zfmisc_1) ).

fof(f48,plain,
    ( ~ in(sK0,sK2)
    | singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
    inference(trivial_inequality_removal,[],[f47]) ).

fof(f47,plain,
    ( singleton(sK0) != singleton(sK0)
    | ~ in(sK0,sK2)
    | singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
    inference(superposition,[],[f26,f42]) ).

fof(f42,plain,
    ( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
    | singleton(sK0) = set_difference(unordered_pair(sK0,sK0),sK2) ),
    inference(resolution,[],[f32,f20]) ).

fof(f20,plain,
    ( ~ in(sK0,sK2)
    | set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( ( ( sK0 != sK1
        & ~ in(sK1,sK2) )
      | in(sK0,sK2)
      | set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) )
    & ( ( ( sK0 = sK1
          | in(sK1,sK2) )
        & ~ in(sK0,sK2) )
      | set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0,X1,X2] :
        ( ( ( X0 != X1
            & ~ in(X1,X2) )
          | in(X0,X2)
          | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
        & ( ( ( X0 = X1
              | in(X1,X2) )
            & ~ in(X0,X2) )
          | set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) )
   => ( ( ( sK0 != sK1
          & ~ in(sK1,sK2) )
        | in(sK0,sK2)
        | set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) )
      & ( ( ( sK0 = sK1
            | in(sK1,sK2) )
          & ~ in(sK0,sK2) )
        | set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1,X2] :
      ( ( ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2)
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ? [X0,X1,X2] :
      ( ( ( X0 != X1
          & ~ in(X1,X2) )
        | in(X0,X2)
        | set_difference(unordered_pair(X0,X1),X2) != singleton(X0) )
      & ( ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) )
        | set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ) ),
    inference(nnf_transformation,[],[f8]) ).

fof(f8,plain,
    ? [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <~> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      <=> ( ( X0 = X1
            | in(X1,X2) )
          & ~ in(X0,X2) ) ),
    inference(negated_conjecture,[],[f5]) ).

fof(f5,conjecture,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
    <=> ( ( X0 = X1
          | in(X1,X2) )
        & ~ in(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t70_zfmisc_1) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f115,plain,
    in(sK0,sK2),
    inference(trivial_inequality_removal,[],[f114]) ).

fof(f114,plain,
    ( sK0 != sK0
    | in(sK0,sK2) ),
    inference(backward_demodulation,[],[f53,f112]) ).

fof(f112,plain,
    sK0 = sK1,
    inference(duplicate_literal_removal,[],[f109]) ).

fof(f109,plain,
    ( sK0 = sK1
    | sK0 = sK1 ),
    inference(resolution,[],[f98,f90]) ).

fof(f90,plain,
    ( in(sK1,sK2)
    | sK0 = sK1 ),
    inference(trivial_inequality_removal,[],[f89]) ).

fof(f89,plain,
    ( singleton(sK0) != singleton(sK0)
    | in(sK1,sK2)
    | sK0 = sK1 ),
    inference(duplicate_literal_removal,[],[f85]) ).

fof(f85,plain,
    ( singleton(sK0) != singleton(sK0)
    | in(sK1,sK2)
    | sK0 = sK1
    | sK0 = sK1 ),
    inference(superposition,[],[f27,f83]) ).

fof(f83,plain,
    ( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
    | sK0 = sK1 ),
    inference(duplicate_literal_removal,[],[f80]) ).

fof(f80,plain,
    ( set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0)
    | sK0 = sK1
    | set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
    inference(resolution,[],[f79,f21]) ).

fof(f21,plain,
    ( in(sK1,sK2)
    | sK0 = sK1
    | set_difference(unordered_pair(sK0,sK1),sK2) = singleton(sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ in(X0,sK2)
      | singleton(sK0) = set_difference(unordered_pair(sK0,X0),sK2) ),
    inference(resolution,[],[f28,f55]) ).

fof(f28,plain,
    ! [X2,X0,X1] :
      ( in(X0,X2)
      | ~ in(X1,X2)
      | set_difference(unordered_pair(X0,X1),X2) = singleton(X0) ),
    inference(cnf_transformation,[],[f15]) ).

fof(f27,plain,
    ! [X2,X0,X1] :
      ( set_difference(unordered_pair(X0,X1),X2) != singleton(X0)
      | in(X1,X2)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f15]) ).

fof(f98,plain,
    ( ~ in(sK1,sK2)
    | sK0 = sK1 ),
    inference(resolution,[],[f91,f55]) ).

fof(f91,plain,
    ( in(sK0,sK2)
    | ~ in(sK1,sK2)
    | sK0 = sK1 ),
    inference(trivial_inequality_removal,[],[f84]) ).

fof(f84,plain,
    ( singleton(sK0) != singleton(sK0)
    | in(sK0,sK2)
    | ~ in(sK1,sK2)
    | sK0 = sK1 ),
    inference(superposition,[],[f22,f83]) ).

fof(f22,plain,
    ( set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0)
    | in(sK0,sK2)
    | ~ in(sK1,sK2) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f53,plain,
    ( sK0 != sK1
    | in(sK0,sK2) ),
    inference(trivial_inequality_removal,[],[f52]) ).

fof(f52,plain,
    ( singleton(sK0) != singleton(sK0)
    | in(sK0,sK2)
    | sK0 != sK1 ),
    inference(backward_demodulation,[],[f33,f51]) ).

fof(f33,plain,
    ( singleton(sK0) != set_difference(unordered_pair(sK0,sK0),sK2)
    | in(sK0,sK2)
    | sK0 != sK1 ),
    inference(inner_rewriting,[],[f23]) ).

fof(f23,plain,
    ( sK0 != sK1
    | in(sK0,sK2)
    | set_difference(unordered_pair(sK0,sK1),sK2) != singleton(sK0) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET927+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.33  % Computer : n025.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit   : 300
% 0.10/0.33  % WCLimit    : 300
% 0.10/0.33  % DateTime   : Tue Apr 30 01:54:26 EDT 2024
% 0.10/0.34  % CPUTime    : 
% 0.10/0.34  % (8297)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.35  % (8300)WARNING: value z3 for option sas not known
% 0.10/0.35  % (8300)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)
% 0.10/0.35  % (8299)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.35  % (8305)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)
% 0.10/0.35  % (8302)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)
% 0.10/0.35  % (8298)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.35  % (8304)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)
% 0.10/0.35  % (8301)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.35  TRYING [1]
% 0.10/0.35  TRYING [2]
% 0.10/0.36  TRYING [3]
% 0.10/0.36  TRYING [1]
% 0.10/0.36  TRYING [1]
% 0.10/0.36  TRYING [2]
% 0.10/0.36  % (8304)First to succeed.
% 0.10/0.36  TRYING [2]
% 0.10/0.36  TRYING [3]
% 0.10/0.36  % (8300)Also succeeded, but the first one will report.
% 0.10/0.36  TRYING [4]
% 0.10/0.36  % (8304)Refutation found. Thanks to Tanya!
% 0.10/0.36  % SZS status Theorem for theBenchmark
% 0.10/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.36  % (8304)------------------------------
% 0.10/0.36  % (8304)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.36  % (8304)Termination reason: Refutation
% 0.10/0.36  
% 0.10/0.36  % (8304)Memory used [KB]: 776
% 0.10/0.36  % (8304)Time elapsed: 0.006 s
% 0.10/0.36  % (8304)Instructions burned: 9 (million)
% 0.10/0.36  % (8304)------------------------------
% 0.10/0.36  % (8304)------------------------------
% 0.10/0.36  % (8297)Success in time 0.019 s
%------------------------------------------------------------------------------