TSTP Solution File: SET645+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 03:36:18 EDT 2022
% Result : Theorem 1.74s 1.95s
% Output : CNFRefutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 172 ( 41 unt; 0 def)
% Number of atoms : 693 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 905 ( 384 ~; 336 |; 122 &)
% ( 20 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 11 con; 0-2 aty)
% Number of variables : 338 ( 20 sgn 168 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(B,D)
& member(C,E) ) ) ) ) ) ) ).
fof(p4,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(p10,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(p13,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(p14,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p15,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(p21,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_7,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ) ).
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,set_type)
=> ! [F] :
( ( ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F) )
=> member(D,B) ) ) ) ) ),
inference(strip,[],[prove_relset_1_7]) ).
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,set_type)
=> ! [F] :
( ( ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F)
& member(D,B) )
=> member(E,C) ) ) ) ) ),
inference(strip,[],[prove_relset_1_7]) ).
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,set_type)
=> ! [F] :
( ( ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F) )
=> member(D,B) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_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,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(B,D)
| ~ member(C,E)
| member(ordered_pair(B,C),cross_product(D,E)) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p21]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(D,B)
& ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(D,B)
& ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F) ) ) ) ),
inference(simplify,[],[normalize_0_6,normalize_0_5]) ).
fof(normalize_0_8,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(D,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(D,E),F) ) ) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(D,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(D,E),F) ) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( ilf_type(skolemFOFtoCNF_D_4,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(skolemFOFtoCNF_D_4,E),F) ) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(skolemFOFtoCNF_D_4,E),F) ) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
( ilf_type(skolemFOFtoCNF_E_1,set_type)
& ? [F] :
( ~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),F) ) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
? [F] :
( ~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B)
& ilf_type(F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),F) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
( ~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B)
& ilf_type(skolemFOFtoCNF_F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
& member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),skolemFOFtoCNF_F) ),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),skolemFOFtoCNF_F),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_0_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C] :
( ( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,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,[],[p10]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,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_0_22]) ).
fof(normalize_0_24,plain,
ilf_type(skolemFOFtoCNF_F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,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_26]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p14]) ).
fof(normalize_0_30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [B] :
( ( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) )
& ( ~ ilf_type(B,set_type)
| ilf_type(power_set(B),set_type) ) ),
inference(clausify,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,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,[],[p13]) ).
fof(normalize_0_34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_2(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,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_0_35]) ).
fof(normalize_0_37,plain,
~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B),
inference(conjunct,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
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)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
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,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(E))]]) ).
cnf(refute_0_8,plain,
( ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(skolemFOFtoCNF_D_4)),bind(C,$fot(skolemFOFtoCNF_E_1)),bind(D,$fot(skolemFOFtoCNF_B)),bind(E,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_10,plain,
member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),skolemFOFtoCNF_F),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(skolemFOFtoCNF_F,member_type(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))))
| empty(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_F,power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_16,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(skolemFOFtoCNF_F,subset_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))
| ilf_type(skolemFOFtoCNF_F,member_type(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))),bind(C,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_19,plain,
ilf_type(skolemFOFtoCNF_F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_21,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(skolemFOFtoCNF_F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))
| ilf_type(skolemFOFtoCNF_F,subset_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(E,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_24,plain,
ilf_type(skolemFOFtoCNF_F,subset_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F,relation_type(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) )],[refute_0_19,refute_0_23]) ).
cnf(refute_0_25,plain,
ilf_type(skolemFOFtoCNF_F,member_type(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F,subset_type(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) )],[refute_0_24,refute_0_18]) ).
cnf(refute_0_26,plain,
( empty(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_F,power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F,member_type(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))) )],[refute_0_25,refute_0_14]) ).
cnf(refute_0_27,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_28,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_27]) ).
cnf(refute_0_29,plain,
~ empty(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))),
inference(subst,[],[refute_0_28:[bind(B,$fot(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_30,plain,
member(skolemFOFtoCNF_F,power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( empty(power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,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_0_36]) ).
cnf(refute_0_32,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_5,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ member(X_167,skolemFOFtoCNF_F)
| ~ member(skolemFOFtoCNF_F,power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)))
| member(X_167,cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_34:[bind(B,$fot(skolemFOFtoCNF_F)),bind(C,$fot(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))),bind(D,$fot(X_167))]]) ).
cnf(refute_0_36,plain,
( ~ member(X_167,skolemFOFtoCNF_F)
| member(X_167,cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F,power_set(cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4))) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),skolemFOFtoCNF_F)
| member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_36:[bind(X_167,$fot(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1)))]]) ).
cnf(refute_0_38,plain,
member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),skolemFOFtoCNF_F) )],[refute_0_10,refute_0_37]) ).
cnf(refute_0_39,plain,
member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_1),cross_product(skolemFOFtoCNF_B,skolemFOFtoCNF_C_4)) )],[refute_0_38,refute_0_9]) ).
cnf(refute_0_40,plain,
~ member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_4,skolemFOFtoCNF_B) )],[refute_0_39,refute_0_40]) ).
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,set_type)
=> ! [F] :
( ( ilf_type(F,relation_type(B,C))
& member(ordered_pair(D,E),F)
& member(D,B) )
=> member(E,C) ) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_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,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_1,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(B,D)
| ~ member(C,E)
| member(ordered_pair(B,C),cross_product(D,E)) ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p21]) ).
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)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,C)
& ilf_type(F,relation_type(B,C))
& member(D,B)
& member(ordered_pair(D,E),F) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_7,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,C)
& ilf_type(F,relation_type(B,C))
& member(D,B)
& member(ordered_pair(D,E),F) ) ) ) ),
inference(simplify,[],[normalize_1_6,normalize_1_5]) ).
fof(normalize_1_8,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(D,skolemFOFtoCNF_B_1)
& member(ordered_pair(D,E),F) ) ) ) ),
inference(skolemize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(D,skolemFOFtoCNF_B_1)
& member(ordered_pair(D,E),F) ) ) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
( ilf_type(skolemFOFtoCNF_D_5,set_type)
& ? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_D_5,E),F)
& member(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_1) ) ) ),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
? [E] :
( ilf_type(E,set_type)
& ? [F] :
( ~ member(E,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_D_5,E),F)
& member(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_1) ) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
( ilf_type(skolemFOFtoCNF_E_2,set_type)
& ? [F] :
( ~ member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),F)
& member(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_1) ) ),
inference(skolemize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
? [F] :
( ~ member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5)
& ilf_type(F,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),F)
& member(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_1) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
( ~ member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5)
& ilf_type(skolemFOFtoCNF_F_1,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),skolemFOFtoCNF_F_1)
& member(skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),skolemFOFtoCNF_F_1),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_1_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [B,C] :
( ( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ) ),
inference(clausify,[],[normalize_1_17]) ).
fof(normalize_1_19,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_18]) ).
fof(normalize_1_20,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,[],[p10]) ).
fof(normalize_1_21,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_20]) ).
fof(normalize_1_22,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_21]) ).
fof(normalize_1_23,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_22]) ).
fof(normalize_1_24,plain,
ilf_type(skolemFOFtoCNF_F_1,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_1_26,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_25]) ).
fof(normalize_1_27,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_26]) ).
fof(normalize_1_28,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_27]) ).
fof(normalize_1_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p14]) ).
fof(normalize_1_30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_1_29]) ).
fof(normalize_1_31,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_30]) ).
fof(normalize_1_32,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_1_31]) ).
fof(normalize_1_33,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,[],[p13]) ).
fof(normalize_1_34,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_33]) ).
fof(normalize_1_35,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_2(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_1_34]) ).
fof(normalize_1_36,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_35]) ).
fof(normalize_1_37,plain,
~ member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5),
inference(conjunct,[],[normalize_1_14]) ).
cnf(refute_1_0,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
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)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
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,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_1_1:[bind(B,$fot(D))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_1_1:[bind(B,$fot(E))]]) ).
cnf(refute_1_8,plain,
( ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
| member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5) ),
inference(subst,[],[refute_1_8:[bind(B,$fot(skolemFOFtoCNF_D_5)),bind(C,$fot(skolemFOFtoCNF_E_2)),bind(D,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_10,plain,
member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),skolemFOFtoCNF_F_1),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_12,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_12]) ).
cnf(refute_1_14,plain,
( ~ ilf_type(skolemFOFtoCNF_F_1,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))))
| empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))
| member(skolemFOFtoCNF_F_1,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) ),
inference(subst,[],[refute_1_13:[bind(B,$fot(skolemFOFtoCNF_F_1)),bind(C,$fot(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))))]]) ).
cnf(refute_1_15,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_16,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_16]) ).
cnf(refute_1_18,plain,
( ~ ilf_type(skolemFOFtoCNF_F_1,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))
| ilf_type(skolemFOFtoCNF_F_1,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))) ),
inference(subst,[],[refute_1_17:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))),bind(C,$fot(skolemFOFtoCNF_F_1))]]) ).
cnf(refute_1_19,plain,
ilf_type(skolemFOFtoCNF_F_1,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_20,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_1_28]) ).
cnf(refute_1_21,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_20]) ).
cnf(refute_1_22,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ ilf_type(skolemFOFtoCNF_F_1,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))
| ilf_type(skolemFOFtoCNF_F_1,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) ),
inference(subst,[],[refute_1_22:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_5)),bind(E,$fot(skolemFOFtoCNF_F_1))]]) ).
cnf(refute_1_24,plain,
ilf_type(skolemFOFtoCNF_F_1,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F_1,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)) )],[refute_1_19,refute_1_23]) ).
cnf(refute_1_25,plain,
ilf_type(skolemFOFtoCNF_F_1,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F_1,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) )],[refute_1_24,refute_1_18]) ).
cnf(refute_1_26,plain,
( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))
| member(skolemFOFtoCNF_F_1,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_F_1,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))) )],[refute_1_25,refute_1_14]) ).
cnf(refute_1_27,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_1_32]) ).
cnf(refute_1_28,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_27]) ).
cnf(refute_1_29,plain,
~ empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))),
inference(subst,[],[refute_1_28:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))]]) ).
cnf(refute_1_30,plain,
member(skolemFOFtoCNF_F_1,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))),
inference(resolve,[$cnf( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) )],[refute_1_26,refute_1_29]) ).
cnf(refute_1_31,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_36]) ).
cnf(refute_1_32,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_1,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_5,refute_1_33]) ).
cnf(refute_1_35,plain,
( ~ member(X_361,skolemFOFtoCNF_F_1)
| ~ member(skolemFOFtoCNF_F_1,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)))
| member(X_361,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)) ),
inference(subst,[],[refute_1_34:[bind(B,$fot(skolemFOFtoCNF_F_1)),bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))),bind(D,$fot(X_361))]]) ).
cnf(refute_1_36,plain,
( ~ member(X_361,skolemFOFtoCNF_F_1)
| member(X_361,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F_1,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5))) )],[refute_1_30,refute_1_35]) ).
cnf(refute_1_37,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),skolemFOFtoCNF_F_1)
| member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)) ),
inference(subst,[],[refute_1_36:[bind(X_361,$fot(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2)))]]) ).
cnf(refute_1_38,plain,
member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),skolemFOFtoCNF_F_1) )],[refute_1_10,refute_1_37]) ).
cnf(refute_1_39,plain,
member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_2),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_5)) )],[refute_1_38,refute_1_9]) ).
cnf(refute_1_40,plain,
~ member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5),
inference(canonicalize,[],[normalize_1_37]) ).
cnf(refute_1_41,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_5) )],[refute_1_39,refute_1_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET645+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 19:24:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.74/1.95 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.74/1.95
% 1.74/1.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.74/1.96
%------------------------------------------------------------------------------