TSTP Solution File: SET881+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SET881+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 : n004.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 0.21s 0.51s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   29 (  15 unt;   0 def)
%            Number of atoms       :  110 (  77 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  130 (  49   ~;  48   |;  26   &)
%                                         (   5 <=>;   2  =>;   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    :   10 (  10 usr;   6 con; 0-3 aty)
%            Number of variables   :   56 (  48   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f77,plain,
    $false,
    inference(subsumption_resolution,[],[f76,f52]) ).

fof(f52,plain,
    empty_set != sF7,
    inference(definition_folding,[],[f32,f51,f50,f49]) ).

fof(f49,plain,
    singleton(sK1) = sF5,
    introduced(function_definition,[]) ).

fof(f50,plain,
    unordered_pair(sK1,sK2) = sF6,
    introduced(function_definition,[]) ).

fof(f51,plain,
    set_difference(sF5,sF6) = sF7,
    introduced(function_definition,[]) ).

fof(f32,plain,
    empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f18]) ).

fof(f18,plain,
    ( ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1))
   => empty_set != set_difference(singleton(sK1),unordered_pair(sK1,sK2)) ),
    introduced(choice_axiom,[]) ).

fof(f13,plain,
    ? [X0,X1] : empty_set != set_difference(singleton(X0),unordered_pair(X0,X1)),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,negated_conjecture,
    ~ ! [X1,X0] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
    inference(negated_conjecture,[],[f8]) ).

fof(f8,conjecture,
    ! [X1,X0] : empty_set = set_difference(singleton(X0),unordered_pair(X0,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

fof(f76,plain,
    empty_set = sF7,
    inference(backward_demodulation,[],[f51,f75]) ).

fof(f75,plain,
    empty_set = set_difference(sF5,sF6),
    inference(forward_demodulation,[],[f73,f49]) ).

fof(f73,plain,
    empty_set = set_difference(singleton(sK1),sF6),
    inference(resolution,[],[f41,f53]) ).

fof(f53,plain,
    in(sK1,sF6),
    inference(superposition,[],[f48,f50]) ).

fof(f48,plain,
    ! [X2,X3] : in(X3,unordered_pair(X3,X2)),
    inference(equality_resolution,[],[f47]) ).

fof(f47,plain,
    ! [X2,X3,X0] :
      ( in(X3,X0)
      | unordered_pair(X3,X2) != X0 ),
    inference(equality_resolution,[],[f36]) ).

fof(f36,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X0)
      | X1 != X3
      | unordered_pair(X1,X2) != X0 ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ( ( ~ in(sK3(X0,X1,X2),X0)
            | ( sK3(X0,X1,X2) != X2
              & sK3(X0,X1,X2) != X1 ) )
          & ( in(sK3(X0,X1,X2),X0)
            | sK3(X0,X1,X2) = X2
            | sK3(X0,X1,X2) = X1 ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,X0)
            | ( X2 != X4
              & X1 != X4 ) )
          & ( in(X4,X0)
            | X2 = X4
            | X1 = X4 ) )
     => ( ( ~ in(sK3(X0,X1,X2),X0)
          | ( sK3(X0,X1,X2) != X2
            & sK3(X0,X1,X2) != X1 ) )
        & ( in(sK3(X0,X1,X2),X0)
          | sK3(X0,X1,X2) = X2
          | sK3(X0,X1,X2) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

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

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

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ( ! [X3] :
            ( ( X2 = X3
              | X1 = X3
              | ~ in(X3,X0) )
            & ( in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) ) )
        | unordered_pair(X1,X2) != X0 )
      & ( unordered_pair(X1,X2) = X0
        | ? [X3] :
            ( ( ~ in(X3,X0)
              | ( X2 != X3
                & X1 != X3 ) )
            & ( in(X3,X0)
              | X2 = X3
              | X1 = X3 ) ) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( ( X2 = X3
            | X1 = X3 )
        <=> in(X3,X0) )
    <=> unordered_pair(X1,X2) = X0 ),
    inference(rectify,[],[f3]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( ! [X3] :
          ( in(X3,X2)
        <=> ( X1 = X3
            | X0 = X3 ) )
    <=> unordered_pair(X0,X1) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

fof(f41,plain,
    ! [X0,X1] :
      ( ~ in(X1,X0)
      | empty_set = set_difference(singleton(X1),X0) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(singleton(X1),X0)
        | ~ in(X1,X0) )
      & ( in(X1,X0)
        | empty_set != set_difference(singleton(X1),X0) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,plain,
    ! [X1,X0] :
      ( ( empty_set = set_difference(singleton(X0),X1)
        | ~ in(X0,X1) )
      & ( in(X0,X1)
        | empty_set != set_difference(singleton(X0),X1) ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X1,X0] :
      ( empty_set = set_difference(singleton(X0),X1)
    <=> in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SET881+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Tue Aug 30 14:25:05 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.21/0.50  % (8070)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.50  % (8058)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)
% 0.21/0.51  % (8042)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)
% 0.21/0.51  % (8061)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.51  % (8070)First to succeed.
% 0.21/0.51  % (8053)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.51  % (8050)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.51  TRYING [1]
% 0.21/0.51  TRYING [2]
% 0.21/0.51  TRYING [3]
% 0.21/0.51  TRYING [4]
% 0.21/0.51  % (8070)Refutation found. Thanks to Tanya!
% 0.21/0.51  % SZS status Theorem for theBenchmark
% 0.21/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51  % (8070)------------------------------
% 0.21/0.51  % (8070)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (8070)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (8070)Termination reason: Refutation
% 0.21/0.51  
% 0.21/0.51  % (8070)Memory used [KB]: 895
% 0.21/0.51  % (8070)Time elapsed: 0.106 s
% 0.21/0.51  % (8070)Instructions burned: 2 (million)
% 0.21/0.51  % (8070)------------------------------
% 0.21/0.51  % (8070)------------------------------
% 0.21/0.51  % (8039)Success in time 0.156 s
%------------------------------------------------------------------------------