TSTP Solution File: SWW469+5 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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 : Thu Jul 21 00:59:44 EDT 2022

% Result   : Theorem 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   33 (  20 unt;   0 def)
%            Number of atoms       :   51 (  41 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   43 (  25   ~;  15   |;   1   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-2 aty)
%            Number of variables   :   40 (  12 sgn  13   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_0_state__not__singleton__def,axiom,
    ( hBOOL(hoare_1883395792gleton)
  <=> ? [S,T] : ti(state,S) != ti(state,T) ) ).

fof(conj_0,hypothesis,
    hBOOL(hoare_1883395792gleton) ).

fof(conj_1,conjecture,
    ! [T] :
      ~ ! [S] : ti(state,S) = ti(state,T) ).

fof(subgoal_0,plain,
    ! [T] :
      ~ ! [S] : ti(state,S) = ti(state,T),
    inference(strip,[],[conj_1]) ).

fof(negate_0_0,plain,
    ~ ! [T] :
        ~ ! [S] : ti(state,S) = ti(state,T),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ( ~ hBOOL(hoare_1883395792gleton)
  <=> ! [S,T] : ti(state,S) = ti(state,T) ),
    inference(canonicalize,[],[fact_0_state__not__singleton__def]) ).

fof(normalize_0_1,plain,
    ! [S,T] :
      ( ( ti(state,skolemFOFtoCNF_S) != ti(state,skolemFOFtoCNF_T)
        | ~ hBOOL(hoare_1883395792gleton) )
      & ( ti(state,S) = ti(state,T)
        | hBOOL(hoare_1883395792gleton) ) ),
    inference(clausify,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ( ti(state,skolemFOFtoCNF_S) != ti(state,skolemFOFtoCNF_T)
    | ~ hBOOL(hoare_1883395792gleton) ),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    hBOOL(hoare_1883395792gleton),
    inference(canonicalize,[],[conj_0]) ).

fof(normalize_0_4,plain,
    ? [T] :
    ! [S] : ti(state,S) = ti(state,T),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ! [S] : ti(state,S) = ti(state,skolemFOFtoCNF_T_1),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [S] : ti(state,S) = ti(state,skolemFOFtoCNF_T_1),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ti(state,skolemFOFtoCNF_S) != ti(state,skolemFOFtoCNF_T)
    | ~ hBOOL(hoare_1883395792gleton) ),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    hBOOL(hoare_1883395792gleton),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_2,plain,
    ti(state,skolemFOFtoCNF_S) != ti(state,skolemFOFtoCNF_T),
    inference(resolve,[$cnf( hBOOL(hoare_1883395792gleton) )],[refute_0_1,refute_0_0]) ).

cnf(refute_0_3,plain,
    ti(state,S) = ti(state,skolemFOFtoCNF_T_1),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_4,plain,
    ti(state,X_1) = ti(state,skolemFOFtoCNF_T_1),
    inference(subst,[],[refute_0_3:[bind(S,$fot(X_1))]]) ).

cnf(refute_0_5,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_6,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_7,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ti(state,X_1) != ti(state,skolemFOFtoCNF_T_1)
    | ti(state,skolemFOFtoCNF_T_1) = ti(state,X_1) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(ti(state,X_1))),bind(Y,$fot(ti(state,skolemFOFtoCNF_T_1)))]]) ).

cnf(refute_0_9,plain,
    ti(state,skolemFOFtoCNF_T_1) = ti(state,X_1),
    inference(resolve,[$cnf( $equal(ti(state,X_1),ti(state,skolemFOFtoCNF_T_1)) )],[refute_0_4,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ti(state,S) != ti(state,skolemFOFtoCNF_T_1)
    | ti(state,skolemFOFtoCNF_T_1) != ti(state,X_1)
    | ti(state,S) = ti(state,X_1) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(ti(state,S),ti(state,X_1)) ),[0],$fot(ti(state,skolemFOFtoCNF_T_1))]]) ).

cnf(refute_0_11,plain,
    ( ti(state,S) != ti(state,skolemFOFtoCNF_T_1)
    | ti(state,S) = ti(state,X_1) ),
    inference(resolve,[$cnf( $equal(ti(state,skolemFOFtoCNF_T_1),ti(state,X_1)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ti(state,S) = ti(state,X_1),
    inference(resolve,[$cnf( $equal(ti(state,S),ti(state,skolemFOFtoCNF_T_1)) )],[refute_0_3,refute_0_11]) ).

cnf(refute_0_13,plain,
    ti(state,skolemFOFtoCNF_S) = ti(state,X_3),
    inference(subst,[],[refute_0_12:[bind(S,$fot(skolemFOFtoCNF_S)),bind(X_1,$fot(X_3))]]) ).

cnf(refute_0_14,plain,
    ( ti(state,X_3) != ti(state,skolemFOFtoCNF_T)
    | ti(state,skolemFOFtoCNF_S) != ti(state,X_3)
    | ti(state,skolemFOFtoCNF_S) = ti(state,skolemFOFtoCNF_T) ),
    introduced(tautology,[equality,[$cnf( $equal(ti(state,skolemFOFtoCNF_S),ti(state,X_3)) ),[1],$fot(ti(state,skolemFOFtoCNF_T))]]) ).

cnf(refute_0_15,plain,
    ( ti(state,X_3) != ti(state,skolemFOFtoCNF_T)
    | ti(state,skolemFOFtoCNF_S) = ti(state,skolemFOFtoCNF_T) ),
    inference(resolve,[$cnf( $equal(ti(state,skolemFOFtoCNF_S),ti(state,X_3)) )],[refute_0_13,refute_0_14]) ).

cnf(refute_0_16,plain,
    ti(state,X_3) != ti(state,skolemFOFtoCNF_T),
    inference(resolve,[$cnf( $equal(ti(state,skolemFOFtoCNF_S),ti(state,skolemFOFtoCNF_T)) )],[refute_0_15,refute_0_2]) ).

cnf(refute_0_17,plain,
    ( ti(state,S) != ti(state,X_1)
    | ti(state,X_1) = ti(state,S) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(ti(state,S))),bind(Y,$fot(ti(state,X_1)))]]) ).

cnf(refute_0_18,plain,
    ti(state,X_1) = ti(state,S),
    inference(resolve,[$cnf( $equal(ti(state,S),ti(state,X_1)) )],[refute_0_12,refute_0_17]) ).

cnf(refute_0_19,plain,
    ti(state,X_3) = ti(state,skolemFOFtoCNF_T),
    inference(subst,[],[refute_0_18:[bind(S,$fot(skolemFOFtoCNF_T)),bind(X_1,$fot(X_3))]]) ).

cnf(refute_0_20,plain,
    $false,
    inference(resolve,[$cnf( $equal(ti(state,X_3),ti(state,skolemFOFtoCNF_T)) )],[refute_0_19,refute_0_16]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SWW469+5 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n017.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  : 600
% 0.13/0.34  % DateTime : Sat Jun  4 20:25:30 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.58  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.58  
% 0.21/0.58  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.58  
%------------------------------------------------------------------------------