TSTP Solution File: SET947+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% 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 03:38:33 EDT 2022
% Result : Theorem 0.21s 0.39s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 90 ( 11 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 88 ( 36 ~; 34 |; 7 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 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 : 70 ( 0 sgn 36 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d1_zfmisc_1,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ) ).
fof(l50_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ) ).
fof(t100_zfmisc_1,conjecture,
! [A] : subset(A,powerset(union(A))) ).
fof(subgoal_0,plain,
! [A] : subset(A,powerset(union(A))),
inference(strip,[],[t100_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A] : subset(A,powerset(union(A))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ subset(A,powerset(union(A))),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ subset(skolemFOFtoCNF_A_2,powerset(union(skolemFOFtoCNF_A_2))),
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_1(A,B),B)
| subset(A,B) )
& ( in(skolemFOFtoCNF_C_1(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_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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(A,B),B)
| ~ subset(skolemFOFtoCNF_C(A,B),A)
| B = powerset(A) )
& ( B = powerset(A)
| in(skolemFOFtoCNF_C(A,B),B)
| subset(skolemFOFtoCNF_C(A,B),A) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A,B] :
( ~ in(A,B)
| subset(A,union(B)) ),
inference(canonicalize,[],[l50_zfmisc_1]) ).
fof(normalize_0_11,plain,
! [A,B] :
( ~ in(A,B)
| subset(A,union(B)) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ subset(skolemFOFtoCNF_A_2,powerset(union(skolemFOFtoCNF_A_2))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ in(skolemFOFtoCNF_C_1(X_63,powerset(union(X_63))),powerset(union(X_63)))
| subset(X_63,powerset(union(X_63))) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_63)),bind(B,$fot(powerset(union(X_63))))]]) ).
cnf(refute_0_3,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_3:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_5,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_6,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ subset(skolemFOFtoCNF_C_1(X_55,X_56),union(X_55))
| in(skolemFOFtoCNF_C_1(X_55,X_56),powerset(union(X_55))) ),
inference(subst,[],[refute_0_6:[bind(A,$fot(union(X_55))),bind(C,$fot(skolemFOFtoCNF_C_1(X_55,X_56)))]]) ).
cnf(refute_0_8,plain,
( ~ in(A,B)
| subset(A,union(B)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ in(skolemFOFtoCNF_C_1(X_35,X_36),X_35)
| subset(skolemFOFtoCNF_C_1(X_35,X_36),union(X_35)) ),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C_1(X_35,X_36))),bind(B,$fot(X_35))]]) ).
cnf(refute_0_10,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_C_1(X_35,X_36),X_35)
| subset(X_35,X_36) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_35)),bind(B,$fot(X_36))]]) ).
cnf(refute_0_12,plain,
( subset(X_35,X_36)
| subset(skolemFOFtoCNF_C_1(X_35,X_36),union(X_35)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(X_35,X_36),X_35) )],[refute_0_11,refute_0_9]) ).
cnf(refute_0_13,plain,
( subset(X_55,X_56)
| subset(skolemFOFtoCNF_C_1(X_55,X_56),union(X_55)) ),
inference(subst,[],[refute_0_12:[bind(X_35,$fot(X_55)),bind(X_36,$fot(X_56))]]) ).
cnf(refute_0_14,plain,
( in(skolemFOFtoCNF_C_1(X_55,X_56),powerset(union(X_55)))
| subset(X_55,X_56) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(X_55,X_56),union(X_55)) )],[refute_0_13,refute_0_7]) ).
cnf(refute_0_15,plain,
( in(skolemFOFtoCNF_C_1(X_63,powerset(union(X_63))),powerset(union(X_63)))
| subset(X_63,powerset(union(X_63))) ),
inference(subst,[],[refute_0_14:[bind(X_55,$fot(X_63)),bind(X_56,$fot(powerset(union(X_63))))]]) ).
cnf(refute_0_16,plain,
subset(X_63,powerset(union(X_63))),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(X_63,powerset(union(X_63))),powerset(union(X_63))) )],[refute_0_15,refute_0_2]) ).
cnf(refute_0_17,plain,
subset(skolemFOFtoCNF_A_2,powerset(union(skolemFOFtoCNF_A_2))),
inference(subst,[],[refute_0_16:[bind(X_63,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,powerset(union(skolemFOFtoCNF_A_2))) )],[refute_0_17,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET947+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n006.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 : 600
% 0.13/0.35 % DateTime : Mon Jul 11 01:14:50 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.39
% 0.21/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.40
%------------------------------------------------------------------------------