TSTP Solution File: SET669+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 03:36:29 EDT 2022
% Result : Theorem 201.14s 201.34s
% Output : CNFRefutation 201.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 176 ( 39 unt; 0 def)
% Number of atoms : 627 ( 50 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 798 ( 347 ~; 320 |; 71 &)
% ( 15 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 298 ( 7 sgn 154 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( subset(identity_relation_of(D),E)
=> ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ) ) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( subset(B,C)
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p9,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( B = C
<=> ( subset(B,C)
& subset(C,B) ) ) ) ) ).
fof(p16,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(p20,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(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p22,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(p28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ) ).
fof(p30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ) ).
fof(p31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(range(B,C,D),subset_type(C)) ) ) ) ).
fof(p32,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_32,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( subset(identity_relation_of(C),D)
=> ( subset(C,domain(B,C,D))
& C = range(B,C,D) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D) )
=> subset(C,domain(B,C,D)) ) ) ),
inference(strip,[],[prove_relset_1_32]) ).
fof(subgoal_1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D)
& subset(C,domain(B,C,D)) )
=> C = range(B,C,D) ) ) ),
inference(strip,[],[prove_relset_1_32]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D) )
=> subset(C,domain(B,C,D)) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ~ subset(C,domain(B,C,D))
& ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p32]) ).
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(C,set_type)
& ? [D] :
( ~ subset(C,domain(B,C,D))
& ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,D))
& ilf_type(D,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),D) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [D] :
( ~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,D))
& ilf_type(D,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),D) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5))
& ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p28]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_1,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(C))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(D))]]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| ~ subset(identity_relation_of(X_3904),skolemFOFtoCNF_D_5)
| subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(X_3904)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_10,plain,
( ~ subset(identity_relation_of(X_3904),skolemFOFtoCNF_D_5)
| subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_15,plain,
domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| ~ subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5))
| subset(X_3904,domain_of(skolemFOFtoCNF_D_5)) ),
introduced(tautology,[equality,[$cnf( subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_17,plain,
( ~ subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5))
| subset(X_3904,domain_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ subset(identity_relation_of(X_3904),skolemFOFtoCNF_D_5)
| subset(X_3904,domain_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( subset(X_3904,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5)
| subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_0_18:[bind(X_3904,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_20,plain,
subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_D_5) )],[refute_0_0,refute_0_19]) ).
cnf(refute_0_21,plain,
~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_22,plain,
( domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| ~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_23,plain,
( ~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_22]) ).
cnf(refute_0_24,plain,
~ subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_4,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_D_5)) )],[refute_0_23,refute_0_21]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_20,refute_0_24]) ).
fof(negate_1_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(B,C))
& subset(identity_relation_of(C),D)
& subset(C,domain(B,C,D)) )
=> C = range(B,C,D) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( C != range(B,C,D)
& ilf_type(D,relation_type(B,C))
& subset(C,domain(B,C,D))
& subset(identity_relation_of(C),D) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p32]) ).
fof(normalize_1_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( C != range(B,C,D)
& ilf_type(D,relation_type(B,C))
& subset(C,domain(B,C,D))
& subset(identity_relation_of(C),D) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( skolemFOFtoCNF_C_5 != range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),D)
& subset(skolemFOFtoCNF_C_5,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,D)) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [D] :
( skolemFOFtoCNF_C_5 != range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),D)
& subset(skolemFOFtoCNF_C_5,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,D)) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( skolemFOFtoCNF_C_5 != range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)
& ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6)
& subset(skolemFOFtoCNF_C_5,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_1_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| ( subset(D,domain(B,C,E))
& subset(D,range(B,C,E)) ) ) ) ) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,domain(B,C,E)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ) ),
inference(clausify,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p30]) ).
fof(normalize_1_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ) ) ),
inference(canonicalize,[],[p9]) ).
fof(normalize_1_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( B != C
<=> ( ~ subset(B,C)
| ~ subset(C,B) ) ) ) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [B,C] :
( ( B != C
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| subset(B,C) )
& ( B != C
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| subset(C,B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ) ),
inference(clausify,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(conjunct,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p7]) ).
fof(normalize_1_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ subset(B,C)
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_1(B,C),set_type)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ) ),
inference(clausify,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(conjunct,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(conjunct,[],[normalize_1_22]) ).
fof(normalize_1_25,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,[],[p22]) ).
fof(normalize_1_26,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_1_25]) ).
fof(normalize_1_27,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_1_26]) ).
fof(normalize_1_28,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_1_27]) ).
fof(normalize_1_29,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,[],[p16]) ).
fof(normalize_1_30,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_1_29]) ).
fof(normalize_1_31,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_1_30]) ).
fof(normalize_1_32,plain,
! [B,C] :
( ~ 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(conjunct,[],[normalize_1_31]) ).
fof(normalize_1_33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ) ) ),
inference(canonicalize,[],[p31]) ).
fof(normalize_1_34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ) ) ),
inference(specialize,[],[normalize_1_33]) ).
fof(normalize_1_35,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ),
inference(clausify,[],[normalize_1_34]) ).
fof(normalize_1_36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p21]) ).
fof(normalize_1_37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_1_36]) ).
fof(normalize_1_38,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_1_37]) ).
fof(normalize_1_39,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_1_38]) ).
fof(normalize_1_40,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,[],[p20]) ).
fof(normalize_1_41,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_1_40]) ).
fof(normalize_1_42,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_3(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_3(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_3(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_1_41]) ).
fof(normalize_1_43,plain,
! [B,C,D] :
( ~ 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(conjunct,[],[normalize_1_42]) ).
fof(normalize_1_44,plain,
skolemFOFtoCNF_C_5 != range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),
inference(conjunct,[],[normalize_1_6]) ).
cnf(refute_1_0,plain,
subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_1,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(C))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(D))]]) ).
cnf(refute_1_8,plain,
( ~ ilf_type(E,relation_type(B,C))
| ~ subset(identity_relation_of(D),E)
| subset(D,range(B,C,E)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
| ~ subset(identity_relation_of(X_9942),skolemFOFtoCNF_D_6)
| subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_1_8:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(X_9942)),bind(E,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_10,plain,
( ~ subset(identity_relation_of(X_9942),skolemFOFtoCNF_D_6)
| subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_12,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_12]) ).
cnf(refute_1_14,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
| range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_15,plain,
range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)) )],[refute_1_1,refute_1_14]) ).
cnf(refute_1_16,plain,
( range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| ~ subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6))
| subset(X_9942,range_of(skolemFOFtoCNF_D_6)) ),
introduced(tautology,[equality,[$cnf( subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) ),[1],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_17,plain,
( ~ subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6))
| subset(X_9942,range_of(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ subset(identity_relation_of(X_9942),skolemFOFtoCNF_D_6)
| subset(X_9942,range_of(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( subset(X_9942,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) )],[refute_1_10,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6)
| subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_1_18:[bind(X_9942,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_20,plain,
subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_C_5),skolemFOFtoCNF_D_6) )],[refute_1_0,refute_1_19]) ).
cnf(refute_1_21,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_22,plain,
( ~ ilf_type(C,set_type)
| ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ subset(B,C)
| ~ subset(C,B)
| B = C ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_22]) ).
cnf(refute_1_24,plain,
( ~ subset(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5)
| ~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6))
| skolemFOFtoCNF_C_5 = range_of(skolemFOFtoCNF_D_6) ),
inference(subst,[],[refute_1_23:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(range_of(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_1_25,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_26,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_25]) ).
cnf(refute_1_27,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_26]) ).
cnf(refute_1_28,plain,
( ~ member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5),skolemFOFtoCNF_C_5)
| subset(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_27:[bind(B,$fot(range_of(skolemFOFtoCNF_D_6))),bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_29,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_30,plain,
( ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_29]) ).
cnf(refute_1_31,plain,
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_30]) ).
cnf(refute_1_32,plain,
( member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C),range_of(skolemFOFtoCNF_D_6))
| subset(range_of(skolemFOFtoCNF_D_6),C) ),
inference(subst,[],[refute_1_31:[bind(B,$fot(range_of(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_1_33,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_1_28]) ).
cnf(refute_1_34,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_33]) ).
cnf(refute_1_35,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_34]) ).
cnf(refute_1_36,plain,
( ~ ilf_type(range_of(skolemFOFtoCNF_D_6),member_type(power_set(skolemFOFtoCNF_C_5)))
| empty(power_set(skolemFOFtoCNF_C_5))
| member(range_of(skolemFOFtoCNF_D_6),power_set(skolemFOFtoCNF_C_5)) ),
inference(subst,[],[refute_1_35:[bind(B,$fot(range_of(skolemFOFtoCNF_D_6))),bind(C,$fot(power_set(skolemFOFtoCNF_C_5)))]]) ).
cnf(refute_1_37,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_1_32]) ).
cnf(refute_1_38,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_37]) ).
cnf(refute_1_39,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_38]) ).
cnf(refute_1_40,plain,
( ~ ilf_type(range_of(skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5))
| ilf_type(range_of(skolemFOFtoCNF_D_6),member_type(power_set(skolemFOFtoCNF_C_5))) ),
inference(subst,[],[refute_1_39:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(range_of(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_1_41,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ),
inference(canonicalize,[],[normalize_1_35]) ).
cnf(refute_1_42,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(range(B,C,D),subset_type(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
| ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) ),
inference(subst,[],[refute_1_43:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_45,plain,
ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)) )],[refute_1_1,refute_1_44]) ).
cnf(refute_1_46,plain,
( range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| ~ ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5))
| ilf_type(range_of(skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) ),
introduced(tautology,[equality,[$cnf( ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) ),[0],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_47,plain,
( ~ ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5))
| ilf_type(range_of(skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_46]) ).
cnf(refute_1_48,plain,
ilf_type(range_of(skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( ilf_type(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) )],[refute_1_45,refute_1_47]) ).
cnf(refute_1_49,plain,
ilf_type(range_of(skolemFOFtoCNF_D_6),member_type(power_set(skolemFOFtoCNF_C_5))),
inference(resolve,[$cnf( ilf_type(range_of(skolemFOFtoCNF_D_6),subset_type(skolemFOFtoCNF_C_5)) )],[refute_1_48,refute_1_40]) ).
cnf(refute_1_50,plain,
( empty(power_set(skolemFOFtoCNF_C_5))
| member(range_of(skolemFOFtoCNF_D_6),power_set(skolemFOFtoCNF_C_5)) ),
inference(resolve,[$cnf( ilf_type(range_of(skolemFOFtoCNF_D_6),member_type(power_set(skolemFOFtoCNF_C_5))) )],[refute_1_49,refute_1_36]) ).
cnf(refute_1_51,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_1_39]) ).
cnf(refute_1_52,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_51]) ).
cnf(refute_1_53,plain,
~ empty(power_set(skolemFOFtoCNF_C_5)),
inference(subst,[],[refute_1_52:[bind(B,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_54,plain,
member(range_of(skolemFOFtoCNF_D_6),power_set(skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( empty(power_set(skolemFOFtoCNF_C_5)) )],[refute_1_50,refute_1_53]) ).
cnf(refute_1_55,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_1_43]) ).
cnf(refute_1_56,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_55]) ).
cnf(refute_1_57,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_56]) ).
cnf(refute_1_58,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_7,refute_1_57]) ).
cnf(refute_1_59,plain,
( ~ member(X_4825,range_of(skolemFOFtoCNF_D_6))
| ~ member(range_of(skolemFOFtoCNF_D_6),power_set(skolemFOFtoCNF_C_5))
| member(X_4825,skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_58:[bind(B,$fot(range_of(skolemFOFtoCNF_D_6))),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(X_4825))]]) ).
cnf(refute_1_60,plain,
( ~ member(X_4825,range_of(skolemFOFtoCNF_D_6))
| member(X_4825,skolemFOFtoCNF_C_5) ),
inference(resolve,[$cnf( member(range_of(skolemFOFtoCNF_D_6),power_set(skolemFOFtoCNF_C_5)) )],[refute_1_54,refute_1_59]) ).
cnf(refute_1_61,plain,
( ~ member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C),range_of(skolemFOFtoCNF_D_6))
| member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C),skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_60:[bind(X_4825,$fot(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C)))]]) ).
cnf(refute_1_62,plain,
( member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C),skolemFOFtoCNF_C_5)
| subset(range_of(skolemFOFtoCNF_D_6),C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),C),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_32,refute_1_61]) ).
cnf(refute_1_63,plain,
( member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5),skolemFOFtoCNF_C_5)
| subset(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_62:[bind(C,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_64,plain,
subset(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5),skolemFOFtoCNF_C_5) )],[refute_1_63,refute_1_28]) ).
cnf(refute_1_65,plain,
( ~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6))
| skolemFOFtoCNF_C_5 = range_of(skolemFOFtoCNF_D_6) ),
inference(resolve,[$cnf( subset(range_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_5) )],[refute_1_64,refute_1_24]) ).
cnf(refute_1_66,plain,
skolemFOFtoCNF_C_5 != range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),
inference(canonicalize,[],[normalize_1_44]) ).
cnf(refute_1_67,plain,
( range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| skolemFOFtoCNF_C_5 != range_of(skolemFOFtoCNF_D_6)
| skolemFOFtoCNF_C_5 = range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) ),[1],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_68,plain,
( skolemFOFtoCNF_C_5 != range_of(skolemFOFtoCNF_D_6)
| skolemFOFtoCNF_C_5 = range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_67]) ).
cnf(refute_1_69,plain,
skolemFOFtoCNF_C_5 != range_of(skolemFOFtoCNF_D_6),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_5,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_D_6)) )],[refute_1_68,refute_1_66]) ).
cnf(refute_1_70,plain,
~ subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)) )],[refute_1_65,refute_1_69]) ).
cnf(refute_1_71,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_5,range_of(skolemFOFtoCNF_D_6)) )],[refute_1_20,refute_1_70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET669+3 : TPTP v8.1.0. Released v2.2.0.
% 0.09/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 12:10:12 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 201.14/201.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 201.14/201.34
% 201.14/201.34 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 201.20/201.35
%------------------------------------------------------------------------------