TSTP Solution File: SET659+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET659+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 03:36:25 EDT 2022
% Result : Theorem 8.26s 8.46s
% Output : CNFRefutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 21
% Syntax : Number of formulae : 236 ( 51 unt; 0 def)
% Number of atoms : 825 ( 88 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1041 ( 452 ~; 420 |; 94 &)
% ( 23 <=>; 52 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 9 con; 0-3 aty)
% Number of variables : 404 ( 16 sgn 216 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(C,domain_of(B))
<=> ? [D] :
( ilf_type(D,set_type)
& member(ordered_pair(C,D),B) ) ) ) ) ).
fof(p4,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
<=> member(D,C) ) )
=> B = C ) ) ) ).
fof(p7,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(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(p22,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ( member(B,power_set(C))
<=> ! [D] :
( ilf_type(D,set_type)
=> ( member(D,B)
=> member(D,C) ) ) ) ) ) ).
fof(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ) ).
fof(p24,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(p27,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(p30,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ) ).
fof(p31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ilf_type(domain(B,C,D),subset_type(B)) ) ) ) ).
fof(p34,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_22,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) )
<=> domain(C,B,D) = C ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) )
=> domain(C,B,D) = C ) ) ),
inference(strip,[],[prove_relset_1_22]) ).
fof(subgoal_1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& domain(C,B,D) = C )
=> ! [E] :
( ( ilf_type(E,set_type)
& member(E,C) )
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) ) ),
inference(strip,[],[prove_relset_1_22]) ).
fof(negate_0_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& ! [E] :
( ilf_type(E,set_type)
=> ( member(E,C)
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) )
=> domain(C,B,D) = C ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| B = C
| ? [D] :
( ilf_type(D,set_type)
& ( ~ member(D,B)
<=> member(D,C) ) ) ) ),
inference(canonicalize,[],[p4]) ).
fof(normalize_0_1,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| B = C
| ? [D] :
( ilf_type(D,set_type)
& ( ~ member(D,B)
<=> member(D,C) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [B,C] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| ilf_type(skolemFOFtoCNF_D_1(B,C),set_type) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p34]) ).
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] :
( domain(C,B,D) != C
& ilf_type(D,relation_type(C,B))
& ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,C)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( domain(C,B,D) != C
& ilf_type(D,relation_type(C,B))
& ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,C)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) ),
inference(simplify,[],[normalize_0_6,normalize_0_5]) ).
fof(normalize_0_8,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D) != skolemFOFtoCNF_C_4
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) ),
inference(skolemize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
? [D] :
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D) != skolemFOFtoCNF_C_4
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4
& ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
& ! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),skolemFOFtoCNF_D_7) ) ) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),skolemFOFtoCNF_D_7) ) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),skolemFOFtoCNF_D_7) ) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [E] :
( ( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| ilf_type(skolemFOFtoCNF_F(E),set_type) )
& ( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| member(ordered_pair(E,skolemFOFtoCNF_F(E)),skolemFOFtoCNF_D_7) ) ),
inference(clausify,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [E] :
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| member(ordered_pair(E,skolemFOFtoCNF_F(E)),skolemFOFtoCNF_D_7) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_16,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,[],[p24]) ).
fof(normalize_0_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| empty(C)
| ( ~ ilf_type(B,member_type(C))
<=> ~ member(B,C) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,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_17]) ).
fof(normalize_0_19,plain,
! [B,C] :
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,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_21,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_20]) ).
fof(normalize_0_22,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_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(canonicalize,[],[p31]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p30]) ).
fof(normalize_0_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(clausify,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(canonicalize,[],[p23]) ).
fof(normalize_0_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ empty(power_set(B))
& ilf_type(power_set(B),set_type) ) ),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,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_32]) ).
fof(normalize_0_34,plain,
! [B] :
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(conjunct,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(B,power_set(C))
<=> ? [D] :
( ~ member(D,C)
& ilf_type(D,set_type)
& member(D,B) ) ) ) ),
inference(canonicalize,[],[p22]) ).
fof(normalize_0_36,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_35]) ).
fof(normalize_0_37,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_5(B,C),C)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ilf_type(skolemFOFtoCNF_D_5(B,C),set_type)
| member(B,power_set(C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| member(B,power_set(C))
| member(skolemFOFtoCNF_D_5(B,C),B) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ) ),
inference(clausify,[],[normalize_0_36]) ).
fof(normalize_0_38,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_37]) ).
fof(normalize_0_39,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4,
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_40,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,domain_of(B))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_41,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,domain_of(B))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B) ) ) ) ),
inference(specialize,[],[normalize_0_40]) ).
fof(normalize_0_42,plain,
! [B,C,D] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| ilf_type(skolemFOFtoCNF_D(B,C),set_type) )
& ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| member(ordered_pair(C,skolemFOFtoCNF_D(B,C)),B) )
& ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ) ),
inference(clausify,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [B,C,D] :
( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ),
inference(conjunct,[],[normalize_0_42]) ).
fof(normalize_0_44,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_0_45,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_44]) ).
fof(normalize_0_46,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_45]) ).
fof(normalize_0_47,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_46]) ).
fof(normalize_0_48,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p27]) ).
fof(normalize_0_49,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_48]) ).
fof(normalize_0_50,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_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)))
| 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,[],[p7]) ).
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)))
| 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_51]) ).
fof(normalize_0_53,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_52]) ).
fof(normalize_0_54,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_53]) ).
cnf(refute_0_0,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(C,set_type)
| ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(C))]]) ).
cnf(refute_0_4,plain,
( ~ member(skolemFOFtoCNF_D_1(B,C),B)
| ~ member(skolemFOFtoCNF_D_1(B,C),C)
| B = C ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7))
| ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4)
| skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_7) ),
inference(subst,[],[refute_0_4:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(domain_of(skolemFOFtoCNF_D_7)))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(E,set_type)
| ~ member(E,skolemFOFtoCNF_C_4)
| member(ordered_pair(E,skolemFOFtoCNF_F(E)),skolemFOFtoCNF_D_7) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_7,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(E))]]) ).
cnf(refute_0_8,plain,
( ~ member(E,skolemFOFtoCNF_C_4)
| member(ordered_pair(E,skolemFOFtoCNF_F(E)),skolemFOFtoCNF_D_7) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4)
| member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_F(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))),skolemFOFtoCNF_D_7) ),
inference(subst,[],[refute_0_8:[bind(E,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7))))]]) ).
cnf(refute_0_10,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_11,plain,
( ~ ilf_type(C,set_type)
| B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
( B = C
| member(skolemFOFtoCNF_D_1(B,C),B)
| member(skolemFOFtoCNF_D_1(B,C),C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_11]) ).
cnf(refute_0_13,plain,
( B = domain_of(skolemFOFtoCNF_D_7)
| member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),B)
| member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)) ),
inference(subst,[],[refute_0_12:[bind(C,$fot(domain_of(skolemFOFtoCNF_D_7)))]]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(B,member_type(C))
| ~ ilf_type(C,set_type)
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ ilf_type(B,member_type(C))
| empty(C)
| member(B,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ ilf_type(domain_of(skolemFOFtoCNF_D_7),member_type(power_set(skolemFOFtoCNF_C_4)))
| empty(power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_7),power_set(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_7))),bind(C,$fot(power_set(skolemFOFtoCNF_C_4)))]]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(C,subset_type(B))
| ilf_type(C,member_type(power_set(B))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ ilf_type(domain_of(skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_7),member_type(power_set(skolemFOFtoCNF_C_4))) ),
inference(subst,[],[refute_0_20:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(domain_of(skolemFOFtoCNF_D_7)))]]) ).
cnf(refute_0_22,plain,
ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_23,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_24,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ ilf_type(D,relation_type(B,C))
| ilf_type(domain(B,C,D),subset_type(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) ),
inference(subst,[],[refute_0_25:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_27,plain,
ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_29,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) = domain_of(skolemFOFtoCNF_D_7) ),
inference(subst,[],[refute_0_30:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_32,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) = domain_of(skolemFOFtoCNF_D_7),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_31]) ).
cnf(refute_0_33,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) != domain_of(skolemFOFtoCNF_D_7)
| ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) ),
introduced(tautology,[equality,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) ),[0],$fot(domain_of(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4))
| ilf_type(domain_of(skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
ilf_type(domain_of(skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( ilf_type(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
ilf_type(domain_of(skolemFOFtoCNF_D_7),member_type(power_set(skolemFOFtoCNF_C_4))),
inference(resolve,[$cnf( ilf_type(domain_of(skolemFOFtoCNF_D_7),subset_type(skolemFOFtoCNF_C_4)) )],[refute_0_35,refute_0_21]) ).
cnf(refute_0_37,plain,
( empty(power_set(skolemFOFtoCNF_C_4))
| member(domain_of(skolemFOFtoCNF_D_7),power_set(skolemFOFtoCNF_C_4)) ),
inference(resolve,[$cnf( ilf_type(domain_of(skolemFOFtoCNF_D_7),member_type(power_set(skolemFOFtoCNF_C_4))) )],[refute_0_36,refute_0_17]) ).
cnf(refute_0_38,plain,
( ~ empty(power_set(B))
| ~ ilf_type(B,set_type) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_39,plain,
~ empty(power_set(B)),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_38]) ).
cnf(refute_0_40,plain,
~ empty(power_set(skolemFOFtoCNF_C_4)),
inference(subst,[],[refute_0_39:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_41,plain,
member(domain_of(skolemFOFtoCNF_D_7),power_set(skolemFOFtoCNF_C_4)),
inference(resolve,[$cnf( empty(power_set(skolemFOFtoCNF_C_4)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_43,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ ilf_type(D,set_type)
| ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_43]) ).
cnf(refute_0_45,plain,
ilf_type(D,set_type),
inference(subst,[],[refute_0_1:[bind(B,$fot(D))]]) ).
cnf(refute_0_46,plain,
( ~ member(B,power_set(C))
| ~ member(D,B)
| member(D,C) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_45,refute_0_44]) ).
cnf(refute_0_47,plain,
( ~ member(X_771,domain_of(skolemFOFtoCNF_D_7))
| ~ member(domain_of(skolemFOFtoCNF_D_7),power_set(skolemFOFtoCNF_C_4))
| member(X_771,skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_46:[bind(B,$fot(domain_of(skolemFOFtoCNF_D_7))),bind(C,$fot(skolemFOFtoCNF_C_4)),bind(D,$fot(X_771))]]) ).
cnf(refute_0_48,plain,
( ~ member(X_771,domain_of(skolemFOFtoCNF_D_7))
| member(X_771,skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(domain_of(skolemFOFtoCNF_D_7),power_set(skolemFOFtoCNF_C_4)) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7))
| member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_48:[bind(X_771,$fot(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7))))]]) ).
cnf(refute_0_50,plain,
( B = domain_of(skolemFOFtoCNF_D_7)
| member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),B)
| member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(B,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_13,refute_0_49]) ).
cnf(refute_0_51,plain,
( skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_7)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4) ),
inference(subst,[],[refute_0_50:[bind(B,$fot(skolemFOFtoCNF_C_4))]]) ).
cnf(refute_0_52,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4,
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_53,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) != domain_of(skolemFOFtoCNF_D_7)
| domain_of(skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) = skolemFOFtoCNF_C_4 ),
introduced(tautology,[equality,[$cnf( ~ $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),skolemFOFtoCNF_C_4) ),[0],$fot(domain_of(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_54,plain,
( domain_of(skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7) = skolemFOFtoCNF_C_4 ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_32,refute_0_53]) ).
cnf(refute_0_55,plain,
domain_of(skolemFOFtoCNF_D_7) != skolemFOFtoCNF_C_4,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_7),skolemFOFtoCNF_C_4) )],[refute_0_54,refute_0_52]) ).
cnf(refute_0_56,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_57,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_58,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_C_4 != domain_of(skolemFOFtoCNF_D_7)
| domain_of(skolemFOFtoCNF_D_7) = skolemFOFtoCNF_C_4 ),
inference(subst,[],[refute_0_58:[bind(X,$fot(skolemFOFtoCNF_C_4)),bind(Y,$fot(domain_of(skolemFOFtoCNF_D_7)))]]) ).
cnf(refute_0_60,plain,
skolemFOFtoCNF_C_4 != domain_of(skolemFOFtoCNF_D_7),
inference(resolve,[$cnf( $equal(domain_of(skolemFOFtoCNF_D_7),skolemFOFtoCNF_C_4) )],[refute_0_59,refute_0_55]) ).
cnf(refute_0_61,plain,
member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_51,refute_0_60]) ).
cnf(refute_0_62,plain,
member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_F(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))),skolemFOFtoCNF_D_7),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4) )],[refute_0_61,refute_0_9]) ).
cnf(refute_0_63,plain,
( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ),
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_64,plain,
( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_63]) ).
cnf(refute_0_65,plain,
( ~ ilf_type(B,binary_relation_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ),
inference(resolve,[$cnf( ilf_type(D,set_type) )],[refute_0_45,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,binary_relation_type)
| ~ member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_F(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))),skolemFOFtoCNF_D_7)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)) ),
inference(subst,[],[refute_0_65:[bind(B,$fot(skolemFOFtoCNF_D_7)),bind(C,$fot(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))),bind(D,$fot(skolemFOFtoCNF_F(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))))]]) ).
cnf(refute_0_67,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,binary_relation_type)
| member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)) ),
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_F(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)))),skolemFOFtoCNF_D_7) )],[refute_0_62,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_69,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ relation_like(skolemFOFtoCNF_D_7)
| ilf_type(skolemFOFtoCNF_D_7,binary_relation_type) ),
inference(subst,[],[refute_0_69:[bind(B,$fot(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_71,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_50]) ).
cnf(refute_0_72,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)))
| relation_like(skolemFOFtoCNF_D_7) ),
inference(subst,[],[refute_0_73:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_75,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_76,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_1,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_3,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(skolemFOFtoCNF_D_7,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_0_77:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_D_7))]]) ).
cnf(refute_0_79,plain,
ilf_type(skolemFOFtoCNF_D_7,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_7,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_22,refute_0_78]) ).
cnf(refute_0_80,plain,
relation_like(skolemFOFtoCNF_D_7),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_7,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) )],[refute_0_79,refute_0_74]) ).
cnf(refute_0_81,plain,
ilf_type(skolemFOFtoCNF_D_7,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_7) )],[refute_0_80,refute_0_70]) ).
cnf(refute_0_82,plain,
member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_7,binary_relation_type) )],[refute_0_81,refute_0_67]) ).
cnf(refute_0_83,plain,
( ~ member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4)
| skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_7) ),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_82,refute_0_5]) ).
cnf(refute_0_84,plain,
skolemFOFtoCNF_C_4 = domain_of(skolemFOFtoCNF_D_7),
inference(resolve,[$cnf( member(skolemFOFtoCNF_D_1(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)),skolemFOFtoCNF_C_4) )],[refute_0_61,refute_0_83]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_4,domain_of(skolemFOFtoCNF_D_7)) )],[refute_0_84,refute_0_60]) ).
fof(negate_1_0,plain,
~ ! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& domain(C,B,D) = C )
=> ! [E] :
( ( ilf_type(E,set_type)
& member(E,C) )
=> ? [F] :
( ilf_type(F,set_type)
& member(ordered_pair(E,F),D) ) ) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( domain(C,B,D) = C
& ilf_type(D,relation_type(C,B))
& ? [E] :
( ilf_type(E,set_type)
& member(E,C)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),D) ) ) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p34]) ).
fof(normalize_1_2,plain,
! [B] : ilf_type(B,set_type),
inference(specialize,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
? [B,C] :
( ilf_type(C,set_type)
& ? [D] :
( domain(C,B,D) = C
& ilf_type(D,relation_type(C,B))
& ? [E] :
( ilf_type(E,set_type)
& member(E,C)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),D) ) ) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D) = skolemFOFtoCNF_C_5
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ilf_type(E,set_type)
& member(E,skolemFOFtoCNF_C_5)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),D) ) ) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [D] :
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D) = skolemFOFtoCNF_C_5
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ilf_type(E,set_type)
& member(E,skolemFOFtoCNF_C_5)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),D) ) ) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) = skolemFOFtoCNF_C_5
& ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
& ? [E] :
( ilf_type(E,set_type)
& member(E,skolemFOFtoCNF_C_5)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),skolemFOFtoCNF_D_8) ) ) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
? [E] :
( ilf_type(E,set_type)
& member(E,skolemFOFtoCNF_C_5)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(E,F),skolemFOFtoCNF_D_8) ) ),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
( ilf_type(skolemFOFtoCNF_E_1,set_type)
& member(skolemFOFtoCNF_E_1,skolemFOFtoCNF_C_5)
& ! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(skolemFOFtoCNF_E_1,F),skolemFOFtoCNF_D_8) ) ),
inference(skolemize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
member(skolemFOFtoCNF_E_1,skolemFOFtoCNF_C_5),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,domain_of(B))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B) ) ) ) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_11,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ~ member(C,domain_of(B))
<=> ! [D] :
( ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B) ) ) ) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [B,C,D] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| ilf_type(skolemFOFtoCNF_D(B,C),set_type) )
& ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| member(ordered_pair(C,skolemFOFtoCNF_D(B,C)),B) )
& ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,set_type)
| ~ member(ordered_pair(C,D),B)
| member(C,domain_of(B)) ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [B,C] :
( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| member(ordered_pair(C,skolemFOFtoCNF_D(B,C)),B) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_15,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p30]) ).
fof(normalize_1_16,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(clausify,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) = skolemFOFtoCNF_C_5,
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_19,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p15]) ).
fof(normalize_1_20,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_19]) ).
fof(normalize_1_21,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_20]) ).
fof(normalize_1_22,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p27]) ).
fof(normalize_1_24,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_23]) ).
fof(normalize_1_25,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_24]) ).
fof(normalize_1_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(canonicalize,[],[p7]) ).
fof(normalize_1_27,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(specialize,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [B,C,D,E] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ),
inference(clausify,[],[normalize_1_27]) ).
fof(normalize_1_29,plain,
! [B,C,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(conjunct,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(skolemFOFtoCNF_E_1,F),skolemFOFtoCNF_D_8) ),
inference(conjunct,[],[normalize_1_8]) ).
fof(normalize_1_31,plain,
! [F] :
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(skolemFOFtoCNF_E_1,F),skolemFOFtoCNF_D_8) ),
inference(specialize,[],[normalize_1_30]) ).
cnf(refute_1_0,plain,
member(skolemFOFtoCNF_E_1,skolemFOFtoCNF_C_5),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_1,plain,
( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(C,set_type)
| ~ member(C,domain_of(B))
| member(ordered_pair(C,skolemFOFtoCNF_D(B,C)),B) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_2,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_3,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_2:[bind(B,$fot(C))]]) ).
cnf(refute_1_4,plain,
( ~ ilf_type(B,binary_relation_type)
| ~ member(C,domain_of(B))
| member(ordered_pair(C,skolemFOFtoCNF_D(B,C)),B) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_1]) ).
cnf(refute_1_5,plain,
( ~ ilf_type(skolemFOFtoCNF_D_8,binary_relation_type)
| ~ member(X_2010,domain_of(skolemFOFtoCNF_D_8))
| member(ordered_pair(X_2010,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,X_2010)),skolemFOFtoCNF_D_8) ),
inference(subst,[],[refute_1_4:[bind(B,$fot(skolemFOFtoCNF_D_8)),bind(C,$fot(X_2010))]]) ).
cnf(refute_1_6,plain,
ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_7,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_8,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_7]) ).
cnf(refute_1_9,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_8]) ).
cnf(refute_1_10,plain,
( ~ ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) = domain_of(skolemFOFtoCNF_D_8) ),
inference(subst,[],[refute_1_9:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_8))]]) ).
cnf(refute_1_11,plain,
domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) = domain_of(skolemFOFtoCNF_D_8),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_6,refute_1_10]) ).
cnf(refute_1_12,plain,
domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) = skolemFOFtoCNF_C_5,
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_13,plain,
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) != domain_of(skolemFOFtoCNF_D_8)
| domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) != skolemFOFtoCNF_C_5
| skolemFOFtoCNF_C_5 = domain_of(skolemFOFtoCNF_D_8) ),
introduced(tautology,[equality,[$cnf( $equal(domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8),domain_of(skolemFOFtoCNF_D_8)) ),[0],$fot(skolemFOFtoCNF_C_5)]]) ).
cnf(refute_1_14,plain,
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8) != domain_of(skolemFOFtoCNF_D_8)
| skolemFOFtoCNF_C_5 = domain_of(skolemFOFtoCNF_D_8) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8),skolemFOFtoCNF_C_5) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
skolemFOFtoCNF_C_5 = domain_of(skolemFOFtoCNF_D_8),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_8),domain_of(skolemFOFtoCNF_D_8)) )],[refute_1_11,refute_1_14]) ).
cnf(refute_1_16,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_17,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_18,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
( skolemFOFtoCNF_C_5 != domain_of(skolemFOFtoCNF_D_8)
| domain_of(skolemFOFtoCNF_D_8) = skolemFOFtoCNF_C_5 ),
inference(subst,[],[refute_1_18:[bind(X,$fot(skolemFOFtoCNF_C_5)),bind(Y,$fot(domain_of(skolemFOFtoCNF_D_8)))]]) ).
cnf(refute_1_20,plain,
domain_of(skolemFOFtoCNF_D_8) = skolemFOFtoCNF_C_5,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C_5,domain_of(skolemFOFtoCNF_D_8)) )],[refute_1_15,refute_1_19]) ).
cnf(refute_1_21,plain,
( domain_of(skolemFOFtoCNF_D_8) != skolemFOFtoCNF_C_5
| ~ member(X_2010,skolemFOFtoCNF_C_5)
| member(X_2010,domain_of(skolemFOFtoCNF_D_8)) ),
introduced(tautology,[equality,[$cnf( ~ member(X_2010,domain_of(skolemFOFtoCNF_D_8)) ),[1],$fot(skolemFOFtoCNF_C_5)]]) ).
cnf(refute_1_22,plain,
( ~ member(X_2010,skolemFOFtoCNF_C_5)
| member(X_2010,domain_of(skolemFOFtoCNF_D_8)) ),
inference(resolve,[$cnf( $equal(domain_of(skolemFOFtoCNF_D_8),skolemFOFtoCNF_C_5) )],[refute_1_20,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ ilf_type(skolemFOFtoCNF_D_8,binary_relation_type)
| ~ member(X_2010,skolemFOFtoCNF_C_5)
| member(ordered_pair(X_2010,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,X_2010)),skolemFOFtoCNF_D_8) ),
inference(resolve,[$cnf( member(X_2010,domain_of(skolemFOFtoCNF_D_8)) )],[refute_1_22,refute_1_5]) ).
cnf(refute_1_24,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_25,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_24]) ).
cnf(refute_1_26,plain,
( ~ relation_like(skolemFOFtoCNF_D_8)
| ilf_type(skolemFOFtoCNF_D_8,binary_relation_type) ),
inference(subst,[],[refute_1_25:[bind(B,$fot(skolemFOFtoCNF_D_8))]]) ).
cnf(refute_1_27,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_25]) ).
cnf(refute_1_28,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_28]) ).
cnf(refute_1_30,plain,
( ~ ilf_type(skolemFOFtoCNF_D_8,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)))
| relation_like(skolemFOFtoCNF_D_8) ),
inference(subst,[],[refute_1_29:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_8))]]) ).
cnf(refute_1_31,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_1_29]) ).
cnf(refute_1_32,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_2,refute_1_31]) ).
cnf(refute_1_33,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_3,refute_1_32]) ).
cnf(refute_1_34,plain,
( ~ ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| ilf_type(skolemFOFtoCNF_D_8,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) ),
inference(subst,[],[refute_1_33:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(E,$fot(skolemFOFtoCNF_D_8))]]) ).
cnf(refute_1_35,plain,
ilf_type(skolemFOFtoCNF_D_8,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_8,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_6,refute_1_34]) ).
cnf(refute_1_36,plain,
relation_like(skolemFOFtoCNF_D_8),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_8,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) )],[refute_1_35,refute_1_30]) ).
cnf(refute_1_37,plain,
ilf_type(skolemFOFtoCNF_D_8,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_8) )],[refute_1_36,refute_1_26]) ).
cnf(refute_1_38,plain,
( ~ member(X_2010,skolemFOFtoCNF_C_5)
| member(ordered_pair(X_2010,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,X_2010)),skolemFOFtoCNF_D_8) ),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_8,binary_relation_type) )],[refute_1_37,refute_1_23]) ).
cnf(refute_1_39,plain,
( ~ member(skolemFOFtoCNF_E_1,skolemFOFtoCNF_C_5)
| member(ordered_pair(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,skolemFOFtoCNF_E_1)),skolemFOFtoCNF_D_8) ),
inference(subst,[],[refute_1_38:[bind(X_2010,$fot(skolemFOFtoCNF_E_1))]]) ).
cnf(refute_1_40,plain,
member(ordered_pair(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,skolemFOFtoCNF_E_1)),skolemFOFtoCNF_D_8),
inference(resolve,[$cnf( member(skolemFOFtoCNF_E_1,skolemFOFtoCNF_C_5) )],[refute_1_0,refute_1_39]) ).
cnf(refute_1_41,plain,
( ~ ilf_type(F,set_type)
| ~ member(ordered_pair(skolemFOFtoCNF_E_1,F),skolemFOFtoCNF_D_8) ),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_42,plain,
ilf_type(F,set_type),
inference(subst,[],[refute_1_2:[bind(B,$fot(F))]]) ).
cnf(refute_1_43,plain,
~ member(ordered_pair(skolemFOFtoCNF_E_1,F),skolemFOFtoCNF_D_8),
inference(resolve,[$cnf( ilf_type(F,set_type) )],[refute_1_42,refute_1_41]) ).
cnf(refute_1_44,plain,
~ member(ordered_pair(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,skolemFOFtoCNF_E_1)),skolemFOFtoCNF_D_8),
inference(subst,[],[refute_1_43:[bind(F,$fot(skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,skolemFOFtoCNF_E_1)))]]) ).
cnf(refute_1_45,plain,
$false,
inference(resolve,[$cnf( member(ordered_pair(skolemFOFtoCNF_E_1,skolemFOFtoCNF_D(skolemFOFtoCNF_D_8,skolemFOFtoCNF_E_1)),skolemFOFtoCNF_D_8) )],[refute_1_40,refute_1_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET659+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n014.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 : Mon Jul 11 00:49:49 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.26/8.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.26/8.46
% 8.26/8.46 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.26/8.47
%------------------------------------------------------------------------------