TSTP Solution File: SET666+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.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 03:36:27 EDT 2022
% Result : Theorem 1.34s 1.52s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 10
% Syntax : Number of formulae : 102 ( 23 unt; 0 def)
% Number of atoms : 351 ( 0 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 446 ( 197 ~; 184 |; 27 &)
% ( 15 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 181 ( 4 sgn 90 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,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(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> subset(identity_relation_of(B),cross_product(B,B)) ) ).
fof(p6,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ilf_type(C,identity_relation_of_type(B))
<=> ilf_type(C,relation_type(B,B)) ) ) ) ).
fof(p12,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(p14,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(p16,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(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p18,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(p24,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_29,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(strip,[],[prove_relset_1_29]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ilf_type(identity_relation_of(B),identity_relation_of_type(B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B))
& ilf_type(B,set_type) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p24]) ).
fof(normalize_0_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B] : ~ ilf_type(identity_relation_of(B),identity_relation_of_type(B)),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
~ ilf_type(identity_relation_of(skolemFOFtoCNF_B_1),identity_relation_of_type(skolemFOFtoCNF_B_1)),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,identity_relation_of_type(B))
<=> ~ ilf_type(C,relation_type(B,B)) ) ) ),
inference(canonicalize,[],[p6]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,identity_relation_of_type(B))
<=> ~ ilf_type(C,relation_type(B,B)) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,identity_relation_of_type(B))
| ~ ilf_type(C,set_type)
| ilf_type(C,relation_type(B,B)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,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,[],[p1]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,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,[],[p12]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,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_15]) ).
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(canonicalize,[],[p18]) ).
fof(normalize_0_18,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_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) )
& ( ~ 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_18]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,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,[],[p16]) ).
fof(normalize_0_22,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_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(identity_relation_of(B),cross_product(B,B)) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_0_27,plain,
! [B] :
( ~ ilf_type(B,set_type)
| subset(identity_relation_of(B),cross_product(B,B)) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,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,[],[p14]) ).
fof(normalize_0_29,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_28]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,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_30]) ).
fof(normalize_0_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p17]) ).
fof(normalize_0_33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,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_33]) ).
fof(normalize_0_35,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_34]) ).
cnf(refute_0_0,plain,
~ ilf_type(identity_relation_of(skolemFOFtoCNF_B_1),identity_relation_of_type(skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
( ~ ilf_type(C,relation_type(B,B))
| ~ ilf_type(C,set_type)
| ilf_type(C,identity_relation_of_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(C))]]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(C,relation_type(B,B))
| ilf_type(C,identity_relation_of_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(identity_relation_of(X_1342),relation_type(X_1342,X_1342))
| ilf_type(identity_relation_of(X_1342),identity_relation_of_type(X_1342)) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(X_1342)),bind(C,$fot(identity_relation_of(X_1342)))]]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(identity_relation_of(X_1341),subset_type(cross_product(X_1341,X_1341)))
| ilf_type(identity_relation_of(X_1341),relation_type(X_1341,X_1341)) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(X_1341)),bind(C,$fot(X_1341)),bind(D,$fot(identity_relation_of(X_1341)))]]) ).
cnf(refute_0_11,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_16]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(identity_relation_of(X_1340),member_type(power_set(cross_product(X_1340,X_1340))))
| ilf_type(identity_relation_of(X_1340),subset_type(cross_product(X_1340,X_1340))) ),
inference(subst,[],[refute_0_13:[bind(B,$fot(cross_product(X_1340,X_1340))),bind(C,$fot(identity_relation_of(X_1340)))]]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_16,plain,
( ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ member(identity_relation_of(X_1339),power_set(cross_product(X_1339,X_1339)))
| empty(power_set(cross_product(X_1339,X_1339)))
| ilf_type(identity_relation_of(X_1339),member_type(power_set(cross_product(X_1339,X_1339)))) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(identity_relation_of(X_1339))),bind(C,$fot(power_set(cross_product(X_1339,X_1339))))]]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ member(skolemFOFtoCNF_D_2(identity_relation_of(X_1338),cross_product(X_1338,X_1338)),cross_product(X_1338,X_1338))
| member(identity_relation_of(X_1338),power_set(cross_product(X_1338,X_1338))) ),
inference(subst,[],[refute_0_21:[bind(B,$fot(identity_relation_of(X_1338))),bind(C,$fot(cross_product(X_1338,X_1338)))]]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_24,plain,
( ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
( member(identity_relation_of(X_232),power_set(C))
| member(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C),identity_relation_of(X_232)) ),
inference(subst,[],[refute_0_25:[bind(B,$fot(identity_relation_of(X_232)))]]) ).
cnf(refute_0_27,plain,
( ~ ilf_type(B,set_type)
| subset(identity_relation_of(B),cross_product(B,B)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_28,plain,
subset(identity_relation_of(B),cross_product(B,B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_27]) ).
cnf(refute_0_29,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_31]) ).
cnf(refute_0_30,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ ilf_type(D,set_type)
| ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(D))]]) ).
cnf(refute_0_33,plain,
( ~ member(D,B)
| ~ subset(B,C)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( ~ member(X_192,identity_relation_of(B))
| ~ subset(identity_relation_of(B),cross_product(B,B))
| member(X_192,cross_product(B,B)) ),
inference(subst,[],[refute_0_33:[bind(B,$fot(identity_relation_of(B))),bind(C,$fot(cross_product(B,B))),bind(D,$fot(X_192))]]) ).
cnf(refute_0_35,plain,
( ~ member(X_192,identity_relation_of(B))
| member(X_192,cross_product(B,B)) ),
inference(resolve,[$cnf( subset(identity_relation_of(B),cross_product(B,B)) )],[refute_0_28,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ member(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C),identity_relation_of(X_232))
| member(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C),cross_product(X_232,X_232)) ),
inference(subst,[],[refute_0_35:[bind(B,$fot(X_232)),bind(X_192,$fot(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C)))]]) ).
cnf(refute_0_37,plain,
( member(identity_relation_of(X_232),power_set(C))
| member(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C),cross_product(X_232,X_232)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(identity_relation_of(X_232),C),identity_relation_of(X_232)) )],[refute_0_26,refute_0_36]) ).
cnf(refute_0_38,plain,
( member(identity_relation_of(X_1338),power_set(cross_product(X_1338,X_1338)))
| member(skolemFOFtoCNF_D_2(identity_relation_of(X_1338),cross_product(X_1338,X_1338)),cross_product(X_1338,X_1338)) ),
inference(subst,[],[refute_0_37:[bind(C,$fot(cross_product(X_1338,X_1338))),bind(X_232,$fot(X_1338))]]) ).
cnf(refute_0_39,plain,
member(identity_relation_of(X_1338),power_set(cross_product(X_1338,X_1338))),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(identity_relation_of(X_1338),cross_product(X_1338,X_1338)),cross_product(X_1338,X_1338)) )],[refute_0_38,refute_0_22]) ).
cnf(refute_0_40,plain,
member(identity_relation_of(X_1339),power_set(cross_product(X_1339,X_1339))),
inference(subst,[],[refute_0_39:[bind(X_1338,$fot(X_1339))]]) ).
cnf(refute_0_41,plain,
( empty(power_set(cross_product(X_1339,X_1339)))
| ilf_type(identity_relation_of(X_1339),member_type(power_set(cross_product(X_1339,X_1339)))) ),
inference(resolve,[$cnf( member(identity_relation_of(X_1339),power_set(cross_product(X_1339,X_1339))) )],[refute_0_40,refute_0_18]) ).
cnf(refute_0_42,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_43,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_42]) ).
cnf(refute_0_44,plain,
~ empty(power_set(cross_product(X_1339,X_1339))),
inference(subst,[],[refute_0_43:[bind(B,$fot(cross_product(X_1339,X_1339)))]]) ).
cnf(refute_0_45,plain,
ilf_type(identity_relation_of(X_1339),member_type(power_set(cross_product(X_1339,X_1339)))),
inference(resolve,[$cnf( empty(power_set(cross_product(X_1339,X_1339))) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
ilf_type(identity_relation_of(X_1340),member_type(power_set(cross_product(X_1340,X_1340)))),
inference(subst,[],[refute_0_45:[bind(X_1339,$fot(X_1340))]]) ).
cnf(refute_0_47,plain,
ilf_type(identity_relation_of(X_1340),subset_type(cross_product(X_1340,X_1340))),
inference(resolve,[$cnf( ilf_type(identity_relation_of(X_1340),member_type(power_set(cross_product(X_1340,X_1340)))) )],[refute_0_46,refute_0_14]) ).
cnf(refute_0_48,plain,
ilf_type(identity_relation_of(X_1341),subset_type(cross_product(X_1341,X_1341))),
inference(subst,[],[refute_0_47:[bind(X_1340,$fot(X_1341))]]) ).
cnf(refute_0_49,plain,
ilf_type(identity_relation_of(X_1341),relation_type(X_1341,X_1341)),
inference(resolve,[$cnf( ilf_type(identity_relation_of(X_1341),subset_type(cross_product(X_1341,X_1341))) )],[refute_0_48,refute_0_10]) ).
cnf(refute_0_50,plain,
ilf_type(identity_relation_of(X_1342),relation_type(X_1342,X_1342)),
inference(subst,[],[refute_0_49:[bind(X_1341,$fot(X_1342))]]) ).
cnf(refute_0_51,plain,
ilf_type(identity_relation_of(X_1342),identity_relation_of_type(X_1342)),
inference(resolve,[$cnf( ilf_type(identity_relation_of(X_1342),relation_type(X_1342,X_1342)) )],[refute_0_50,refute_0_6]) ).
cnf(refute_0_52,plain,
ilf_type(identity_relation_of(skolemFOFtoCNF_B_1),identity_relation_of_type(skolemFOFtoCNF_B_1)),
inference(subst,[],[refute_0_51:[bind(X_1342,$fot(skolemFOFtoCNF_B_1))]]) ).
cnf(refute_0_53,plain,
$false,
inference(resolve,[$cnf( ilf_type(identity_relation_of(skolemFOFtoCNF_B_1),identity_relation_of_type(skolemFOFtoCNF_B_1)) )],[refute_0_52,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jul 10 17:07:26 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.34/1.52 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.34/1.52
% 1.34/1.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.34/1.52
%------------------------------------------------------------------------------