TSTP Solution File: SET686+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET686+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 03:36:38 EDT 2022
% Result : Theorem 121.40s 121.59s
% Output : CNFRefutation 121.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 268 ( 60 unt; 0 def)
% Number of atoms : 1072 ( 23 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 1417 ( 613 ~; 520 |; 209 &)
% ( 20 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 13 con; 0-4 aty)
% Number of variables : 554 ( 23 sgn 246 !; 80 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,binary_relation_type)
=> ( member(C,inverse2(D,B))
<=> ? [E] :
( ilf_type(E,set_type)
& member(ordered_pair(C,E),D)
& member(E,B) ) ) ) ) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,set_type)
=> ! [F] :
( ilf_type(F,relation_type(B,C))
=> ( member(ordered_pair(D,E),F)
=> ( member(D,B)
& member(E,C) ) ) ) ) ) ) ) ).
fof(p5,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ilf_type(E,relation_type(B,C))
=> ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ) ).
fof(p7,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ( ilf_type(B,member_type(C))
<=> member(B,C) ) ) ) ).
fof(p15,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ) ).
fof(p17,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(p24,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ) ).
fof(p25,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ) ).
fof(p27,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_53,conjecture,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ! [F] :
( ilf_type(F,member_type(B))
=> ( member(F,inverse4(B,D,E,C))
<=> ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ! [F] :
( ( ilf_type(F,member_type(B))
& member(F,inverse4(B,D,E,C)) )
=> ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) ) ) ) ) ),
inference(strip,[],[prove_relset_1_53]) ).
fof(subgoal_1,plain,
! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ! [F] :
( ( ilf_type(F,member_type(B))
& ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) )
=> member(F,inverse4(B,D,E,C)) ) ) ) ) ),
inference(strip,[],[prove_relset_1_53]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ! [F] :
( ( ilf_type(F,member_type(B))
& member(F,inverse4(B,D,E,C)) )
=> ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) ) ) ) ) ),
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,[],[p7]) ).
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,[],[p27]) ).
fof(normalize_0_5,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,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_8]) ).
fof(normalize_0_10,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,[],[p17]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,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_11]) ).
fof(normalize_0_13,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_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_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_15]) ).
fof(normalize_0_17,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_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_2(B,C),B) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p21]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,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_24,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_12]) ).
fof(normalize_0_25,plain,
? [B] :
( ~ empty(B)
& ilf_type(B,set_type)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,D))
& ? [F] :
( ilf_type(F,member_type(B))
& member(F,inverse4(B,D,E,C))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,C)
| ~ member(ordered_pair(F,G),E) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_26,plain,
? [B] :
( ~ empty(B)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,D))
& ? [F] :
( ilf_type(F,member_type(B))
& member(F,inverse4(B,D,E,C))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,C)
| ~ member(ordered_pair(F,G),E) ) ) ) ) ) ),
inference(simplify,[],[normalize_0_25,normalize_0_5]) ).
fof(normalize_0_27,plain,
( ~ empty(skolemFOFtoCNF_B_1)
& ? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,D))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,D,E,C))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,C)
| ~ member(ordered_pair(F,G),E) ) ) ) ) ) ),
inference(skolemize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,D))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,D,E,C))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,C)
| ~ member(ordered_pair(F,G),E) ) ) ) ) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
( ~ empty(skolemFOFtoCNF_C_4)
& ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,D))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,D,E,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),E) ) ) ) ) ),
inference(skolemize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,D))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,D,E,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(D))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),E) ) ) ) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
( ~ empty(skolemFOFtoCNF_D_4)
& ilf_type(skolemFOFtoCNF_D_4,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,E,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),E) ) ) ) ),
inference(skolemize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,E,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),E) ) ) ),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
& ? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),skolemFOFtoCNF_E_2) ) ) ),
inference(skolemize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [B,C,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_36,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_37,plain,
? [F] :
( ilf_type(F,member_type(skolemFOFtoCNF_B_1))
& member(F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(F,G),skolemFOFtoCNF_E_2) ) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_38,plain,
( ilf_type(skolemFOFtoCNF_F,member_type(skolemFOFtoCNF_B_1))
& member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
& ! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(skolemFOFtoCNF_F,G),skolemFOFtoCNF_E_2) ) ),
inference(skolemize,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(canonicalize,[],[p25]) ).
fof(normalize_0_41,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(specialize,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(clausify,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ( ~ member(C,inverse2(D,B))
<=> ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D) ) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_44,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ( ~ member(C,inverse2(D,B))
<=> ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D) ) ) ) ) ),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| ilf_type(skolemFOFtoCNF_E(B,C,D),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ) ),
inference(clausify,[],[normalize_0_44]) ).
fof(normalize_0_46,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) ),
inference(conjunct,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_0_48,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_47]) ).
fof(normalize_0_49,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_48]) ).
fof(normalize_0_50,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_49]) ).
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)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p24]) ).
fof(normalize_0_52,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_51]) ).
fof(normalize_0_53,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_52]) ).
fof(normalize_0_54,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ! [F] :
( ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| ( member(D,B)
& member(E,C) ) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_55,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ! [F] :
( ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| ( member(D,B)
& member(E,C) ) ) ) ) ) ),
inference(specialize,[],[normalize_0_54]) ).
fof(normalize_0_56,plain,
! [B,C,D,E,F] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(D,B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ) ),
inference(clausify,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [B,C,D,E,F] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(conjunct,[],[normalize_0_56]) ).
fof(normalize_0_58,plain,
~ empty(skolemFOFtoCNF_D_4),
inference(conjunct,[],[normalize_0_31]) ).
fof(normalize_0_59,plain,
! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(skolemFOFtoCNF_F,G),skolemFOFtoCNF_E_2) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_60,plain,
! [G] :
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(skolemFOFtoCNF_F,G),skolemFOFtoCNF_E_2) ),
inference(specialize,[],[normalize_0_59]) ).
fof(normalize_0_61,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) ),
inference(conjunct,[],[normalize_0_45]) ).
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,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_4)
| empty(skolemFOFtoCNF_D_4)
| ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4)) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2))),bind(C,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(cross_product(B,C),subset_type(cross_product(B,C)))
| ilf_type(cross_product(B,C),relation_type(B,C)) ),
inference(subst,[],[refute_0_8:[bind(D,$fot(cross_product(B,C)))]]) ).
cnf(refute_0_10,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_13]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(C,member_type(power_set(B)))
| ilf_type(C,subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(X_67,member_type(power_set(X_67)))
| ilf_type(X_67,subset_type(X_67)) ),
inference(subst,[],[refute_0_12:[bind(B,$fot(X_67)),bind(C,$fot(X_67))]]) ).
cnf(refute_0_14,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_17]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ member(skolemFOFtoCNF_D_2(B,C),C)
| member(B,power_set(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ member(skolemFOFtoCNF_D_2(X_31,X_31),X_31)
| member(X_31,power_set(X_31)) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(X_31)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_18,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_18]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( member(B,power_set(C))
| member(skolemFOFtoCNF_D_2(B,C),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( member(X_31,power_set(X_31))
| member(skolemFOFtoCNF_D_2(X_31,X_31),X_31) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(X_31)),bind(C,$fot(X_31))]]) ).
cnf(refute_0_22,plain,
member(X_31,power_set(X_31)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_2(X_31,X_31),X_31) )],[refute_0_21,refute_0_17]) ).
cnf(refute_0_23,plain,
member(X_65,power_set(X_65)),
inference(subst,[],[refute_0_22:[bind(X_31,$fot(X_65))]]) ).
cnf(refute_0_24,plain,
( ~ member(X_65,power_set(X_65))
| empty(power_set(X_65))
| ilf_type(X_65,member_type(power_set(X_65))) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(X_65)),bind(C,$fot(power_set(X_65)))]]) ).
cnf(refute_0_25,plain,
( empty(power_set(X_65))
| ilf_type(X_65,member_type(power_set(X_65))) ),
inference(resolve,[$cnf( member(X_65,power_set(X_65)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_27,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_26]) ).
cnf(refute_0_28,plain,
~ empty(power_set(X_65)),
inference(subst,[],[refute_0_27:[bind(B,$fot(X_65))]]) ).
cnf(refute_0_29,plain,
ilf_type(X_65,member_type(power_set(X_65))),
inference(resolve,[$cnf( empty(power_set(X_65)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
ilf_type(X_67,member_type(power_set(X_67))),
inference(subst,[],[refute_0_29:[bind(X_65,$fot(X_67))]]) ).
cnf(refute_0_31,plain,
ilf_type(X_67,subset_type(X_67)),
inference(resolve,[$cnf( ilf_type(X_67,member_type(power_set(X_67))) )],[refute_0_30,refute_0_13]) ).
cnf(refute_0_32,plain,
ilf_type(cross_product(B,C),subset_type(cross_product(B,C))),
inference(subst,[],[refute_0_31:[bind(X_67,$fot(cross_product(B,C)))]]) ).
cnf(refute_0_33,plain,
ilf_type(cross_product(B,C),relation_type(B,C)),
inference(resolve,[$cnf( ilf_type(cross_product(B,C),subset_type(cross_product(B,C))) )],[refute_0_32,refute_0_9]) ).
cnf(refute_0_34,plain,
ilf_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)),
inference(subst,[],[refute_0_33:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_35,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_23]) ).
cnf(refute_0_36,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))))
| empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))
| member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) ),
inference(subst,[],[refute_0_37:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))))]]) ).
cnf(refute_0_39,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_24]) ).
cnf(refute_0_40,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))
| ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))) ),
inference(subst,[],[refute_0_41:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))),bind(C,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_43,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_44,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_45,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
| ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) ),
inference(subst,[],[refute_0_46:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_4)),bind(E,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_48,plain,
ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_43,refute_0_47]) ).
cnf(refute_0_49,plain,
ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) )],[refute_0_48,refute_0_42]) ).
cnf(refute_0_50,plain,
( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))
| member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))) )],[refute_0_49,refute_0_38]) ).
cnf(refute_0_51,plain,
~ empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))),
inference(subst,[],[refute_0_27:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_0_52,plain,
member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))),
inference(resolve,[$cnf( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_54,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_54]) ).
cnf(refute_0_56,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_57,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_56,refute_0_55]) ).
cnf(refute_0_58,plain,
( ~ member(X_119,skolemFOFtoCNF_E_2)
| ~ member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))
| member(X_119,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) ),
inference(subst,[],[refute_0_57:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))),bind(D,$fot(X_119))]]) ).
cnf(refute_0_59,plain,
( ~ member(X_119,skolemFOFtoCNF_E_2)
| member(X_119,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2)
| member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) ),
inference(subst,[],[refute_0_59:[bind(X_119,$fot(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2))))]]) ).
cnf(refute_0_61,plain,
member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_62,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_63,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_63]) ).
cnf(refute_0_65,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(E))]]) ).
cnf(refute_0_66,plain,
( ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
| inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,X_367) = inverse2(skolemFOFtoCNF_E_2,X_367) ),
inference(subst,[],[refute_0_66:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_4)),bind(D,$fot(skolemFOFtoCNF_E_2)),bind(E,$fot(X_367))]]) ).
cnf(refute_0_68,plain,
inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,X_367) = inverse2(skolemFOFtoCNF_E_2,X_367),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_43,refute_0_67]) ).
cnf(refute_0_69,plain,
inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4) = inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4),
inference(subst,[],[refute_0_68:[bind(X_367,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_70,plain,
( inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4) != inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)
| ~ member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) ),
introduced(tautology,[equality,[$cnf( member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) ),[1],$fot(inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_71,plain,
( ~ member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4),inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F,inverse4(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) )],[refute_0_61,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) ),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_74,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| ~ member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
| member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_75:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_77,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) )],[refute_0_72,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_79,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ relation_like(skolemFOFtoCNF_E_2)
| ilf_type(skolemFOFtoCNF_E_2,binary_relation_type) ),
inference(subst,[],[refute_0_79:[bind(B,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_81,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_53]) ).
cnf(refute_0_82,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))
| relation_like(skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_83:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_D_4)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_85,plain,
relation_like(skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))) )],[refute_0_48,refute_0_84]) ).
cnf(refute_0_86,plain,
ilf_type(skolemFOFtoCNF_E_2,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_E_2) )],[refute_0_85,refute_0_80]) ).
cnf(refute_0_87,plain,
member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,binary_relation_type) )],[refute_0_86,refute_0_77]) ).
cnf(refute_0_88,plain,
member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2) )],[refute_0_87,refute_0_60]) ).
cnf(refute_0_89,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_90,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ ilf_type(E,set_type)
| ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_56,refute_0_91]) ).
cnf(refute_0_93,plain,
( ~ ilf_type(F,relation_type(B,C))
| ~ member(ordered_pair(D,E),F)
| member(E,C) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_65,refute_0_92]) ).
cnf(refute_0_94,plain,
( ~ ilf_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),relation_type(X_1086,X_1087))
| ~ member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
| member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),X_1087) ),
inference(subst,[],[refute_0_93:[bind(B,$fot(X_1086)),bind(C,$fot(X_1087)),bind(D,$fot(skolemFOFtoCNF_F)),bind(E,$fot(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2))),bind(F,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_0_95,plain,
( ~ ilf_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),relation_type(X_1086,X_1087))
| member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),X_1087) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_88,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ ilf_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4))
| member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_95:[bind(X_1086,$fot(skolemFOFtoCNF_B_1)),bind(X_1087,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_97,plain,
member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_34,refute_0_96]) ).
cnf(refute_0_98,plain,
( empty(skolemFOFtoCNF_D_4)
| ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_D_4) )],[refute_0_97,refute_0_5]) ).
cnf(refute_0_99,plain,
~ empty(skolemFOFtoCNF_D_4),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_100,plain,
ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4)),
inference(resolve,[$cnf( empty(skolemFOFtoCNF_D_4) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ ilf_type(G,member_type(skolemFOFtoCNF_D_4))
| ~ member(G,skolemFOFtoCNF_C_4)
| ~ member(ordered_pair(skolemFOFtoCNF_F,G),skolemFOFtoCNF_E_2) ),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_102,plain,
( ~ ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4))
| ~ member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2)
| ~ member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_101:[bind(G,$fot(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)))]]) ).
cnf(refute_0_103,plain,
( ~ ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4))
| ~ member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_F,skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2)),skolemFOFtoCNF_E_2) )],[refute_0_87,refute_0_102]) ).
cnf(refute_0_104,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) ),
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_105,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_105]) ).
cnf(refute_0_107,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| ~ member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_106:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_F)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_108,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,binary_relation_type)
| member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F,inverse2(skolemFOFtoCNF_E_2,skolemFOFtoCNF_C_4)) )],[refute_0_72,refute_0_107]) ).
cnf(refute_0_109,plain,
member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,binary_relation_type) )],[refute_0_86,refute_0_108]) ).
cnf(refute_0_110,plain,
~ ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),skolemFOFtoCNF_C_4) )],[refute_0_109,refute_0_103]) ).
cnf(refute_0_111,plain,
$false,
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E(skolemFOFtoCNF_C_4,skolemFOFtoCNF_F,skolemFOFtoCNF_E_2),member_type(skolemFOFtoCNF_D_4)) )],[refute_0_100,refute_0_110]) ).
fof(negate_1_0,plain,
~ ! [B] :
( ( ~ empty(B)
& ilf_type(B,set_type) )
=> ! [C] :
( ( ~ empty(C)
& ilf_type(C,set_type) )
=> ! [D] :
( ( ~ empty(D)
& ilf_type(D,set_type) )
=> ! [E] :
( ilf_type(E,relation_type(B,D))
=> ! [F] :
( ( ilf_type(F,member_type(B))
& ? [G] :
( ilf_type(G,member_type(D))
& member(ordered_pair(F,G),E)
& member(G,C) ) )
=> member(F,inverse4(B,D,E,C)) ) ) ) ) ),
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] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,D))
& ? [F] :
( ~ member(F,inverse4(B,D,E,C))
& ilf_type(F,member_type(B))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,C)
& member(ordered_pair(F,G),E) ) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p27]) ).
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] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,D))
& ? [F] :
( ~ member(F,inverse4(B,D,E,C))
& ilf_type(F,member_type(B))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,C)
& member(ordered_pair(F,G),E) ) ) ) ) ) ),
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] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,D))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,D,E,C))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,C)
& member(ordered_pair(F,G),E) ) ) ) ) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [C] :
( ~ empty(C)
& ilf_type(C,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,D))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,D,E,C))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,C)
& member(ordered_pair(F,G),E) ) ) ) ) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( ~ empty(skolemFOFtoCNF_C_5)
& ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,D))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,D,E,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),E) ) ) ) ) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
? [D] :
( ~ empty(D)
& ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,D))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,D,E,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(D))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),E) ) ) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
( ~ empty(skolemFOFtoCNF_D_5)
& ilf_type(skolemFOFtoCNF_D_5,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,E,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),E) ) ) ) ),
inference(skolemize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,E,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),E) ) ) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
( ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))
& ? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),skolemFOFtoCNF_E_3) ) ) ),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
? [F] :
( ~ member(F,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))
& ilf_type(F,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(F,G),skolemFOFtoCNF_E_3) ) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
( ~ member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))
& ilf_type(skolemFOFtoCNF_F_1,member_type(skolemFOFtoCNF_B_2))
& ? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(skolemFOFtoCNF_F_1,G),skolemFOFtoCNF_E_3) ) ),
inference(skolemize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
? [G] :
( ilf_type(G,member_type(skolemFOFtoCNF_D_5))
& member(G,skolemFOFtoCNF_C_5)
& member(ordered_pair(skolemFOFtoCNF_F_1,G),skolemFOFtoCNF_E_3) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
( ilf_type(skolemFOFtoCNF_G,member_type(skolemFOFtoCNF_D_5))
& member(ordered_pair(skolemFOFtoCNF_F_1,skolemFOFtoCNF_G),skolemFOFtoCNF_E_3)
& member(skolemFOFtoCNF_G,skolemFOFtoCNF_C_5) ),
inference(skolemize,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
member(skolemFOFtoCNF_G,skolemFOFtoCNF_C_5),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
member(ordered_pair(skolemFOFtoCNF_F_1,skolemFOFtoCNF_G),skolemFOFtoCNF_E_3),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ( ~ member(C,inverse2(D,B))
<=> ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D) ) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_18,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,binary_relation_type)
| ( ~ member(C,inverse2(D,B))
<=> ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D) ) ) ) ) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| ilf_type(skolemFOFtoCNF_E(B,C,D),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(ordered_pair(C,skolemFOFtoCNF_E(B,C,D)),D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ member(C,inverse2(D,B))
| member(skolemFOFtoCNF_E(B,C,D),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ) ),
inference(clausify,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_1_22,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_21]) ).
fof(normalize_1_23,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_22]) ).
fof(normalize_1_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p24]) ).
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)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_1_25]) ).
fof(normalize_1_27,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_26]) ).
fof(normalize_1_28,plain,
ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p5]) ).
fof(normalize_1_30,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_29]) ).
fof(normalize_1_31,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_30]) ).
fof(normalize_1_32,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_31]) ).
fof(normalize_1_33,plain,
~ member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_34,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(canonicalize,[],[p25]) ).
fof(normalize_1_35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(specialize,[],[normalize_1_34]) ).
fof(normalize_1_36,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(clausify,[],[normalize_1_35]) ).
cnf(refute_1_0,plain,
member(skolemFOFtoCNF_G,skolemFOFtoCNF_C_5),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_1,plain,
member(ordered_pair(skolemFOFtoCNF_F_1,skolemFOFtoCNF_G),skolemFOFtoCNF_E_3),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(C))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ ilf_type(E,set_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(E))]]) ).
cnf(refute_1_8,plain,
( ~ ilf_type(D,binary_relation_type)
| ~ member(E,B)
| ~ member(ordered_pair(C,E),D)
| member(C,inverse2(D,B)) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_1_7,refute_1_6]) ).
cnf(refute_1_9,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_F_1,skolemFOFtoCNF_G),skolemFOFtoCNF_E_3)
| ~ member(skolemFOFtoCNF_G,X_6323)
| member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,X_6323)) ),
inference(subst,[],[refute_1_8:[bind(B,$fot(X_6323)),bind(C,$fot(skolemFOFtoCNF_F_1)),bind(D,$fot(skolemFOFtoCNF_E_3)),bind(E,$fot(skolemFOFtoCNF_G))]]) ).
cnf(refute_1_10,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,binary_relation_type)
| ~ member(skolemFOFtoCNF_G,X_6323)
| member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,X_6323)) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_F_1,skolemFOFtoCNF_G),skolemFOFtoCNF_E_3) )],[refute_1_1,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_12,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_11]) ).
cnf(refute_1_13,plain,
( ~ relation_like(skolemFOFtoCNF_E_3)
| ilf_type(skolemFOFtoCNF_E_3,binary_relation_type) ),
inference(subst,[],[refute_1_12:[bind(B,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_14,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_27]) ).
cnf(refute_1_15,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_14]) ).
cnf(refute_1_16,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)))
| relation_like(skolemFOFtoCNF_E_3) ),
inference(subst,[],[refute_1_16:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_D_5)),bind(D,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_18,plain,
ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)),
inference(canonicalize,[],[normalize_1_28]) ).
cnf(refute_1_19,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_1_32]) ).
cnf(refute_1_20,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_19]) ).
cnf(refute_1_21,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_20]) ).
cnf(refute_1_22,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))
| ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))) ),
inference(subst,[],[refute_1_21:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_D_5)),bind(E,$fot(skolemFOFtoCNF_E_3))]]) ).
cnf(refute_1_23,plain,
ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)) )],[refute_1_18,refute_1_22]) ).
cnf(refute_1_24,plain,
relation_like(skolemFOFtoCNF_E_3),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,subset_type(cross_product(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))) )],[refute_1_23,refute_1_17]) ).
cnf(refute_1_25,plain,
ilf_type(skolemFOFtoCNF_E_3,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_E_3) )],[refute_1_24,refute_1_13]) ).
cnf(refute_1_26,plain,
( ~ member(skolemFOFtoCNF_G,X_6323)
| member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,X_6323)) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,binary_relation_type) )],[refute_1_25,refute_1_10]) ).
cnf(refute_1_27,plain,
( ~ member(skolemFOFtoCNF_G,skolemFOFtoCNF_C_5)
| member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) ),
inference(subst,[],[refute_1_26:[bind(X_6323,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_28,plain,
member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_G,skolemFOFtoCNF_C_5) )],[refute_1_0,refute_1_27]) ).
cnf(refute_1_29,plain,
~ member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)),
inference(canonicalize,[],[normalize_1_33]) ).
cnf(refute_1_30,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(canonicalize,[],[normalize_1_36]) ).
cnf(refute_1_31,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_30]) ).
cnf(refute_1_32,plain,
( ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_1_7,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))
| inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,X_1469) = inverse2(skolemFOFtoCNF_E_3,X_1469) ),
inference(subst,[],[refute_1_33:[bind(B,$fot(skolemFOFtoCNF_B_2)),bind(C,$fot(skolemFOFtoCNF_D_5)),bind(D,$fot(skolemFOFtoCNF_E_3)),bind(E,$fot(X_1469))]]) ).
cnf(refute_1_35,plain,
inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,X_1469) = inverse2(skolemFOFtoCNF_E_3,X_1469),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_3,relation_type(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)) )],[refute_1_18,refute_1_34]) ).
cnf(refute_1_36,plain,
inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5) = inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5),
inference(subst,[],[refute_1_35:[bind(X_1469,$fot(skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_37,plain,
( inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5) != inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)
| ~ member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))
| member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) ),
introduced(tautology,[equality,[$cnf( ~ member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) ),[1],$fot(inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))]]) ).
cnf(refute_1_38,plain,
( ~ member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5))
| member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5),inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
~ member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_F_1,inverse4(skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) )],[refute_1_38,refute_1_29]) ).
cnf(refute_1_40,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_F_1,inverse2(skolemFOFtoCNF_E_3,skolemFOFtoCNF_C_5)) )],[refute_1_28,refute_1_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET686+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 03:31:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 121.40/121.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 121.40/121.59
% 121.40/121.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 121.40/121.62
%------------------------------------------------------------------------------