TSTP Solution File: SET681+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 03:36:35 EDT 2022
% Result : Theorem 16.55s 16.71s
% Output : CNFRefutation 16.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 17
% Syntax : Number of formulae : 232 ( 48 unt; 0 def)
% Number of atoms : 843 ( 29 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1084 ( 473 ~; 398 |; 141 &)
% ( 20 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 11 con; 0-3 aty)
% Number of variables : 422 ( 15 sgn 225 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,binary_relation_type)
=> ( member(B,range_of(C))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(D,B),C) ) ) ) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(ordered_pair(B,C),D)
=> ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ) ) ).
fof(p6,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(p8,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(p17,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ) ).
fof(p19,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(p22,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(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p26,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ) ).
fof(p27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ) ).
fof(p28,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ) ).
fof(p29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ) ).
fof(p31,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_48,conjecture,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ilf_type(E,member_type(B))
=> ( member(E,range(C,B,D))
<=> ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ( ilf_type(E,member_type(B))
& member(E,range(C,B,D)) )
=> ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ),
inference(strip,[],[prove_relset_1_48]) ).
fof(subgoal_1,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ( ilf_type(E,member_type(B))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) )
=> member(E,range(C,B,D)) ) ) ) ),
inference(strip,[],[prove_relset_1_48]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ( ilf_type(E,member_type(B))
& member(E,range(C,B,D)) )
=> ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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,[],[p8]) ).
fof(normalize_0_1,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_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,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_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p31]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_0_2]) ).
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(canonicalize,[],[p19]) ).
fof(normalize_0_8,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_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)) )
& ( ~ 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_8]) ).
fof(normalize_0_10,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_9]) ).
fof(normalize_0_11,plain,
? [B] :
( ~ empty(B)
& ilf_type(B,set_type)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,B))
& ? [E] :
( ilf_type(E,member_type(B))
& member(E,range(C,B,D))
& ! [F] :
( ~ ilf_type(F,member_type(C))
| ~ member(ordered_pair(F,E),D) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
? [B] :
( ~ empty(B)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,B))
& ? [E] :
( ilf_type(E,member_type(B))
& member(E,range(C,B,D))
& ! [F] :
( ~ ilf_type(F,member_type(C))
| ~ member(ordered_pair(F,E),D) ) ) ) ) ),
inference(simplify,[],[normalize_0_11,normalize_0_5]) ).
fof(normalize_0_13,plain,
( ~ empty(skolemFOFtoCNF_B_1)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,skolemFOFtoCNF_B_1))
& ? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(C,skolemFOFtoCNF_B_1,D))
& ! [F] :
( ~ ilf_type(F,member_type(C))
| ~ member(ordered_pair(F,E),D) ) ) ) ) ),
inference(skolemize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,skolemFOFtoCNF_B_1))
& ? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(C,skolemFOFtoCNF_B_1,D))
& ! [F] :
( ~ ilf_type(F,member_type(C))
| ~ member(ordered_pair(F,E),D) ) ) ) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
( ~ empty(skolemFOFtoCNF_C_4)
& ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D))
& ! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,E),D) ) ) ) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
? [D] :
( ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D))
& ! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,E),D) ) ) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
& ! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,E),skolemFOFtoCNF_D_5) ) ) ),
inference(skolemize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(canonicalize,[],[p28]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p27]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(clausify,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p23]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,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_26]) ).
fof(normalize_0_28,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,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,[],[p22]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_3(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_3(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_3(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_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)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
? [E] :
( ilf_type(E,member_type(skolemFOFtoCNF_B_1))
& member(E,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
& ! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,E),skolemFOFtoCNF_D_5) ) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_34,plain,
( ilf_type(skolemFOFtoCNF_E_1,member_type(skolemFOFtoCNF_B_1))
& member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
& ! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ) ),
inference(skolemize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p29]) ).
fof(normalize_0_37,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ~ member(B,range_of(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_40,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ~ member(B,range_of(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| ilf_type(skolemFOFtoCNF_D(B,C),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| member(ordered_pair(skolemFOFtoCNF_D(B,C),B),C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ) ),
inference(clausify,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| member(ordered_pair(skolemFOFtoCNF_D(B,C),B),C) ),
inference(conjunct,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p17]) ).
fof(normalize_0_44,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p26]) ).
fof(normalize_0_48,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_0_48]) ).
fof(normalize_0_50,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,[],[p6]) ).
fof(normalize_0_51,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_50]) ).
fof(normalize_0_52,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_51]) ).
fof(normalize_0_53,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_52]) ).
fof(normalize_0_54,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_55,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| ( member(B,domain_of(D))
& member(C,range_of(D)) ) ) ) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(C,range_of(D)) ) ),
inference(clausify,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(conjunct,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
~ empty(skolemFOFtoCNF_C_4),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_59,plain,
! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_60,plain,
! [F] :
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(specialize,[],[normalize_0_59]) ).
cnf(refute_0_0,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_3]) ).
cnf(refute_0_1,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(C))]]) ).
cnf(refute_0_4,plain,
( ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4)
| empty(skolemFOFtoCNF_C_4)
| ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(domain_of(skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4)))
| empty(power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_8:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5))),bind(C,$fot(power_set(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(domain_of(skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(domain_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_14,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_16,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_17:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_19,plain,
ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_14,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_21,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_24,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_14,refute_0_23]) ).
cnf(refute_0_25,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) ),
introduced(tautology,[equality,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) ),[0],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
ilf_type(domain_of(skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) )],[refute_0_19,refute_0_26]) ).
cnf(refute_0_28,plain,
ilf_type(domain_of(skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(domain_of(skolemFOFtoCNF_D_5),subset_type(skolemFOFtoCNF_C_4)) )],[refute_0_27,refute_0_13]) ).
cnf(refute_0_29,plain,
( empty(power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( ilf_type(domain_of(skolemFOFtoCNF_D_5),member_type(power_set(skolemFOFtoCNF_C_4))) )],[refute_0_28,refute_0_9]) ).
cnf(refute_0_30,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_31,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_30]) ).
cnf(refute_0_32,plain,
~ empty(power_set(skolemFOFtoCNF_C_4)),
inference(subst,[],[refute_0_31:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_33,plain,
member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( empty(power_set(skolemFOFtoCNF_C_4)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_35,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_35]) ).
cnf(refute_0_37,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_38,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_37,refute_0_36]) ).
cnf(refute_0_39,plain,
( ~ member(X_831,domain_of(skolemFOFtoCNF_D_5))
| ~ member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4))
| member(X_831,skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_38:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(X_831))]]) ).
cnf(refute_0_40,plain,
( ~ member(X_831,domain_of(skolemFOFtoCNF_D_5))
| member(X_831,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(domain_of(skolemFOFtoCNF_D_5),power_set(skolemFOFtoCNF_C_4)) )],[refute_0_33,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5))
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_40:[bind(X_831,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_42,plain,
member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_43,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_44,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = range_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_45:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_47,plain,
range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) = range_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_14,refute_0_46]) ).
cnf(refute_0_48,plain,
( range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5) != range_of(skolemFOFtoCNF_D_5)
| ~ member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
| member(skolemFOFtoCNF_E_1,range_of(skolemFOFtoCNF_D_5)) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) ),[1],$fot(range_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_49,plain,
( ~ member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5))
| member(skolemFOFtoCNF_E_1,range_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5),range_of(skolemFOFtoCNF_D_5)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
member(skolemFOFtoCNF_E_1,range_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_1,range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_5)) )],[refute_0_42,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| member(ordered_pair(skolemFOFtoCNF_D(B,C),B),C) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_52,plain,
( ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| member(ordered_pair(skolemFOFtoCNF_D(B,C),B),C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| ~ member(skolemFOFtoCNF_E_1,range_of(skolemFOFtoCNF_D_5))
| member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_52:[bind(B,$fot(skolemFOFtoCNF_E_1)),bind(C,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_54,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_1,range_of(skolemFOFtoCNF_D_5)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_56,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ relation_like(skolemFOFtoCNF_D_5)
| ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) ),
inference(subst,[],[refute_0_56:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_58,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_0_49]) ).
cnf(refute_0_59,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)))
| relation_like(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_60:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_62,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_53]) ).
cnf(refute_0_63,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_0_64:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_66,plain,
ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_14,refute_0_65]) ).
cnf(refute_0_67,plain,
relation_like(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) )],[refute_0_66,refute_0_61]) ).
cnf(refute_0_68,plain,
ilf_type(skolemFOFtoCNF_D_5,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_5) )],[refute_0_67,refute_0_57]) ).
cnf(refute_0_69,plain,
member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) )],[refute_0_68,refute_0_54]) ).
cnf(refute_0_70,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_71,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(ordered_pair(B,C),D)
| member(B,domain_of(D)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) ),
inference(subst,[],[refute_0_72:[bind(B,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5))),bind(C,$fot(skolemFOFtoCNF_E_1)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_0_74,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) )],[refute_0_69,refute_0_73]) ).
cnf(refute_0_75,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) )],[refute_0_68,refute_0_74]) ).
cnf(refute_0_76,plain,
member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_0_75,refute_0_41]) ).
cnf(refute_0_77,plain,
( empty(skolemFOFtoCNF_C_4)
| ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_C_4) )],[refute_0_76,refute_0_5]) ).
cnf(refute_0_78,plain,
~ empty(skolemFOFtoCNF_C_4),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_79,plain,
ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_C_4) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ ilf_type(F,member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(F,skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_81,plain,
( ~ ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4))
| ~ member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_0_80:[bind(F,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_0_82,plain,
~ ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),skolemFOFtoCNF_E_1),skolemFOFtoCNF_D_5) )],[refute_0_69,refute_0_81]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D_5),member_type(skolemFOFtoCNF_C_4)) )],[refute_0_79,refute_0_82]) ).
fof(negate_1_0,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ! [E] :
( ( ilf_type(E,member_type(B))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) )
=> member(E,range(C,B,D)) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ~ empty(B)
& ilf_type(B,set_type)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,B))
& ? [E] :
( ~ member(E,range(C,B,D))
& ilf_type(E,member_type(B))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p31]) ).
fof(normalize_1_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [B] :
( ~ empty(B)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,B))
& ? [E] :
( ~ member(E,range(C,B,D))
& ilf_type(E,member_type(B))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( ~ empty(skolemFOFtoCNF_B_2)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,skolemFOFtoCNF_B_2))
& ? [E] :
( ~ member(E,range(C,skolemFOFtoCNF_B_2,D))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,relation_type(C,skolemFOFtoCNF_B_2))
& ? [E] :
( ~ member(E,range(C,skolemFOFtoCNF_B_2,D))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(C))
& member(ordered_pair(F,E),D) ) ) ) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( ~ empty(skolemFOFtoCNF_C_5)
& ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ~ member(E,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,E),D) ) ) ) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
? [D] :
( ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ~ member(E,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,E),D) ) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ~ member(E,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,E),skolemFOFtoCNF_D_6) ) ) ),
inference(skolemize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [E] :
( ~ member(E,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
& ilf_type(E,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,E),skolemFOFtoCNF_D_6) ) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
( ~ member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6))
& ilf_type(skolemFOFtoCNF_E_2,member_type(skolemFOFtoCNF_B_2))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6) ) ),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
( ilf_type(skolemFOFtoCNF_F,member_type(skolemFOFtoCNF_C_5))
& member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6) ),
inference(skolemize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ~ member(B,range_of(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_15,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,binary_relation_type)
| ( ~ member(B,range_of(C))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C) ) ) ) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| ilf_type(skolemFOFtoCNF_D(B,C),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ member(B,range_of(C))
| member(ordered_pair(skolemFOFtoCNF_D(B,C),B),C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ) ),
inference(clausify,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p17]) ).
fof(normalize_1_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p26]) ).
fof(normalize_1_23,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_8]) ).
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(canonicalize,[],[p6]) ).
fof(normalize_1_27,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_26]) ).
fof(normalize_1_28,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_27]) ).
fof(normalize_1_29,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_28]) ).
fof(normalize_1_30,plain,
~ member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_31,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p29]) ).
fof(normalize_1_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_1_31]) ).
fof(normalize_1_33,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_1_32]) ).
cnf(refute_1_0,plain,
member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_1,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_3,plain,
( ~ ilf_type(C,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_1]) ).
cnf(refute_1_4,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_1_2:[bind(B,$fot(D))]]) ).
cnf(refute_1_5,plain,
( ~ ilf_type(C,binary_relation_type)
| ~ member(ordered_pair(D,B),C)
| member(B,range_of(C)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6)
| member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_1_5:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(skolemFOFtoCNF_D_6)),bind(D,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_1_7,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,binary_relation_type)
| member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_6) )],[refute_1_0,refute_1_6]) ).
cnf(refute_1_8,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_9,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ relation_like(skolemFOFtoCNF_D_6)
| ilf_type(skolemFOFtoCNF_D_6,binary_relation_type) ),
inference(subst,[],[refute_1_9:[bind(B,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_12,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_11]) ).
cnf(refute_1_13,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_2:[bind(B,$fot(C))]]) ).
cnf(refute_1_14,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_13,refute_1_12]) ).
cnf(refute_1_15,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)))
| relation_like(skolemFOFtoCNF_D_6) ),
inference(subst,[],[refute_1_14:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_16,plain,
ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_17,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_18,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_13,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| ilf_type(skolemFOFtoCNF_D_6,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) ),
inference(subst,[],[refute_1_19:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(E,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_21,plain,
ilf_type(skolemFOFtoCNF_D_6,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_16,refute_1_20]) ).
cnf(refute_1_22,plain,
relation_like(skolemFOFtoCNF_D_6),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) )],[refute_1_21,refute_1_15]) ).
cnf(refute_1_23,plain,
ilf_type(skolemFOFtoCNF_D_6,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_6) )],[refute_1_22,refute_1_10]) ).
cnf(refute_1_24,plain,
member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,binary_relation_type) )],[refute_1_23,refute_1_7]) ).
cnf(refute_1_25,plain,
~ member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)),
inference(canonicalize,[],[normalize_1_30]) ).
cnf(refute_1_26,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_1_33]) ).
cnf(refute_1_27,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_26]) ).
cnf(refute_1_28,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_13,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6) ),
inference(subst,[],[refute_1_28:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_30,plain,
range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) = range_of(skolemFOFtoCNF_D_6),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_6,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_16,refute_1_29]) ).
cnf(refute_1_31,plain,
( range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6) != range_of(skolemFOFtoCNF_D_6)
| ~ member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6))
| member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
introduced(tautology,[equality,[$cnf( ~ member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),[1],$fot(range_of(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_1_32,plain,
( ~ member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6))
| member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6),range_of(skolemFOFtoCNF_D_6)) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
~ member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_2,range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_6)) )],[refute_1_32,refute_1_25]) ).
cnf(refute_1_34,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_2,range_of(skolemFOFtoCNF_D_6)) )],[refute_1_24,refute_1_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET681+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.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 : Sun Jul 10 18:02:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 16.55/16.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.55/16.71
% 16.55/16.71 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.56/16.73
%------------------------------------------------------------------------------