TSTP Solution File: SET647+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET647+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:36:19 EDT 2022
% Result : Theorem 4.60s 4.81s
% Output : CNFRefutation 4.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 108 ( 21 unt; 0 def)
% Number of atoms : 388 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 490 ( 210 ~; 201 |; 38 &)
% ( 12 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 182 ( 4 sgn 98 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> subset(B,cross_product(domain_of(B),range_of(B))) ) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ( subset(B,C)
=> ( subset(cross_product(B,D),cross_product(C,D))
& subset(cross_product(D,B),cross_product(D,C)) ) ) ) ) ) ).
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(p12,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(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,subset_type(B))
<=> ilf_type(C,member_type(power_set(B))) ) ) ) ).
fof(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p21,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ) ).
fof(p26,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_9,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( subset(domain_of(C),B)
=> ilf_type(C,relation_type(B,range_of(C))) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,binary_relation_type)
& subset(domain_of(C),B) )
=> ilf_type(C,relation_type(B,range_of(C))) ) ),
inference(strip,[],[prove_relset_1_9]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ilf_type(C,binary_relation_type)
& subset(domain_of(C),B) )
=> ilf_type(C,relation_type(B,range_of(C))) ) ),
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,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_1,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_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p26]) ).
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)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_0_7,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p22]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p20]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_5(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_5(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_15]) ).
fof(normalize_0_17,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_5(B,C),B) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ~ ilf_type(C,relation_type(B,range_of(C)))
& ilf_type(C,binary_relation_type)
& subset(domain_of(C),B) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_20,plain,
? [B,C] :
( ~ ilf_type(C,relation_type(B,range_of(C)))
& ilf_type(C,binary_relation_type)
& subset(domain_of(C),B) ),
inference(simplify,[],[normalize_0_19,normalize_0_5]) ).
fof(normalize_0_21,plain,
( ~ ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))
& ilf_type(skolemFOFtoCNF_C_4,binary_relation_type)
& subset(domain_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1) ),
inference(skolemize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
ilf_type(skolemFOFtoCNF_C_4,binary_relation_type),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| subset(B,cross_product(domain_of(B),range_of(B))) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| subset(B,cross_product(domain_of(B),range_of(B))) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,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,[],[p12]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_3(B,C),C)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_3(B,C),set_type)
| subset(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(skolemFOFtoCNF_D_3(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_26]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,plain,
subset(domain_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_30,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ subset(B,C)
| ( subset(cross_product(B,D),cross_product(C,D))
& subset(cross_product(D,B),cross_product(D,C)) ) ) ) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_0_31,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ~ subset(B,C)
| ( subset(cross_product(B,D),cross_product(C,D))
& subset(cross_product(D,B),cross_product(D,C)) ) ) ) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(D,B),cross_product(D,C)) ) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) ),
inference(conjunct,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p21]) ).
fof(normalize_0_35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,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_35]) ).
fof(normalize_0_37,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
~ ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),
inference(conjunct,[],[normalize_0_21]) ).
cnf(refute_0_0,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(canonicalize,[],[normalize_0_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,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(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,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(skolemFOFtoCNF_C_4,subset_type(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))
| ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(range_of(skolemFOFtoCNF_C_4))),bind(D,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(skolemFOFtoCNF_C_4,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))))
| ilf_type(skolemFOFtoCNF_C_4,subset_type(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ member(skolemFOFtoCNF_C_4,power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))
| empty(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))
| ilf_type(skolemFOFtoCNF_C_4,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))))]]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_C_4,power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_5(B,C),B) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_5(B,C),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( member(B,power_set(C))
| member(skolemFOFtoCNF_D_5(B,C),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( member(skolemFOFtoCNF_C_4,power_set(C))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_22,plain,
ilf_type(skolemFOFtoCNF_C_4,binary_relation_type),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(B,binary_relation_type)
| subset(B,cross_product(domain_of(B),range_of(B))) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_24,plain,
( ~ ilf_type(skolemFOFtoCNF_C_4,binary_relation_type)
| subset(skolemFOFtoCNF_C_4,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_23:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_25,plain,
subset(skolemFOFtoCNF_C_4,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_C_4,binary_relation_type) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_27,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_27]) ).
cnf(refute_0_29,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_30,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ member(X_267,skolemFOFtoCNF_C_4)
| ~ subset(skolemFOFtoCNF_C_4,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4)))
| member(X_267,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_30:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4)))),bind(D,$fot(X_267))]]) ).
cnf(refute_0_32,plain,
( ~ member(X_267,skolemFOFtoCNF_C_4)
| member(X_267,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) ),
inference(resolve,[$cnf( subset(skolemFOFtoCNF_C_4,cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) )],[refute_0_25,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),skolemFOFtoCNF_C_4)
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_32:[bind(X_267,$fot(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C)))]]) ).
cnf(refute_0_34,plain,
( member(skolemFOFtoCNF_C_4,power_set(C))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),skolemFOFtoCNF_C_4) )],[refute_0_21,refute_0_33]) ).
cnf(refute_0_35,plain,
subset(domain_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_36,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_37,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ ilf_type(D,set_type)
| ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ subset(B,C)
| subset(cross_product(B,D),cross_product(C,D)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_29,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ subset(domain_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1)
| subset(cross_product(domain_of(skolemFOFtoCNF_C_4),X_56),cross_product(skolemFOFtoCNF_B_1,X_56)) ),
inference(subst,[],[refute_0_39:[bind(B,$fot(domain_of(skolemFOFtoCNF_C_4))),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(X_56))]]) ).
cnf(refute_0_41,plain,
subset(cross_product(domain_of(skolemFOFtoCNF_C_4),X_56),cross_product(skolemFOFtoCNF_B_1,X_56)),
inference(resolve,[$cnf( subset(domain_of(skolemFOFtoCNF_C_4),skolemFOFtoCNF_B_1) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ member(X_267,cross_product(domain_of(skolemFOFtoCNF_C_4),X_56))
| ~ subset(cross_product(domain_of(skolemFOFtoCNF_C_4),X_56),cross_product(skolemFOFtoCNF_B_1,X_56))
| member(X_267,cross_product(skolemFOFtoCNF_B_1,X_56)) ),
inference(subst,[],[refute_0_30:[bind(B,$fot(cross_product(domain_of(skolemFOFtoCNF_C_4),X_56))),bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,X_56))),bind(D,$fot(X_267))]]) ).
cnf(refute_0_43,plain,
( ~ member(X_267,cross_product(domain_of(skolemFOFtoCNF_C_4),X_56))
| member(X_267,cross_product(skolemFOFtoCNF_B_1,X_56)) ),
inference(resolve,[$cnf( subset(cross_product(domain_of(skolemFOFtoCNF_C_4),X_56),cross_product(skolemFOFtoCNF_B_1,X_56)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_43:[bind(X_267,$fot(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C))),bind(X_56,$fot(range_of(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_45,plain,
( member(skolemFOFtoCNF_C_4,power_set(C))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,C),cross_product(domain_of(skolemFOFtoCNF_C_4),range_of(skolemFOFtoCNF_C_4))) )],[refute_0_34,refute_0_44]) ).
cnf(refute_0_46,plain,
( member(skolemFOFtoCNF_C_4,power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_45:[bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_47,plain,
member(skolemFOFtoCNF_C_4,power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_C_4,cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) )],[refute_0_46,refute_0_17]) ).
cnf(refute_0_48,plain,
( empty(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))
| ilf_type(skolemFOFtoCNF_C_4,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_C_4,power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))) )],[refute_0_47,refute_0_13]) ).
cnf(refute_0_49,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_50,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_49]) ).
cnf(refute_0_51,plain,
~ empty(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))),
inference(subst,[],[refute_0_50:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_52,plain,
ilf_type(skolemFOFtoCNF_C_4,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))),
inference(resolve,[$cnf( empty(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
ilf_type(skolemFOFtoCNF_C_4,subset_type(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_C_4,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))))) )],[refute_0_52,refute_0_9]) ).
cnf(refute_0_54,plain,
ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_C_4,subset_type(cross_product(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4)))) )],[refute_0_53,refute_0_5]) ).
cnf(refute_0_55,plain,
~ ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_56,plain,
$false,
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_C_4,relation_type(skolemFOFtoCNF_B_1,range_of(skolemFOFtoCNF_C_4))) )],[refute_0_54,refute_0_55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET647+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n027.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun Jul 10 00:43:32 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.60/4.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.60/4.81
% 4.60/4.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.60/4.82
%------------------------------------------------------------------------------