%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 03:38:28 EDT 2022
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 123 ( 14 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 125 ( 51 ~; 50 |; 10 &)
% ( 9 <=>; 5 =>; 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; 2 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 45 !; 6 ?)
% 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(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(A,B)
& subset(B,C) )
=> subset(A,C) ) ).
fof(t79_zfmisc_1,conjecture,
! [A,B] :
( subset(A,B)
=> subset(powerset(A),powerset(B)) ) ).
fof(subgoal_0,plain,
! [A,B] :
( subset(A,B)
=> subset(powerset(A),powerset(B)) ),
inference(strip,[],[t79_zfmisc_1]) ).
fof(negate_0_0,plain,
~ ! [A,B] :
( subset(A,B)
=> subset(powerset(A),powerset(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(canonicalize,[],[d3_tarski]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ subset(A,B)
<=> ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(canonicalize,[],[d1_zfmisc_1]) ).
fof(normalize_0_5,plain,
! [A,B] :
( B != powerset(A)
<=> ? [C] :
( ~ in(C,B)
<=> subset(C,A) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,plain,
! [A,B,C] :
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [A,B] :
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_10,plain,
? [A,B] :
( ~ subset(powerset(A),powerset(B))
& subset(A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B))
& subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[t1_xboole_1]) ).
fof(normalize_0_14,plain,
! [A,B,C] :
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ in(skolemFOFtoCNF_C_1(A,B),B)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),powerset(skolemFOFtoCNF_B))
| subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(powerset(skolemFOFtoCNF_A_2))),bind(B,$fot(powerset(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_2,plain,
( B != powerset(A)
| ~ subset(C,A)
| in(C,B) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( powerset(A) != powerset(A)
| ~ subset(C,A)
| in(C,powerset(A)) ),
inference(subst,[],[refute_0_2:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_4,plain,
powerset(A) = powerset(A),
introduced(tautology,[refl,[$fot(powerset(A))]]) ).
cnf(refute_0_5,plain,
( ~ subset(C,A)
| in(C,powerset(A)) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29),skolemFOFtoCNF_B)
| in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29),powerset(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29)))]]) ).
cnf(refute_0_7,plain,
( B != powerset(A)
| ~ in(C,B)
| subset(C,A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
( powerset(A) != powerset(A)
| ~ in(C,powerset(A))
| subset(C,A) ),
inference(subst,[],[refute_0_7:[bind(B,$fot(powerset(A)))]]) ).
cnf(refute_0_9,plain,
( ~ in(C,powerset(A))
| subset(C,A) ),
inference(resolve,[$cnf( $equal(powerset(A),powerset(A)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ in(skolemFOFtoCNF_C_1(powerset(A),X_12),powerset(A))
| subset(skolemFOFtoCNF_C_1(powerset(A),X_12),A) ),
inference(subst,[],[refute_0_9:[bind(C,$fot(skolemFOFtoCNF_C_1(powerset(A),X_12)))]]) ).
cnf(refute_0_11,plain,
( in(skolemFOFtoCNF_C_1(A,B),A)
| subset(A,B) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_12,plain,
( in(skolemFOFtoCNF_C_1(powerset(A),X_12),powerset(A))
| subset(powerset(A),X_12) ),
inference(subst,[],[refute_0_11:[bind(A,$fot(powerset(A))),bind(B,$fot(X_12))]]) ).
cnf(refute_0_13,plain,
( subset(powerset(A),X_12)
| subset(skolemFOFtoCNF_C_1(powerset(A),X_12),A) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(powerset(A),X_12),powerset(A)) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( subset(powerset(skolemFOFtoCNF_A_2),X_12)
| subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12),skolemFOFtoCNF_A_2) ),
inference(subst,[],[refute_0_13:[bind(A,$fot(skolemFOFtoCNF_A_2))]]) ).
cnf(refute_0_15,plain,
subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ subset(A,B)
| ~ subset(B,C)
| subset(A,C) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
( ~ subset(X_25,skolemFOFtoCNF_A_2)
| ~ subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B)
| subset(X_25,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_25)),bind(B,$fot(skolemFOFtoCNF_A_2)),bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_18,plain,
( ~ subset(X_25,skolemFOFtoCNF_A_2)
| subset(X_25,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_A_2,skolemFOFtoCNF_B) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12),skolemFOFtoCNF_A_2)
| subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_18:[bind(X_25,$fot(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12)))]]) ).
cnf(refute_0_20,plain,
( subset(powerset(skolemFOFtoCNF_A_2),X_12)
| subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12),skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_12),skolemFOFtoCNF_A_2) )],[refute_0_14,refute_0_19]) ).
cnf(refute_0_21,plain,
( subset(powerset(skolemFOFtoCNF_A_2),X_29)
| subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29),skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_20:[bind(X_12,$fot(X_29))]]) ).
cnf(refute_0_22,plain,
( in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29),powerset(skolemFOFtoCNF_B))
| subset(powerset(skolemFOFtoCNF_A_2),X_29) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),X_29),skolemFOFtoCNF_B) )],[refute_0_21,refute_0_6]) ).
cnf(refute_0_23,plain,
( in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),powerset(skolemFOFtoCNF_B))
| subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_22:[bind(X_29,$fot(powerset(skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_24,plain,
subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C_1(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),powerset(skolemFOFtoCNF_B)) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
~ subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( subset(powerset(skolemFOFtoCNF_A_2),powerset(skolemFOFtoCNF_B)) )],[refute_0_24,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET932+1 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 05:13:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35
% 0.13/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.13/0.36
%------------------------------------------------------------------------------