TSTP Solution File: SET878+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET878+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 : n027.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 18:25:59 EDT 2022

% Result   : Theorem 0.21s 0.57s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   31 (  17 unt;   0 def)
%            Number of atoms       :  108 (  78 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  125 (  48   ~;  45   |;  24   &)
%                                         (   4 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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;   2 con; 0-3 aty)
%            Number of variables   :   72 (  62   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f59,plain,
    $false,
    inference(trivial_inequality_removal,[],[f58]) ).

fof(f58,plain,
    singleton(sK4) != singleton(sK4),
    inference(backward_demodulation,[],[f49,f57]) ).

fof(f57,plain,
    ! [X0,X1] : set_intersection2(singleton(X1),unordered_pair(X0,X1)) = singleton(X1),
    inference(forward_demodulation,[],[f54,f32]) ).

fof(f32,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X1,X0] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f54,plain,
    ! [X0,X1] : set_intersection2(unordered_pair(X0,X1),singleton(X1)) = singleton(X1),
    inference(resolution,[],[f30,f45]) ).

fof(f45,plain,
    ! [X1,X4] : in(X4,unordered_pair(X1,X4)),
    inference(equality_resolution,[],[f44]) ).

fof(f44,plain,
    ! [X2,X1,X4] :
      ( in(X4,X2)
      | unordered_pair(X1,X4) != X2 ),
    inference(equality_resolution,[],[f36]) ).

fof(f36,plain,
    ! [X2,X0,X1,X4] :
      ( in(X4,X2)
      | X0 != X4
      | unordered_pair(X1,X0) != X2 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X0) = X2
        | ( ( ( sK1(X0,X1,X2) != X0
              & sK1(X0,X1,X2) != X1 )
            | ~ in(sK1(X0,X1,X2),X2) )
          & ( sK1(X0,X1,X2) = X0
            | sK1(X0,X1,X2) = X1
            | in(sK1(X0,X1,X2),X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X0 != X4
                & X1 != X4 ) )
            & ( X0 = X4
              | X1 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X1,X0) != X2 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ( X0 != X3
              & X1 != X3 )
            | ~ in(X3,X2) )
          & ( X0 = X3
            | X1 = X3
            | in(X3,X2) ) )
     => ( ( ( sK1(X0,X1,X2) != X0
            & sK1(X0,X1,X2) != X1 )
          | ~ in(sK1(X0,X1,X2),X2) )
        & ( sK1(X0,X1,X2) = X0
          | sK1(X0,X1,X2) = X1
          | in(sK1(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ( X0 != X3
                & X1 != X3 )
              | ~ in(X3,X2) )
            & ( X0 = X3
              | X1 = X3
              | in(X3,X2) ) ) )
      & ( ! [X4] :
            ( ( in(X4,X2)
              | ( X0 != X4
                & X1 != X4 ) )
            & ( X0 = X4
              | X1 = X4
              | ~ in(X4,X2) ) )
        | unordered_pair(X1,X0) != X2 ) ),
    inference(rectify,[],[f21]) ).

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

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( unordered_pair(X1,X0) = X2
        | ? [X3] :
            ( ( ( X0 != X3
                & X1 != X3 )
              | ~ in(X3,X2) )
            & ( X0 = X3
              | X1 = X3
              | in(X3,X2) ) ) )
      & ( ! [X3] :
            ( ( in(X3,X2)
              | ( X0 != X3
                & X1 != X3 ) )
            & ( X0 = X3
              | X1 = X3
              | ~ in(X3,X2) ) )
        | unordered_pair(X1,X0) != X2 ) ),
    inference(nnf_transformation,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1,X2] :
      ( unordered_pair(X1,X0) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X0 = X3
            | X1 = X3 ) ) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0,X2] :
      ( unordered_pair(X0,X1) = X2
    <=> ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).

fof(f30,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | set_intersection2(X0,singleton(X1)) = singleton(X1) ),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( set_intersection2(X0,singleton(X1)) = singleton(X1)
      | ~ in(X1,X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X1,X0] :
      ( in(X1,X0)
     => set_intersection2(X0,singleton(X1)) = singleton(X1) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0] :
      ( in(X0,X1)
     => singleton(X0) = set_intersection2(X1,singleton(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l32_zfmisc_1) ).

fof(f49,plain,
    set_intersection2(singleton(sK4),unordered_pair(sK3,sK4)) != singleton(sK4),
    inference(forward_demodulation,[],[f43,f42]) ).

fof(f42,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/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

fof(f43,plain,
    singleton(sK4) != set_intersection2(singleton(sK4),unordered_pair(sK4,sK3)),
    inference(cnf_transformation,[],[f29]) ).

fof(f29,plain,
    singleton(sK4) != set_intersection2(singleton(sK4),unordered_pair(sK4,sK3)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f27,f28]) ).

fof(f28,plain,
    ( ? [X0,X1] : set_intersection2(singleton(X1),unordered_pair(X1,X0)) != singleton(X1)
   => singleton(sK4) != set_intersection2(singleton(sK4),unordered_pair(sK4,sK3)) ),
    introduced(choice_axiom,[]) ).

fof(f27,plain,
    ? [X0,X1] : set_intersection2(singleton(X1),unordered_pair(X1,X0)) != singleton(X1),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ? [X1,X0] : singleton(X0) != set_intersection2(singleton(X0),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1] : singleton(X0) = set_intersection2(singleton(X0),unordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1] : singleton(X0) = set_intersection2(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SET878+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 : n027.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 14:43:16 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.55  % (8934)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.55  % (8957)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.56  % (8950)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)
% 0.21/0.56  % (8957)First to succeed.
% 0.21/0.57  % (8941)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.57  % (8950)Also succeeded, but the first one will report.
% 0.21/0.57  % (8957)Refutation found. Thanks to Tanya!
% 0.21/0.57  % SZS status Theorem for theBenchmark
% 0.21/0.57  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.57  % (8957)------------------------------
% 0.21/0.57  % (8957)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.57  % (8957)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.57  % (8957)Termination reason: Refutation
% 0.21/0.57  
% 0.21/0.57  % (8957)Memory used [KB]: 5373
% 0.21/0.57  % (8957)Time elapsed: 0.082 s
% 0.21/0.57  % (8957)Instructions burned: 3 (million)
% 0.21/0.57  % (8957)------------------------------
% 0.21/0.57  % (8957)------------------------------
% 0.21/0.57  % (8933)Success in time 0.213 s
%------------------------------------------------------------------------------