TSTP Solution File: SET961+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n019.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 : Sat Sep  2 00:05:54 EDT 2023

% Result   : Theorem 0.16s 0.41s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   49 (   7 unt;   0 def)
%            Number of atoms       :  156 (  70 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  179 (  72   ~;  70   |;  27   &)
%                                         (   3 <=>;   6  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   86 (;  74   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f868,plain,
    $false,
    inference(trivial_inequality_removal,[],[f867]) ).

fof(f867,plain,
    empty_set != empty_set,
    inference(superposition,[],[f33,f723]) ).

fof(f723,plain,
    empty_set = sK0,
    inference(trivial_inequality_removal,[],[f667]) ).

fof(f667,plain,
    ( empty_set != empty_set
    | empty_set = sK0 ),
    inference(superposition,[],[f34,f665]) ).

fof(f665,plain,
    ( empty_set = sK1
    | empty_set = sK0 ),
    inference(trivial_inequality_removal,[],[f602]) ).

fof(f602,plain,
    ( sK0 != sK0
    | empty_set = sK0
    | empty_set = sK1 ),
    inference(superposition,[],[f35,f559]) ).

fof(f559,plain,
    ( sK0 = sK1
    | empty_set = sK0
    | empty_set = sK1 ),
    inference(resolution,[],[f529,f38]) ).

fof(f38,plain,
    ! [X0] :
      ( in(sK2(X0),X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0] :
      ( ( empty_set = X0
        | in(sK2(X0),X0) )
      & ( ! [X2] : ~ in(X2,X0)
        | empty_set != X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f20,f21]) ).

fof(f21,plain,
    ! [X0] :
      ( ? [X1] : in(X1,X0)
     => in(sK2(X0),X0) ),
    introduced(choice_axiom,[]) ).

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

fof(f19,plain,
    ! [X0] :
      ( ( empty_set = X0
        | ? [X1] : in(X1,X0) )
      & ( ! [X1] : ~ in(X1,X0)
        | empty_set != X0 ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] :
      ( empty_set = X0
    <=> ! [X1] : ~ in(X1,X0) ),
    file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',d1_xboole_0) ).

fof(f529,plain,
    ! [X3] :
      ( ~ in(X3,sK1)
      | sK0 = sK1
      | empty_set = sK0 ),
    inference(resolution,[],[f527,f38]) ).

fof(f527,plain,
    ! [X0,X1] :
      ( ~ in(X1,sK0)
      | ~ in(X0,sK1)
      | sK0 = sK1 ),
    inference(duplicate_literal_removal,[],[f510]) ).

fof(f510,plain,
    ! [X0,X1] :
      ( sK0 = sK1
      | ~ in(X0,sK1)
      | ~ in(X1,sK0)
      | sK0 = sK1 ),
    inference(resolution,[],[f509,f415]) ).

fof(f415,plain,
    ! [X0] :
      ( ~ in(sK3(sK1,sK0),sK1)
      | ~ in(X0,sK0)
      | sK0 = sK1 ),
    inference(factoring,[],[f118]) ).

fof(f118,plain,
    ! [X6,X5] :
      ( ~ in(sK3(X6,sK0),sK1)
      | ~ in(sK3(X6,sK0),X6)
      | ~ in(X5,sK0)
      | sK0 = X6 ),
    inference(resolution,[],[f104,f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ in(sK3(X0,X1),X1)
      | ~ in(sK3(X0,X1),X0)
      | X0 = X1 ),
    inference(cnf_transformation,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ( ( ~ in(sK3(X0,X1),X1)
          | ~ in(sK3(X0,X1),X0) )
        & ( in(sK3(X0,X1),X1)
          | in(sK3(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f23,f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) )
     => ( ( ~ in(sK3(X0,X1),X1)
          | ~ in(sK3(X0,X1),X0) )
        & ( in(sK3(X0,X1),X1)
          | in(sK3(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( ( ~ in(X2,X1)
            | ~ in(X2,X0) )
          & ( in(X2,X1)
            | in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ? [X2] :
          ( in(X2,X0)
        <~> in(X2,X1) ) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X0)
        <=> in(X2,X1) )
     => X0 = X1 ),
    file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',t2_tarski) ).

fof(f104,plain,
    ! [X8,X9] :
      ( in(X8,sK0)
      | ~ in(X9,sK0)
      | ~ in(X8,sK1) ),
    inference(resolution,[],[f47,f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
      | in(X1,sK0) ),
    inference(superposition,[],[f46,f32]) ).

fof(f32,plain,
    cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0),
    inference(cnf_transformation,[],[f18]) ).

fof(f18,plain,
    ( sK0 != sK1
    & empty_set != sK1
    & empty_set != sK0
    & cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f17]) ).

fof(f17,plain,
    ( ? [X0,X1] :
        ( X0 != X1
        & empty_set != X1
        & empty_set != X0
        & cartesian_product2(X0,X1) = cartesian_product2(X1,X0) )
   => ( sK0 != sK1
      & empty_set != sK1
      & empty_set != sK0
      & cartesian_product2(sK0,sK1) = cartesian_product2(sK1,sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f14,plain,
    ? [X0,X1] :
      ( X0 != X1
      & empty_set != X1
      & empty_set != X0
      & cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
    inference(flattening,[],[f13]) ).

fof(f13,plain,
    ? [X0,X1] :
      ( X0 != X1
      & empty_set != X1
      & empty_set != X0
      & cartesian_product2(X0,X1) = cartesian_product2(X1,X0) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,negated_conjecture,
    ~ ! [X0,X1] :
        ( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
       => ( X0 = X1
          | empty_set = X1
          | empty_set = X0 ) ),
    inference(negated_conjecture,[],[f10]) ).

fof(f10,conjecture,
    ! [X0,X1] :
      ( cartesian_product2(X0,X1) = cartesian_product2(X1,X0)
     => ( X0 = X1
        | empty_set = X1
        | empty_set = X0 ) ),
    file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',t114_zfmisc_1) ).

fof(f46,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X1,X3) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
        | ~ in(X1,X3)
        | ~ in(X0,X2) )
      & ( ( in(X1,X3)
          & in(X0,X2) )
        | ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
    inference(nnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2,X3] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
    <=> ( in(X1,X3)
        & in(X0,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184',l55_zfmisc_1) ).

fof(f47,plain,
    ! [X2,X3,X0,X1] :
      ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | ~ in(X1,X3)
      | ~ in(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f509,plain,
    ! [X0] :
      ( in(sK3(sK1,sK0),sK1)
      | sK0 = sK1
      | ~ in(X0,sK1) ),
    inference(duplicate_literal_removal,[],[f493]) ).

fof(f493,plain,
    ! [X0] :
      ( ~ in(X0,sK1)
      | sK0 = sK1
      | sK0 = sK1
      | in(sK3(sK1,sK0),sK1) ),
    inference(resolution,[],[f488,f43]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( in(sK3(X0,X1),X1)
      | X0 = X1
      | in(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f25]) ).

fof(f488,plain,
    ! [X0] :
      ( ~ in(sK3(sK1,sK0),sK0)
      | ~ in(X0,sK1)
      | sK0 = sK1 ),
    inference(factoring,[],[f425]) ).

fof(f425,plain,
    ! [X6,X5] :
      ( ~ in(sK3(sK1,sK0),sK0)
      | ~ in(X6,sK1)
      | ~ in(X5,sK0)
      | sK0 = sK1 ),
    inference(resolution,[],[f415,f105]) ).

fof(f105,plain,
    ! [X10,X11] :
      ( in(X11,sK1)
      | ~ in(X11,sK0)
      | ~ in(X10,sK1) ),
    inference(resolution,[],[f47,f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(sK0,sK1))
      | in(X0,sK1) ),
    inference(superposition,[],[f45,f32]) ).

fof(f45,plain,
    ! [X2,X3,X0,X1] :
      ( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
      | in(X0,X2) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f35,plain,
    sK0 != sK1,
    inference(cnf_transformation,[],[f18]) ).

fof(f34,plain,
    empty_set != sK1,
    inference(cnf_transformation,[],[f18]) ).

fof(f33,plain,
    empty_set != sK0,
    inference(cnf_transformation,[],[f18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12  % Problem    : SET961+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.09/0.13  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.12/0.33  % Computer : n019.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Wed Aug 30 15:48:42 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.12/0.39  % (28291)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.39  % (28295)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.12/0.39  % (28296)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 Vampire---4 for (531ds/0Mi)
% 0.12/0.39  % (28293)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.12/0.39  % (28294)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 Vampire---4 for (569ds/0Mi)
% 0.12/0.39  % (28298)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 Vampire---4 for (497ds/0Mi)
% 0.12/0.39  % (28292)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.12/0.39  % (28297)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 Vampire---4 for (522ds/0Mi)
% 0.12/0.39  Detected minimum model sizes of [3]
% 0.12/0.39  Detected maximum model sizes of [max]
% 0.12/0.39  TRYING [3]
% 0.12/0.39  Detected minimum model sizes of [3]
% 0.12/0.39  Detected maximum model sizes of [max]
% 0.12/0.39  TRYING [3]
% 0.12/0.40  TRYING [4]
% 0.12/0.40  TRYING [5]
% 0.12/0.40  TRYING [4]
% 0.16/0.41  % (28297)First to succeed.
% 0.16/0.41  % (28297)Refutation found. Thanks to Tanya!
% 0.16/0.41  % SZS status Theorem for Vampire---4
% 0.16/0.41  % SZS output start Proof for Vampire---4
% See solution above
% 0.16/0.41  % (28297)------------------------------
% 0.16/0.41  % (28297)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.41  % (28297)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.41  % (28297)Termination reason: Refutation
% 0.16/0.41  
% 0.16/0.41  % (28297)Memory used [KB]: 1279
% 0.16/0.41  % (28297)Time elapsed: 0.022 s
% 0.16/0.41  % (28297)------------------------------
% 0.16/0.41  % (28297)------------------------------
% 0.16/0.41  % (28291)Success in time 0.081 s
% 0.16/0.41  28294 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.4HLULQcqRV/Vampire---4.8_28184
% 0.16/0.41  % (28294)------------------------------
% 0.16/0.41  % (28294)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.16/0.41  % (28294)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.16/0.41  % (28294)Termination reason: Unknown
% 0.16/0.41  % (28294)Termination phase: Saturation
% 0.16/0.41  
% 0.16/0.41  % (28294)Memory used [KB]: 5373
% 0.16/0.41  % (28294)Time elapsed: 0.024 s
% 0.16/0.41  % (28294)------------------------------
% 0.16/0.41  % (28294)------------------------------
% 0.16/0.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------