%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET667+3 : TPTP v8.1.0. Released v2.2.0.
% 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 03:36:28 EDT 2022
% Result : Theorem 78.06s 78.22s
% Output : CNFRefutation 78.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 212 ( 37 unt; 0 def)
% Number of atoms : 749 ( 20 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 941 ( 404 ~; 384 |; 93 &)
% ( 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 : 20 ( 20 usr; 10 con; 0-3 aty)
% Number of variables : 391 ( 15 sgn 189 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
<=> member(ordered_pair(C,C),identity_relation_of(B)) ) ) ) ).
fof(p5,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(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(p13,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ) ).
fof(p24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ) ).
fof(p27,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(p29,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) ).
fof(prove_relset_1_30,conjecture,
! [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(subgoal_0,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)) ) ) ) ),
inference(strip,[],[prove_relset_1_30]) ).
fof(subgoal_1,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(strip,[],[prove_relset_1_30]) ).
fof(negate_0_0,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)) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_0_1,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_0_0]) ).
fof(normalize_0_2,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_0_1]) ).
fof(normalize_0_3,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_0_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p31]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_0_2]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_8,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,domain(B,C,E))
& ilf_type(E,relation_type(B,C))
& subset(identity_relation_of(D),E) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,domain(B,C,E))
& ilf_type(E,relation_type(B,C))
& subset(identity_relation_of(D),E) ) ) ),
inference(simplify,[],[normalize_0_11,normalize_0_5]) ).
fof(normalize_0_13,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(D),E) ) ) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(D),E) ) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
( ilf_type(skolemFOFtoCNF_D_5,set_type)
& ? [E] :
( ~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_D_5),E) ) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
? [E] :
( ~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_D_5),E) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( ~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2))
& ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& subset(identity_relation_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_2) ),
inference(skolemize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
subset(identity_relation_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_2),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C,D] :
( ~ 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(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p13]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p24]) ).
fof(normalize_0_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_32,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,[],[p5]) ).
fof(normalize_0_33,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_32]) ).
fof(normalize_0_34,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_33]) ).
fof(normalize_0_35,plain,
! [B,C,E] :
( ~ 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(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_37,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,[],[p27]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,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_38]) ).
cnf(refute_0_0,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(C))]]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)),domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_D_5)),bind(C,$fot(domain_of(skolemFOFtoCNF_E_2)))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( member(skolemFOFtoCNF_D_1(X_23,C),X_23)
| subset(X_23,C) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(X_23))]]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_D_1(X_23,C),X_23)
| member(ordered_pair(skolemFOFtoCNF_D_1(X_23,C),skolemFOFtoCNF_D_1(X_23,C)),identity_relation_of(X_23)) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(X_23)),bind(C,$fot(skolemFOFtoCNF_D_1(X_23,C)))]]) ).
cnf(refute_0_14,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(X_23,C),skolemFOFtoCNF_D_1(X_23,C)),identity_relation_of(X_23))
| subset(X_23,C) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_23,C),X_23) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),identity_relation_of(skolemFOFtoCNF_D_5))
| subset(skolemFOFtoCNF_D_5,C) ),
inference(subst,[],[refute_0_14:[bind(X_23,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_16,plain,
subset(identity_relation_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_2),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_17,plain,
( ~ 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(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_18]) ).
cnf(refute_0_20,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_21,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_20,refute_0_19]) ).
cnf(refute_0_22,plain,
( ~ member(X_690,identity_relation_of(skolemFOFtoCNF_D_5))
| ~ subset(identity_relation_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_2)
| member(X_690,skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_21:[bind(B,$fot(identity_relation_of(skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_E_2)),bind(D,$fot(X_690))]]) ).
cnf(refute_0_23,plain,
( ~ member(X_690,identity_relation_of(skolemFOFtoCNF_D_5))
| member(X_690,skolemFOFtoCNF_E_2) ),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_2) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),identity_relation_of(skolemFOFtoCNF_D_5))
| member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_23:[bind(X_690,$fot(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C))))]]) ).
cnf(refute_0_25,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),skolemFOFtoCNF_E_2)
| subset(skolemFOFtoCNF_D_5,C) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),identity_relation_of(skolemFOFtoCNF_D_5)) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_27,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),skolemFOFtoCNF_E_2)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),domain_of(skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_28:[bind(B,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C))),bind(C,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C))),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_30,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,C) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C)),skolemFOFtoCNF_E_2) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_32,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ relation_like(skolemFOFtoCNF_E_2)
| ilf_type(skolemFOFtoCNF_E_2,binary_relation_type) ),
inference(subst,[],[refute_0_32:[bind(B,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_35,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| relation_like(skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_36:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_38,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_39,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_40,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_41:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(E,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_43,plain,
ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_38,refute_0_42]) ).
cnf(refute_0_44,plain,
relation_like(skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) )],[refute_0_43,refute_0_37]) ).
cnf(refute_0_45,plain,
ilf_type(skolemFOFtoCNF_E_2,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_E_2) )],[refute_0_44,refute_0_33]) ).
cnf(refute_0_46,plain,
( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,C),domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,C) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,binary_relation_type) )],[refute_0_45,refute_0_30]) ).
cnf(refute_0_47,plain,
( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)),domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)) ),
inference(subst,[],[refute_0_46:[bind(C,$fot(domain_of(skolemFOFtoCNF_E_2)))]]) ).
cnf(refute_0_48,plain,
subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)),domain_of(skolemFOFtoCNF_E_2)) )],[refute_0_47,refute_0_5]) ).
cnf(refute_0_49,plain,
~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_50,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_39]) ).
cnf(refute_0_51,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2) = domain_of(skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_52:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_54,plain,
domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2) = domain_of(skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_38,refute_0_53]) ).
cnf(refute_0_55,plain,
( domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2) != domain_of(skolemFOFtoCNF_E_2)
| ~ subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)) ),[1],$fot(domain_of(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_56,plain,
( ~ subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2))
| subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2),domain_of(skolemFOFtoCNF_E_2)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
~ subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_5,domain(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4,skolemFOFtoCNF_E_2)) )],[refute_0_56,refute_0_49]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_5,domain_of(skolemFOFtoCNF_E_2)) )],[refute_0_48,refute_0_57]) ).
fof(negate_1_0,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(negate,[],[subgoal_1]) ).
fof(normalize_1_0,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_1,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_0]) ).
fof(normalize_1_2,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_1]) ).
fof(normalize_1_3,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_2]) ).
fof(normalize_1_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p31]) ).
fof(normalize_1_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_1_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,B)
<=> ~ member(ordered_pair(C,C),identity_relation_of(B)) ) ) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(ordered_pair(C,C),identity_relation_of(B))
| member(C,B) ) ),
inference(clausify,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,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_2]) ).
fof(normalize_1_11,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,range(B,C,E))
& ilf_type(E,relation_type(B,C))
& subset(D,domain(B,C,E))
& subset(identity_relation_of(D),E) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_12,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,range(B,C,E))
& ilf_type(E,relation_type(B,C))
& subset(D,domain(B,C,E))
& subset(identity_relation_of(D),E) ) ) ),
inference(simplify,[],[normalize_1_11,normalize_1_5]) ).
fof(normalize_1_13,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(D,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& subset(identity_relation_of(D),E) ) ) ),
inference(skolemize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ~ subset(D,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(D,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& subset(identity_relation_of(D),E) ) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
( ilf_type(skolemFOFtoCNF_D_6,set_type)
& ? [E] :
( ~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_D_6),E)
& subset(skolemFOFtoCNF_D_6,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E)) ) ),
inference(skolemize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
? [E] :
( ~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E))
& ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_D_6),E)
& subset(skolemFOFtoCNF_D_6,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,E)) ),
inference(conjunct,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
( ~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3))
& ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
& subset(identity_relation_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_3)
& subset(skolemFOFtoCNF_D_6,domain(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)) ),
inference(skolemize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
subset(identity_relation_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_3),
inference(conjunct,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B,C,D] :
( ~ 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(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ) ),
inference(clausify,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ),
inference(conjunct,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p13]) ).
fof(normalize_1_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_1_24]) ).
fof(normalize_1_26,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p24]) ).
fof(normalize_1_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_1_29]) ).
fof(normalize_1_31,plain,
ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)),
inference(conjunct,[],[normalize_1_17]) ).
fof(normalize_1_32,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,[],[p5]) ).
fof(normalize_1_33,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_1_32]) ).
fof(normalize_1_34,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_1_33]) ).
fof(normalize_1_35,plain,
! [B,C,E] :
( ~ 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(conjunct,[],[normalize_1_34]) ).
fof(normalize_1_36,plain,
~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)),
inference(conjunct,[],[normalize_1_17]) ).
fof(normalize_1_37,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,[],[p29]) ).
fof(normalize_1_38,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_37]) ).
fof(normalize_1_39,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_38]) ).
cnf(refute_1_0,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_3]) ).
cnf(refute_1_1,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_2,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_0]) ).
cnf(refute_1_3,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_1:[bind(B,$fot(C))]]) ).
cnf(refute_1_4,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),C)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)),range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)) ),
inference(subst,[],[refute_1_4:[bind(B,$fot(skolemFOFtoCNF_D_6)),bind(C,$fot(range_of(skolemFOFtoCNF_E_3)))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_7,plain,
( ~ ilf_type(C,set_type)
| ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_6]) ).
cnf(refute_1_8,plain,
( ~ member(C,B)
| member(ordered_pair(C,C),identity_relation_of(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ member(skolemFOFtoCNF_D_1(X_1261,X_1262),X_1261)
| member(ordered_pair(skolemFOFtoCNF_D_1(X_1261,X_1262),skolemFOFtoCNF_D_1(X_1261,X_1262)),identity_relation_of(X_1261)) ),
inference(subst,[],[refute_1_8:[bind(B,$fot(X_1261)),bind(C,$fot(skolemFOFtoCNF_D_1(X_1261,X_1262)))]]) ).
cnf(refute_1_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_10]) ).
cnf(refute_1_12,plain,
( member(skolemFOFtoCNF_D_1(B,C),B)
| subset(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_11]) ).
cnf(refute_1_13,plain,
( member(skolemFOFtoCNF_D_1(X_1261,X_1262),X_1261)
| subset(X_1261,X_1262) ),
inference(subst,[],[refute_1_12:[bind(B,$fot(X_1261)),bind(C,$fot(X_1262))]]) ).
cnf(refute_1_14,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(X_1261,X_1262),skolemFOFtoCNF_D_1(X_1261,X_1262)),identity_relation_of(X_1261))
| subset(X_1261,X_1262) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(X_1261,X_1262),X_1261) )],[refute_1_13,refute_1_9]) ).
cnf(refute_1_15,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),identity_relation_of(skolemFOFtoCNF_D_6))
| subset(skolemFOFtoCNF_D_6,X_1262) ),
inference(subst,[],[refute_1_14:[bind(X_1261,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_16,plain,
subset(identity_relation_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_3),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_17,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_18,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_18]) ).
cnf(refute_1_20,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_1_1:[bind(B,$fot(D))]]) ).
cnf(refute_1_21,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_20,refute_1_19]) ).
cnf(refute_1_22,plain,
( ~ member(X_2028,identity_relation_of(skolemFOFtoCNF_D_6))
| ~ subset(identity_relation_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_3)
| member(X_2028,skolemFOFtoCNF_E_3) ),
inference(subst,[],[refute_1_21:[bind(B,$fot(identity_relation_of(skolemFOFtoCNF_D_6))),bind(C,$fot(skolemFOFtoCNF_E_3)),bind(D,$fot(X_2028))]]) ).
cnf(refute_1_23,plain,
( ~ member(X_2028,identity_relation_of(skolemFOFtoCNF_D_6))
| member(X_2028,skolemFOFtoCNF_E_3) ),
inference(resolve,[$cnf( subset(identity_relation_of(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_3) )],[refute_1_16,refute_1_22]) ).
cnf(refute_1_24,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),identity_relation_of(skolemFOFtoCNF_D_6))
| member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),skolemFOFtoCNF_E_3) ),
inference(subst,[],[refute_1_23:[bind(X_2028,$fot(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262))))]]) ).
cnf(refute_1_25,plain,
( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),skolemFOFtoCNF_E_3)
| subset(skolemFOFtoCNF_D_6,X_1262) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),identity_relation_of(skolemFOFtoCNF_D_6)) )],[refute_1_15,refute_1_24]) ).
cnf(refute_1_26,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_27,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_26]) ).
cnf(refute_1_28,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),skolemFOFtoCNF_E_3)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),range_of(skolemFOFtoCNF_E_3)) ),
inference(subst,[],[refute_1_28:[bind(B,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262))),bind(C,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262))),bind(D,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_30,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,binary_relation_type)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,X_1262) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262)),skolemFOFtoCNF_E_3) )],[refute_1_25,refute_1_29]) ).
cnf(refute_1_31,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_32,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ relation_like(skolemFOFtoCNF_E_3)
| ilf_type(skolemFOFtoCNF_E_3,binary_relation_type) ),
inference(subst,[],[refute_1_32:[bind(B,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_34,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_1_30]) ).
cnf(refute_1_35,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_34]) ).
cnf(refute_1_36,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_35]) ).
cnf(refute_1_37,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)))
| relation_like(skolemFOFtoCNF_E_3) ),
inference(subst,[],[refute_1_36:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_38,plain,
ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_39,plain,
( ~ 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(canonicalize,[],[normalize_1_35]) ).
cnf(refute_1_40,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_39]) ).
cnf(refute_1_41,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_40]) ).
cnf(refute_1_42,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
| ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))) ),
inference(subst,[],[refute_1_41:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(E,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_43,plain,
ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)) )],[refute_1_38,refute_1_42]) ).
cnf(refute_1_44,plain,
relation_like(skolemFOFtoCNF_E_3),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))) )],[refute_1_43,refute_1_37]) ).
cnf(refute_1_45,plain,
ilf_type(skolemFOFtoCNF_E_3,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_E_3) )],[refute_1_44,refute_1_33]) ).
cnf(refute_1_46,plain,
( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,X_1262),range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,X_1262) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,binary_relation_type) )],[refute_1_45,refute_1_30]) ).
cnf(refute_1_47,plain,
( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)),range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)) ),
inference(subst,[],[refute_1_46:[bind(X_1262,$fot(range_of(skolemFOFtoCNF_E_3)))]]) ).
cnf(refute_1_48,plain,
subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)),range_of(skolemFOFtoCNF_E_3)) )],[refute_1_47,refute_1_5]) ).
cnf(refute_1_49,plain,
~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)),
inference(canonicalize,[],[normalize_1_36]) ).
cnf(refute_1_50,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_1_39]) ).
cnf(refute_1_51,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_50]) ).
cnf(refute_1_52,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_51]) ).
cnf(refute_1_53,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5))
| range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3) = range_of(skolemFOFtoCNF_E_3) ),
inference(subst,[],[refute_1_52:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(D,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_54,plain,
range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3) = range_of(skolemFOFtoCNF_E_3),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5)) )],[refute_1_38,refute_1_53]) ).
cnf(refute_1_55,plain,
( range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3) != range_of(skolemFOFtoCNF_E_3)
| ~ subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)) ),
introduced(tautology,[equality,[$cnf( ~ subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)) ),[1],$fot(range_of(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_56,plain,
( ~ subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3))
| subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3),range_of(skolemFOFtoCNF_E_3)) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
~ subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_6,range(skolemFOFtoCNF_B_2,skolemFOFtoCNF_C_5,skolemFOFtoCNF_E_3)) )],[refute_1_56,refute_1_49]) ).
cnf(refute_1_58,plain,
$false,
inference(resolve,[$cnf( subset(skolemFOFtoCNF_D_6,range_of(skolemFOFtoCNF_E_3)) )],[refute_1_48,refute_1_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET667+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 00:33:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 78.06/78.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.06/78.22
% 78.06/78.22 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 78.06/78.24
%------------------------------------------------------------------------------