%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET644+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 03:36:18 EDT 2022
% Result : Theorem 11.14s 11.30s
% Output : CNFRefutation 11.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 140 ( 28 unt; 0 def)
% Number of atoms : 575 ( 46 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 783 ( 348 ~; 315 |; 69 &)
% ( 15 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 289 ( 24 sgn 142 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
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)
=> ( member(ordered_pair(B,C),cross_product(D,E))
<=> ( member(B,D)
& member(C,E) ) ) ) ) ) ) ).
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(p14,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(p19,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(p20,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p21,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(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( relation_like(B)
<=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,B)
=> ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,set_type)
& C = ordered_pair(D,E) ) ) ) ) ) ) ).
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(p27,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_6,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ilf_type(E,relation_type(B,C))
=> ( member(D,E)
=> ? [F] :
( ilf_type(F,set_type)
& ? [G] :
( ilf_type(G,set_type)
& D = ordered_pair(F,G)
& member(F,B)
& member(G,C) ) ) ) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ( ilf_type(E,relation_type(B,C))
& member(D,E) )
=> ? [F] :
( ilf_type(F,set_type)
& ? [G] :
( ilf_type(G,set_type)
& D = ordered_pair(F,G)
& member(F,B)
& member(G,C) ) ) ) ) ) ),
inference(strip,[],[prove_relset_1_6]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,set_type)
=> ! [E] :
( ( ilf_type(E,relation_type(B,C))
& member(D,E) )
=> ? [F] :
( ilf_type(F,set_type)
& ? [G] :
( ilf_type(G,set_type)
& D = ordered_pair(F,G)
& member(F,B)
& member(G,C) ) ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,C))
& member(D,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( D != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,B)
| ~ member(G,C) ) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p27]) ).
fof(normalize_0_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(B,C))
& member(D,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( D != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,B)
| ~ member(G,C) ) ) ) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& member(D,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( D != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ) ) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [D] :
( ilf_type(D,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& member(D,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( D != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ) ) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( ilf_type(skolemFOFtoCNF_D_6,set_type)
& ? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& member(skolemFOFtoCNF_D_6,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ) ) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
? [E] :
( ilf_type(E,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& member(skolemFOFtoCNF_D_6,E)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
& member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2)
& ! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(canonicalize,[],[p21]) ).
fof(normalize_0_11,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B,C] :
( ( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(B,C)
| empty(C)
| ilf_type(B,member_type(C)) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ ilf_type(C,member_type(power_set(B)))
<=> ~ ilf_type(C,subset_type(B)) ) ) ),
inference(canonicalize,[],[p14]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,member_type(power_set(B)))
| ~ ilf_type(C,set_type)
| ilf_type(C,subset_type(B)) )
& ( ~ 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_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_19,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_20,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_19]) ).
fof(normalize_0_21,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_20]) ).
fof(normalize_0_22,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_21]) ).
fof(normalize_0_23,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p20]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,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_24]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,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,[],[p19]) ).
fof(normalize_0_28,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_27]) ).
fof(normalize_0_29,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_4(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_4(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_4(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_28]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_0_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( ~ ilf_type(E,set_type)
| ( ~ member(ordered_pair(B,C),cross_product(D,E))
<=> ( ~ member(B,D)
| ~ member(C,E) ) ) ) ) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(B,D)
| ~ member(C,E)
| member(ordered_pair(B,C),cross_product(D,E)) ) ),
inference(clausify,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ relation_like(B)
<=> ? [C] :
( ilf_type(C,set_type)
& member(C,B)
& ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( C != ordered_pair(D,E)
| ~ ilf_type(E,set_type) ) ) ) ) ),
inference(canonicalize,[],[p23]) ).
fof(normalize_0_36,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ relation_like(B)
<=> ? [C] :
( ilf_type(C,set_type)
& member(C,B)
& ! [D] :
( ~ ilf_type(D,set_type)
| ! [E] :
( C != ordered_pair(D,E)
| ~ ilf_type(E,set_type) ) ) ) ) ),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ilf_type(skolemFOFtoCNF_C_2(B),set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| member(skolemFOFtoCNF_C_2(B),B)
| relation_like(B) )
& ( skolemFOFtoCNF_C_2(B) != ordered_pair(D,E)
| ~ ilf_type(B,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| C = ordered_pair(skolemFOFtoCNF_D_5(C),skolemFOFtoCNF_E_1(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| ilf_type(skolemFOFtoCNF_D_5(C),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| ilf_type(skolemFOFtoCNF_E_1(C),set_type) ) ),
inference(clausify,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| C = ordered_pair(skolemFOFtoCNF_D_5(C),skolemFOFtoCNF_E_1(C)) ),
inference(conjunct,[],[normalize_0_37]) ).
fof(normalize_0_39,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_40,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_39]) ).
fof(normalize_0_41,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_40]) ).
fof(normalize_0_42,plain,
! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_43,plain,
! [F] :
( ~ ilf_type(F,set_type)
| ! [G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ) ),
inference(specialize,[],[normalize_0_42]) ).
fof(normalize_0_44,plain,
! [F,G] :
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(F,set_type)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ),
inference(clausify,[],[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,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(conjunct,[],[normalize_0_33]) ).
cnf(refute_0_0,plain,
member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_1,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_13]) ).
cnf(refute_0_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_3,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(C))]]) ).
cnf(refute_0_5,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))))
| empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_5:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))))]]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_8,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))) ),
inference(subst,[],[refute_0_9:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),bind(C,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_11,plain,
ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(E,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_16,plain,
ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,relation_type(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) )],[refute_0_16,refute_0_10]) ).
cnf(refute_0_18,plain,
( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,member_type(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))) )],[refute_0_17,refute_0_6]) ).
cnf(refute_0_19,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_20,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_19]) ).
cnf(refute_0_21,plain,
~ empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),
inference(subst,[],[refute_0_20:[bind(B,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_22,plain,
member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( empty(power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,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_30]) ).
cnf(refute_0_24,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(D))]]) ).
cnf(refute_0_27,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
( ~ member(X_252,skolemFOFtoCNF_E_2)
| ~ member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| member(X_252,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_27:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))),bind(D,$fot(X_252))]]) ).
cnf(refute_0_29,plain,
( ~ member(X_252,skolemFOFtoCNF_E_2)
| member(X_252,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_2,power_set(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) )],[refute_0_22,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2)
| member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_29:[bind(X_252,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_0_31,plain,
member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2) )],[refute_0_0,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_33,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_26,refute_0_34]) ).
cnf(refute_0_36,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(E))]]) ).
cnf(refute_0_37,plain,
( ~ member(ordered_pair(B,C),cross_product(D,E))
| member(B,D) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),D) ),
inference(subst,[],[refute_0_37:[bind(B,$fot(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6))),bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_0_39,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| C = ordered_pair(skolemFOFtoCNF_D_5(C),skolemFOFtoCNF_E_1(C)) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_40,plain,
( ~ ilf_type(C,set_type)
| ~ member(C,B)
| ~ relation_like(B)
| C = ordered_pair(skolemFOFtoCNF_D_5(C),skolemFOFtoCNF_E_1(C)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ member(C,B)
| ~ relation_like(B)
| C = ordered_pair(skolemFOFtoCNF_D_5(C),skolemFOFtoCNF_E_1(C)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2)
| ~ relation_like(skolemFOFtoCNF_E_2)
| skolemFOFtoCNF_D_6 = ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) ),
inference(subst,[],[refute_0_41:[bind(B,$fot(skolemFOFtoCNF_E_2)),bind(C,$fot(skolemFOFtoCNF_D_6))]]) ).
cnf(refute_0_43,plain,
( ~ relation_like(skolemFOFtoCNF_E_2)
| skolemFOFtoCNF_D_6 = ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_6,skolemFOFtoCNF_E_2) )],[refute_0_0,refute_0_42]) ).
cnf(refute_0_44,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_41]) ).
cnf(refute_0_45,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)))
| relation_like(skolemFOFtoCNF_E_2) ),
inference(subst,[],[refute_0_46:[bind(B,$fot(skolemFOFtoCNF_B_1)),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(skolemFOFtoCNF_E_2))]]) ).
cnf(refute_0_48,plain,
relation_like(skolemFOFtoCNF_E_2),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_E_2,subset_type(cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))) )],[refute_0_16,refute_0_47]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_D_6 = ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_E_2) )],[refute_0_48,refute_0_43]) ).
cnf(refute_0_50,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_51,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_52,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_D_6 != ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))
| ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) = skolemFOFtoCNF_D_6 ),
inference(subst,[],[refute_0_52:[bind(X,$fot(skolemFOFtoCNF_D_6)),bind(Y,$fot(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))))]]) ).
cnf(refute_0_54,plain,
ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) = skolemFOFtoCNF_D_6,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_6,ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
( ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) != skolemFOFtoCNF_D_6
| ~ member(skolemFOFtoCNF_D_6,cross_product(D,E))
| member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E)) ),
introduced(tautology,[equality,[$cnf( ~ member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E)) ),[0],$fot(skolemFOFtoCNF_D_6)]]) ).
cnf(refute_0_56,plain,
( ~ member(skolemFOFtoCNF_D_6,cross_product(D,E))
| member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E)) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),skolemFOFtoCNF_D_6) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ member(skolemFOFtoCNF_D_6,cross_product(D,E))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),D) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E)) )],[refute_0_56,refute_0_38]) ).
cnf(refute_0_58,plain,
( ~ member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1) ),
inference(subst,[],[refute_0_57:[bind(D,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_59,plain,
member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_31,refute_0_58]) ).
cnf(refute_0_60,plain,
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(F,set_type)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_61,plain,
ilf_type(F,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(F))]]) ).
cnf(refute_0_62,plain,
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ ilf_type(G,set_type)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( ilf_type(F,set_type) )],[refute_0_61,refute_0_60]) ).
cnf(refute_0_63,plain,
ilf_type(G,set_type),
inference(subst,[],[refute_0_2:[bind(B,$fot(G))]]) ).
cnf(refute_0_64,plain,
( skolemFOFtoCNF_D_6 != ordered_pair(F,G)
| ~ member(F,skolemFOFtoCNF_B_1)
| ~ member(G,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( ilf_type(G,set_type) )],[refute_0_63,refute_0_62]) ).
cnf(refute_0_65,plain,
( skolemFOFtoCNF_D_6 != ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))
| ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1)
| ~ member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_64:[bind(F,$fot(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6))),bind(G,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_0_66,plain,
( ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) != skolemFOFtoCNF_D_6
| skolemFOFtoCNF_D_6 != skolemFOFtoCNF_D_6
| skolemFOFtoCNF_D_6 = ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_D_6,ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))) ),[1],$fot(skolemFOFtoCNF_D_6)]]) ).
cnf(refute_0_67,plain,
( skolemFOFtoCNF_D_6 != skolemFOFtoCNF_D_6
| skolemFOFtoCNF_D_6 = ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)) ),
inference(resolve,[$cnf( $equal(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),skolemFOFtoCNF_D_6) )],[refute_0_54,refute_0_66]) ).
cnf(refute_0_68,plain,
( skolemFOFtoCNF_D_6 != skolemFOFtoCNF_D_6
| ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1)
| ~ member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_6,ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6))) )],[refute_0_67,refute_0_65]) ).
cnf(refute_0_69,plain,
skolemFOFtoCNF_D_6 = skolemFOFtoCNF_D_6,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_D_6)]]) ).
cnf(refute_0_70,plain,
( ~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1)
| ~ member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_D_6,skolemFOFtoCNF_D_6) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_72,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_2,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ ilf_type(D,set_type)
| ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_4,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ ilf_type(E,set_type)
| ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_26,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ member(ordered_pair(B,C),cross_product(D,E))
| member(C,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_36,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E))
| member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),E) ),
inference(subst,[],[refute_0_75:[bind(B,$fot(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6))),bind(C,$fot(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)))]]) ).
cnf(refute_0_77,plain,
( ~ member(skolemFOFtoCNF_D_6,cross_product(D,E))
| member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),E) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6)),cross_product(D,E)) )],[refute_0_56,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4))
| member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_77:[bind(D,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_79,plain,
member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_6,cross_product(skolemFOFtoCNF_B_1,skolemFOFtoCNF_C_4)) )],[refute_0_31,refute_0_78]) ).
cnf(refute_0_80,plain,
~ member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_1(skolemFOFtoCNF_D_6),skolemFOFtoCNF_C_4) )],[refute_0_79,refute_0_70]) ).
cnf(refute_0_81,plain,
$false,
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_5(skolemFOFtoCNF_D_6),skolemFOFtoCNF_B_1) )],[refute_0_59,refute_0_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET644+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.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 20:41:17 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 11.14/11.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.14/11.30
% 11.14/11.30 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.14/11.32
%------------------------------------------------------------------------------