TSTP Solution File: SEU140+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %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  : 600s
% DateTime : Tue Jul 19 12:38:40 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   45 (  14 unt;   0 def)
%            Number of atoms       :   85 (  26 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   73 (  33   ~;  24   |;   8   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   49 (   0 sgn  36   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(d7_xboole_0,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> set_intersection2(A,B) = empty_set ) ).

fof(t26_xboole_1,axiom,
    ! [A,B,C] :
      ( subset(A,B)
     => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ).

fof(t3_xboole_1,axiom,
    ! [A] :
      ( subset(A,empty_set)
     => A = empty_set ) ).

fof(t63_xboole_1,conjecture,
    ! [A,B,C] :
      ( ( subset(A,B)
        & disjoint(B,C) )
     => disjoint(A,C) ) ).

fof(subgoal_0,plain,
    ! [A,B,C] :
      ( ( subset(A,B)
        & disjoint(B,C) )
     => disjoint(A,C) ),
    inference(strip,[],[t63_xboole_1]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C] :
        ( ( subset(A,B)
          & disjoint(B,C) )
       => disjoint(A,C) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [A,B] :
      ( set_intersection2(A,B) != empty_set
    <=> ~ disjoint(A,B) ),
    inference(canonicalize,[],[d7_xboole_0]) ).

fof(normalize_0_1,plain,
    ! [A,B] :
      ( set_intersection2(A,B) != empty_set
    <=> ~ disjoint(A,B) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [A,B] :
      ( ( set_intersection2(A,B) != empty_set
        | disjoint(A,B) )
      & ( ~ disjoint(A,B)
        | set_intersection2(A,B) = empty_set ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,B] :
      ( set_intersection2(A,B) != empty_set
      | disjoint(A,B) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [A] :
      ( ~ subset(A,empty_set)
      | A = empty_set ),
    inference(canonicalize,[],[t3_xboole_1]) ).

fof(normalize_0_5,plain,
    ! [A] :
      ( ~ subset(A,empty_set)
      | A = empty_set ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ? [A,B,C] :
      ( ~ disjoint(A,C)
      & disjoint(B,C)
      & subset(A,B) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_7,plain,
    ( ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)
    & disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(canonicalize,[],[t26_xboole_1]) ).

fof(normalize_0_10,plain,
    ! [A,B] :
      ( ~ subset(A,B)
      | ! [C] : subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [A,B,C] :
      ( ~ subset(A,B)
      | subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(clausify,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_13,plain,
    ! [A,B] :
      ( ~ disjoint(A,B)
      | set_intersection2(A,B) = empty_set ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_14,plain,
    ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(conjunct,[],[normalize_0_7]) ).

cnf(refute_0_0,plain,
    ( set_intersection2(A,B) != empty_set
    | disjoint(A,B) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != empty_set
    | disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
    inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_2,plain,
    ( ~ subset(A,empty_set)
    | A = empty_set ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set)
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
    inference(subst,[],[refute_0_2:[bind(A,$fot(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C)))]]) ).

cnf(refute_0_4,plain,
    subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_5,plain,
    ( ~ subset(A,B)
    | subset(set_intersection2(A,C),set_intersection2(B,C)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_6,plain,
    ( ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
    | subset(set_intersection2(skolemFOFtoCNF_A_2,X_27),set_intersection2(skolemFOFtoCNF_B,X_27)) ),
    inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_A_2)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(X_27))]]) ).

cnf(refute_0_7,plain,
    subset(set_intersection2(skolemFOFtoCNF_A_2,X_27),set_intersection2(skolemFOFtoCNF_B,X_27)),
    inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)),
    inference(subst,[],[refute_0_7:[bind(X_27,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_9,plain,
    disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_10,plain,
    ( ~ disjoint(A,B)
    | set_intersection2(A,B) = empty_set ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_11,plain,
    ( ~ disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    | set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = empty_set ),
    inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_C))]]) ).

cnf(refute_0_12,plain,
    set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) = empty_set,
    inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C) != empty_set
    | ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
    | subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),
    introduced(tautology,[equality,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) ),[1],$fot(empty_set)]]) ).

cnf(refute_0_14,plain,
    ( ~ subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
    | subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C),empty_set) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set),
    inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),set_intersection2(skolemFOFtoCNF_B,skolemFOFtoCNF_C)) )],[refute_0_8,refute_0_14]) ).

cnf(refute_0_16,plain,
    set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set,
    inference(resolve,[$cnf( subset(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_15,refute_0_3]) ).

cnf(refute_0_17,plain,
    ( empty_set != empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) != empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
    introduced(tautology,[equality,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) ),[1],$fot(empty_set)]]) ).

cnf(refute_0_18,plain,
    ( empty_set != empty_set
    | set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) = empty_set ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( empty_set != empty_set
    | disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) ),
    inference(resolve,[$cnf( $equal(set_intersection2(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),empty_set) )],[refute_0_18,refute_0_1]) ).

cnf(refute_0_20,plain,
    empty_set = empty_set,
    introduced(tautology,[refl,[$fot(empty_set)]]) ).

cnf(refute_0_21,plain,
    disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_20,refute_0_19]) ).

cnf(refute_0_22,plain,
    ~ disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( disjoint(skolemFOFtoCNF_A_2,skolemFOFtoCNF_C) )],[refute_0_21,refute_0_22]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SEU140+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n027.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  : 600
% 0.12/0.33  % DateTime : Sun Jun 19 05:15:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------