%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU113+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 12:38:27 EDT 2022
% Result : Theorem 0.42s 0.64s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 18 unt; 0 def)
% Number of atoms : 160 ( 13 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 169 ( 68 ~; 67 |; 19 &)
% ( 12 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 105 ( 3 sgn 56 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(d5_finsub_1,axiom,
! [A,B] :
( preboolean(B)
=> ( B = finite_subsets(A)
<=> ! [C] :
( in(C,B)
<=> ( subset(C,A)
& finite(C) ) ) ) ) ).
fof(dt_k5_finsub_1,axiom,
! [A] : preboolean(finite_subsets(A)) ).
fof(fc1_finsub_1,axiom,
! [A] :
( ~ empty(powerset(A))
& cup_closed(powerset(A))
& diff_closed(powerset(A))
& preboolean(powerset(A)) ) ).
fof(t26_finsub_1,conjecture,
! [A] : subset(finite_subsets(A),powerset(A)) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ) ).
fof(subgoal_0,plain,
! [A] : subset(finite_subsets(A),powerset(A)),
inference(strip,[],[t26_finsub_1]) ).
fof(negate_0_0,plain,
~ ! [A] : subset(finite_subsets(A),powerset(A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ subset(finite_subsets(A),powerset(A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(finite_subsets(skolemFOFtoCNF_A_4),powerset(skolemFOFtoCNF_A_4)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( ( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) )
& ( ~ in(C,A)
| ~ subset(A,B)
| in(C,B) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[t2_subset]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(canonicalize,[],[t3_subset]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ element(A,powerset(B))
<=> ~ subset(A,B) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ( ~ element(A,powerset(B))
| subset(A,B) )
& ( ~ subset(A,B)
| element(A,powerset(B)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( ~ preboolean(B)
| ( B != finite_subsets(A)
<=> ? [C] :
( ~ in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
inference(canonicalize,[],[d5_finsub_1]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ preboolean(B)
| ( B != finite_subsets(A)
<=> ? [C] :
( ~ in(C,B)
<=> ( finite(C)
& subset(C,A) ) ) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ( B != finite_subsets(A)
| ~ in(C,B)
| ~ preboolean(B)
| finite(C) )
& ( B != finite_subsets(A)
| ~ in(C,B)
| ~ preboolean(B)
| subset(C,A) )
& ( ~ preboolean(B)
| B = finite_subsets(A)
| finite(skolemFOFtoCNF_C_1(A,B))
| in(skolemFOFtoCNF_C_1(A,B),B) )
& ( ~ preboolean(B)
| B = finite_subsets(A)
| in(skolemFOFtoCNF_C_1(A,B),B)
| subset(skolemFOFtoCNF_C_1(A,B),A) )
& ( B != finite_subsets(A)
| ~ finite(C)
| ~ preboolean(B)
| ~ subset(C,A)
| in(C,B) )
& ( ~ finite(skolemFOFtoCNF_C_1(A,B))
| ~ in(skolemFOFtoCNF_C_1(A,B),B)
| ~ preboolean(B)
| ~ subset(skolemFOFtoCNF_C_1(A,B),A)
| B = finite_subsets(A) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A,B,C] :
( B != finite_subsets(A)
| ~ in(C,B)
| ~ preboolean(B)
| subset(C,A) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : preboolean(finite_subsets(A)),
inference(canonicalize,[],[dt_k5_finsub_1]) ).
fof(normalize_0_17,plain,
! [A] : preboolean(finite_subsets(A)),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B] :
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_19,plain,
( ! [A] : ~ empty(powerset(A))
& ! [A] : cup_closed(powerset(A))
& ! [A] : diff_closed(powerset(A))
& ! [A] : preboolean(powerset(A)) ),
inference(canonicalize,[],[fc1_finsub_1]) ).
fof(normalize_0_20,plain,
! [A] : ~ empty(powerset(A)),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A] : ~ empty(powerset(A)),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
~ subset(finite_subsets(skolemFOFtoCNF_A_4),powerset(skolemFOFtoCNF_A_4)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ in(skolemFOFtoCNF_C(finite_subsets(X_148),powerset(X_148)),powerset(X_148))
| subset(finite_subsets(X_148),powerset(X_148)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(finite_subsets(X_148))),bind(B,$fot(powerset(X_148)))]]) ).
cnf(refute_0_3,plain,
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_4,plain,
( ~ element(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137))
| empty(powerset(X_137))
| in(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137)) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_C(finite_subsets(X_137),X_138))),bind(B,$fot(powerset(X_137)))]]) ).
cnf(refute_0_5,plain,
( ~ subset(A,B)
| element(A,powerset(B)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ subset(skolemFOFtoCNF_C(finite_subsets(X_135),X_136),X_135)
| element(skolemFOFtoCNF_C(finite_subsets(X_135),X_136),powerset(X_135)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_C(finite_subsets(X_135),X_136))),bind(B,$fot(X_135))]]) ).
cnf(refute_0_7,plain,
( B != finite_subsets(A)
| ~ in(C,B)
| ~ preboolean(B)
| subset(C,A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_8,plain,
( finite_subsets(A) != finite_subsets(A)
| ~ in(C,finite_subsets(A))
| ~ preboolean(finite_subsets(A))
| subset(C,A) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(finite_subsets(A)))]]) ).
cnf(refute_0_9,plain,
finite_subsets(A) = finite_subsets(A),
introduced(tautology,[refl,[$fot(finite_subsets(A))]]) ).
cnf(refute_0_10,plain,
( ~ in(C,finite_subsets(A))
| ~ preboolean(finite_subsets(A))
| subset(C,A) ),
inference(resolve,[$cnf( $equal(finite_subsets(A),finite_subsets(A)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
preboolean(finite_subsets(A)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_12,plain,
( ~ in(C,finite_subsets(A))
| subset(C,A) ),
inference(resolve,[$cnf( preboolean(finite_subsets(A)) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
( ~ in(skolemFOFtoCNF_C(finite_subsets(A),X_62),finite_subsets(A))
| subset(skolemFOFtoCNF_C(finite_subsets(A),X_62),A) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(skolemFOFtoCNF_C(finite_subsets(A),X_62)))]]) ).
cnf(refute_0_14,plain,
( in(skolemFOFtoCNF_C(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( in(skolemFOFtoCNF_C(finite_subsets(A),X_62),finite_subsets(A))
| subset(finite_subsets(A),X_62) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(finite_subsets(A))),bind(B,$fot(X_62))]]) ).
cnf(refute_0_16,plain,
( subset(finite_subsets(A),X_62)
| subset(skolemFOFtoCNF_C(finite_subsets(A),X_62),A) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(finite_subsets(A),X_62),finite_subsets(A)) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
( subset(finite_subsets(X_135),X_136)
| subset(skolemFOFtoCNF_C(finite_subsets(X_135),X_136),X_135) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_135)),bind(X_62,$fot(X_136))]]) ).
cnf(refute_0_18,plain,
( element(skolemFOFtoCNF_C(finite_subsets(X_135),X_136),powerset(X_135))
| subset(finite_subsets(X_135),X_136) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C(finite_subsets(X_135),X_136),X_135) )],[refute_0_17,refute_0_6]) ).
cnf(refute_0_19,plain,
( element(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137))
| subset(finite_subsets(X_137),X_138) ),
inference(subst,[],[refute_0_18:[bind(X_135,$fot(X_137)),bind(X_136,$fot(X_138))]]) ).
cnf(refute_0_20,plain,
( empty(powerset(X_137))
| in(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137))
| subset(finite_subsets(X_137),X_138) ),
inference(resolve,[$cnf( element(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137)) )],[refute_0_19,refute_0_4]) ).
cnf(refute_0_21,plain,
~ empty(powerset(A)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_22,plain,
~ empty(powerset(X_137)),
inference(subst,[],[refute_0_21:[bind(A,$fot(X_137))]]) ).
cnf(refute_0_23,plain,
( in(skolemFOFtoCNF_C(finite_subsets(X_137),X_138),powerset(X_137))
| subset(finite_subsets(X_137),X_138) ),
inference(resolve,[$cnf( empty(powerset(X_137)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( in(skolemFOFtoCNF_C(finite_subsets(X_148),powerset(X_148)),powerset(X_148))
| subset(finite_subsets(X_148),powerset(X_148)) ),
inference(subst,[],[refute_0_23:[bind(X_137,$fot(X_148)),bind(X_138,$fot(powerset(X_148)))]]) ).
cnf(refute_0_25,plain,
subset(finite_subsets(X_148),powerset(X_148)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(finite_subsets(X_148),powerset(X_148)),powerset(X_148)) )],[refute_0_24,refute_0_2]) ).
cnf(refute_0_26,plain,
subset(finite_subsets(skolemFOFtoCNF_A_4),powerset(skolemFOFtoCNF_A_4)),
inference(subst,[],[refute_0_25:[bind(X_148,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_27,plain,
$false,
inference(resolve,[$cnf( subset(finite_subsets(skolemFOFtoCNF_A_4),powerset(skolemFOFtoCNF_A_4)) )],[refute_0_26,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU113+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n008.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 : Sun Jun 19 04:12:37 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.64
% 0.42/0.64 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.49/0.64
%------------------------------------------------------------------------------