TSTP Solution File: SET662+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 03:36:26 EDT 2022
% Result : Theorem 0.19s 0.36s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 72 ( 19 unt; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 289 ( 127 ~; 111 |; 22 &)
% ( 9 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 123 ( 14 sgn 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ~ member(B,empty_set) ) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
fof(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ) ).
fof(p20,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_25,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(strip,[],[prove_relset_1_25]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ilf_type(empty_set,relation_type(B,C)) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p20]) ).
fof(normalize_0_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B,C] :
( ~ ilf_type(empty_set,relation_type(B,C))
& ilf_type(C,set_type) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ ilf_type(empty_set,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& ilf_type(skolemFOFtoCNF_C_4,set_type) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
~ ilf_type(empty_set,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(canonicalize,[],[p7]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p12]) ).
fof(normalize_0_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_2(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p14]) ).
fof(normalize_0_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C] :
( ( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p13]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B] :
( ( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) )
& ( ~ ilf_type(B,set_type)
| ilf_type(power_set(B),set_type) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(conjunct,[],[normalize_0_26]) ).
cnf(refute_0_0,plain,
~ ilf_type(empty_set,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(C))]]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(empty_set,member_type(power_set(X_47)))
| ilf_type(empty_set,subset_type(X_47)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_47)),bind(C,$fot(empty_set))]]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(B,set_type)
| ~ member(B,empty_set) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
~ member(B,empty_set),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
~ member(skolemFOFtoCNF_D_2(empty_set,X_33),empty_set),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_D_2(empty_set,X_33)))]]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
( member(empty_set,power_set(X_33))
| member(skolemFOFtoCNF_D_2(empty_set,X_33),empty_set) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(empty_set)),bind(C,$fot(X_33))]]) ).
cnf(refute_0_14,plain,
member(empty_set,power_set(X_33)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(empty_set,X_33),empty_set) )],[refute_0_13,refute_0_9]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_16,plain,
( ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ member(empty_set,power_set(X_33))
| empty(power_set(X_33))
| ilf_type(empty_set,member_type(power_set(X_33))) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(empty_set)),bind(C,$fot(power_set(X_33)))]]) ).
cnf(refute_0_19,plain,
( empty(power_set(X_33))
| ilf_type(empty_set,member_type(power_set(X_33))) ),
inference(resolve,[$cnf( member(empty_set,power_set(X_33)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_21,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_20]) ).
cnf(refute_0_22,plain,
~ empty(power_set(X_33)),
inference(subst,[],[refute_0_21:[bind(B,$fot(X_33))]]) ).
cnf(refute_0_23,plain,
ilf_type(empty_set,member_type(power_set(X_33))),
inference(resolve,[$cnf( empty(power_set(X_33)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
ilf_type(empty_set,member_type(power_set(X_47))),
inference(subst,[],[refute_0_23:[bind(X_33,$fot(X_47))]]) ).
cnf(refute_0_25,plain,
ilf_type(empty_set,subset_type(X_47)),
inference(resolve,[$cnf( ilf_type(empty_set,member_type(power_set(X_47))) )],[refute_0_24,refute_0_6]) ).
cnf(refute_0_26,plain,
ilf_type(empty_set,subset_type(cross_product(X_81,X_82))),
inference(subst,[],[refute_0_25:[bind(X_47,$fot(cross_product(X_81,X_82)))]]) ).
cnf(refute_0_27,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_28,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ ilf_type(empty_set,subset_type(cross_product(X_81,X_82)))
| ilf_type(empty_set,relation_type(X_81,X_82)) ),
inference(subst,[],[refute_0_29:[bind(B,$fot(X_81)),bind(C,$fot(X_82)),bind(D,$fot(empty_set))]]) ).
cnf(refute_0_31,plain,
ilf_type(empty_set,relation_type(X_81,X_82)),
inference(resolve,[$cnf( ilf_type(empty_set,subset_type(cross_product(X_81,X_82))) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
ilf_type(empty_set,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(subst,[],[refute_0_31:[bind(X_81,$fot(skolemFOFtoCNF_B)),bind(X_82,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_33,plain,
$false,
inference(resolve,[$cnf( ilf_type(empty_set,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) )],[refute_0_32,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET662+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n022.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 03:40:40 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.36
% 0.19/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------