TSTP Solution File: SET880+1 by SnakeForV-SAT---1.0

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%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n016.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 18:26:00 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   22 (   4 unt;   0 def)
%            Number of atoms       :   76 (  52 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :   88 (  34   ~;  30   |;  17   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 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   :   40 (  31   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f53,plain,
    $false,
    inference(subsumption_resolution,[],[f52,f28]) ).

fof(f28,plain,
    sK2 != sK1,
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ( sK2 != sK1
    & empty_set = set_difference(singleton(sK2),singleton(sK1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f14,f15]) ).

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

fof(f14,plain,
    ? [X0,X1] :
      ( X0 != X1
      & empty_set = set_difference(singleton(X1),singleton(X0)) ),
    inference(rectify,[],[f9]) ).

fof(f9,plain,
    ? [X1,X0] :
      ( X0 != X1
      & empty_set = set_difference(singleton(X0),singleton(X1)) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X1,X0] :
        ( empty_set = set_difference(singleton(X0),singleton(X1))
       => X0 = X1 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X1,X0] :
      ( empty_set = set_difference(singleton(X0),singleton(X1))
     => X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_zfmisc_1) ).

fof(f52,plain,
    sK2 = sK1,
    inference(trivial_inequality_removal,[],[f50]) ).

fof(f50,plain,
    ( empty_set != empty_set
    | sK2 = sK1 ),
    inference(superposition,[],[f46,f27]) ).

fof(f27,plain,
    empty_set = set_difference(singleton(sK2),singleton(sK1)),
    inference(cnf_transformation,[],[f16]) ).

fof(f46,plain,
    ! [X6,X7] :
      ( empty_set != set_difference(singleton(X6),singleton(X7))
      | X6 = X7 ),
    inference(resolution,[],[f26,f38]) ).

fof(f38,plain,
    ! [X2,X0] :
      ( ~ in(X2,singleton(X0))
      | X0 = X2 ),
    inference(equality_resolution,[],[f33]) ).

fof(f33,plain,
    ! [X2,X0,X1] :
      ( X0 = X2
      | ~ in(X2,X1)
      | singleton(X0) != X1 ),
    inference(cnf_transformation,[],[f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ( ( sK4(X0,X1) != X0
            | ~ in(sK4(X0,X1),X1) )
          & ( sK4(X0,X1) = X0
            | in(sK4(X0,X1),X1) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ( X0 != X3
            | ~ in(X3,X1) )
          & ( X0 = X3
            | in(X3,X1) ) )
     => ( ( sK4(X0,X1) != X0
          | ~ in(sK4(X0,X1),X1) )
        & ( sK4(X0,X1) = X0
          | in(sK4(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X3] :
            ( ( X0 != X3
              | ~ in(X3,X1) )
            & ( X0 = X3
              | in(X3,X1) ) ) ) ),
    inference(rectify,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ( in(X2,X1)
              | X0 != X2 )
            & ( X0 = X2
              | ~ in(X2,X1) ) )
        | singleton(X0) != X1 )
      & ( singleton(X0) = X1
        | ? [X2] :
            ( ( X0 != X2
              | ~ in(X2,X1) )
            & ( X0 = X2
              | in(X2,X1) ) ) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
        <=> X0 = X2 )
    <=> singleton(X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

fof(f26,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty_set != set_difference(singleton(X0),X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ( in(X0,X1)
        | empty_set != set_difference(singleton(X0),X1) )
      & ( empty_set = set_difference(singleton(X0),X1)
        | ~ in(X0,X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
    <=> empty_set = set_difference(singleton(X0),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET880+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:50:31 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.48  % (11367)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.48  % (11376)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.48  % (11367)Instruction limit reached!
% 0.20/0.48  % (11367)------------------------------
% 0.20/0.48  % (11367)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.48  % (11376)First to succeed.
% 0.20/0.48  % (11367)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.48  % (11367)Termination reason: Unknown
% 0.20/0.48  % (11367)Termination phase: Blocked clause elimination
% 0.20/0.48  
% 0.20/0.48  % (11367)Memory used [KB]: 895
% 0.20/0.48  % (11367)Time elapsed: 0.003 s
% 0.20/0.48  % (11367)Instructions burned: 2 (million)
% 0.20/0.48  % (11367)------------------------------
% 0.20/0.48  % (11367)------------------------------
% 0.20/0.49  % (11376)Refutation found. Thanks to Tanya!
% 0.20/0.49  % SZS status Theorem for theBenchmark
% 0.20/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.49  % (11376)------------------------------
% 0.20/0.49  % (11376)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.49  % (11376)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.49  % (11376)Termination reason: Refutation
% 0.20/0.49  
% 0.20/0.49  % (11376)Memory used [KB]: 5373
% 0.20/0.49  % (11376)Time elapsed: 0.081 s
% 0.20/0.49  % (11376)Instructions burned: 2 (million)
% 0.20/0.49  % (11376)------------------------------
% 0.20/0.49  % (11376)------------------------------
% 0.20/0.49  % (11355)Success in time 0.135 s
%------------------------------------------------------------------------------