TSTP Solution File: SEU147+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 12:38:45 EDT 2022
% Result : Theorem 0.15s 0.37s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 19 unt; 0 def)
% Number of atoms : 149 ( 79 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 152 ( 64 ~; 69 |; 6 &)
% ( 12 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 73 ( 1 sgn 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ) ).
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set) ).
fof(t3_xboole_1,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ) ).
fof(subgoal_0,plain,
powerset(empty_set) = singleton(empty_set),
inference(strip,[],[t1_zfmisc_1]) ).
fof(negate_0_0,plain,
powerset(empty_set) != singleton(empty_set),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_1,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] :
( ( B != powerset(A)
| ~ in(C,B)
| subset(C,A) )
& ( B != powerset(A)
| ~ subset(C,A)
| in(C,B) )
& ( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| subset(skolemFOFtoCNF_C_1(A,B),A) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),A)
| B = powerset(A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(canonicalize,[],[d1_tarski]) ).
fof(normalize_0_5,plain,
! [A,B] :
( B != singleton(A)
<=> ? [C] :
( C != A
<=> in(C,B) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B,C] :
( ( B != singleton(A)
| C != A
| in(C,B) )
& ( B != singleton(A)
| ~ in(C,B)
| C = A )
& ( skolemFOFtoCNF_C(A,B) != A
| ~ in(skolemFOFtoCNF_C(A,B),B)
| B = singleton(A) )
& ( B = singleton(A)
| skolemFOFtoCNF_C(A,B) = A
| in(skolemFOFtoCNF_C(A,B),B) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[t3_xboole_1]) ).
fof(normalize_0_9,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( B = powerset(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| subset(skolemFOFtoCNF_C_1(A,B),A) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
powerset(empty_set) != singleton(empty_set),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( B != singleton(A)
| C != A
| in(C,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [A] : subset(A,A),
inference(canonicalize,[],[reflexivity_r1_tarski]) ).
fof(normalize_0_14,plain,
! [A] : subset(A,A),
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),A)
| B = powerset(A) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),singleton(empty_set))
| ~ subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set)
| singleton(empty_set) = powerset(empty_set) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(empty_set)),bind(B,$fot(singleton(empty_set)))]]) ).
cnf(refute_0_2,plain,
( B != singleton(A)
| ~ in(C,B)
| C = A ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( singleton(A) != singleton(A)
| ~ in(C,singleton(A))
| C = A ),
inference(subst,[],[refute_0_2:[bind(B,$fot(singleton(A)))]]) ).
cnf(refute_0_4,plain,
singleton(A) = singleton(A),
introduced(tautology,[refl,[$fot(singleton(A))]]) ).
cnf(refute_0_5,plain,
( ~ in(C,singleton(A))
| C = A ),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ in(skolemFOFtoCNF_C_1(empty_set,singleton(A)),singleton(A))
| skolemFOFtoCNF_C_1(empty_set,singleton(A)) = A ),
inference(subst,[],[refute_0_5:[bind(C,$fot(skolemFOFtoCNF_C_1(empty_set,singleton(A))))]]) ).
cnf(refute_0_7,plain,
( ~ subset(A,empty_set)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ subset(skolemFOFtoCNF_C_1(empty_set,X_20),empty_set)
| skolemFOFtoCNF_C_1(empty_set,X_20) = empty_set ),
inference(subst,[],[refute_0_7:[bind(A,$fot(skolemFOFtoCNF_C_1(empty_set,X_20)))]]) ).
cnf(refute_0_9,plain,
( B = powerset(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| subset(skolemFOFtoCNF_C_1(A,B),A) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( X_20 = powerset(empty_set)
| in(skolemFOFtoCNF_C_1(empty_set,X_20),X_20)
| subset(skolemFOFtoCNF_C_1(empty_set,X_20),empty_set) ),
inference(subst,[],[refute_0_9:[bind(A,$fot(empty_set)),bind(B,$fot(X_20))]]) ).
cnf(refute_0_11,plain,
( X_20 = powerset(empty_set)
| skolemFOFtoCNF_C_1(empty_set,X_20) = empty_set
| in(skolemFOFtoCNF_C_1(empty_set,X_20),X_20) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(empty_set,X_20),empty_set) )],[refute_0_10,refute_0_8]) ).
cnf(refute_0_12,plain,
( singleton(A) = powerset(empty_set)
| skolemFOFtoCNF_C_1(empty_set,singleton(A)) = empty_set
| in(skolemFOFtoCNF_C_1(empty_set,singleton(A)),singleton(A)) ),
inference(subst,[],[refute_0_11:[bind(X_20,$fot(singleton(A)))]]) ).
cnf(refute_0_13,plain,
( singleton(A) = powerset(empty_set)
| skolemFOFtoCNF_C_1(empty_set,singleton(A)) = A
| skolemFOFtoCNF_C_1(empty_set,singleton(A)) = empty_set ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(empty_set,singleton(A)),singleton(A)) )],[refute_0_12,refute_0_6]) ).
cnf(refute_0_14,plain,
( singleton(empty_set) = powerset(empty_set)
| skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)) = empty_set ),
inference(subst,[],[refute_0_13:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_15,plain,
powerset(empty_set) != singleton(empty_set),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
( singleton(empty_set) != powerset(empty_set)
| powerset(empty_set) = singleton(empty_set) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(singleton(empty_set))),bind(Y,$fot(powerset(empty_set)))]]) ).
cnf(refute_0_20,plain,
singleton(empty_set) != powerset(empty_set),
inference(resolve,[$cnf( $equal(powerset(empty_set),singleton(empty_set)) )],[refute_0_19,refute_0_15]) ).
cnf(refute_0_21,plain,
skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)) = empty_set,
inference(resolve,[$cnf( $equal(singleton(empty_set),powerset(empty_set)) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
( skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)) != empty_set
| ~ in(empty_set,singleton(empty_set))
| in(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),singleton(empty_set)) ),
introduced(tautology,[equality,[$cnf( ~ in(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),singleton(empty_set)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_23,plain,
( ~ in(empty_set,singleton(empty_set))
| in(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),singleton(empty_set)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ in(empty_set,singleton(empty_set))
| ~ subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set)
| singleton(empty_set) = powerset(empty_set) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),singleton(empty_set)) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
( skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)) != empty_set
| ~ subset(empty_set,empty_set)
| subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_26,plain,
( ~ subset(empty_set,empty_set)
| subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ in(empty_set,singleton(empty_set))
| ~ subset(empty_set,empty_set)
| singleton(empty_set) = powerset(empty_set) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(empty_set,singleton(empty_set)),empty_set) )],[refute_0_26,refute_0_24]) ).
cnf(refute_0_28,plain,
( B != singleton(A)
| C != A
| in(C,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_29,plain,
( A != A
| singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(subst,[],[refute_0_28:[bind(B,$fot(singleton(A))),bind(C,$fot(A))]]) ).
cnf(refute_0_30,plain,
A = A,
introduced(tautology,[refl,[$fot(A)]]) ).
cnf(refute_0_31,plain,
( singleton(A) != singleton(A)
| in(A,singleton(A)) ),
inference(resolve,[$cnf( $equal(A,A) )],[refute_0_30,refute_0_29]) ).
cnf(refute_0_32,plain,
in(A,singleton(A)),
inference(resolve,[$cnf( $equal(singleton(A),singleton(A)) )],[refute_0_4,refute_0_31]) ).
cnf(refute_0_33,plain,
in(empty_set,singleton(empty_set)),
inference(subst,[],[refute_0_32:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_34,plain,
( ~ subset(empty_set,empty_set)
| singleton(empty_set) = powerset(empty_set) ),
inference(resolve,[$cnf( in(empty_set,singleton(empty_set)) )],[refute_0_33,refute_0_27]) ).
cnf(refute_0_35,plain,
subset(A,A),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_36,plain,
subset(empty_set,empty_set),
inference(subst,[],[refute_0_35:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_37,plain,
singleton(empty_set) = powerset(empty_set),
inference(resolve,[$cnf( subset(empty_set,empty_set) )],[refute_0_36,refute_0_34]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( $equal(singleton(empty_set),powerset(empty_set)) )],[refute_0_37,refute_0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU147+3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jun 18 22:16:25 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.37
% 0.15/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.15/0.38
%------------------------------------------------------------------------------