%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SET675+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 03:36:33 EDT 2022
% Result : Theorem 1.10s 1.31s
% Output : CNFRefutation 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 32
% Syntax : Number of formulae : 226 ( 57 unt; 0 def)
% Number of atoms : 636 ( 221 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 760 ( 350 ~; 320 |; 43 &)
% ( 5 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-4 aty)
% Number of variables : 367 ( 12 sgn 191 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p1,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> image(B,domain_of(B)) = range_of(B) ) ).
fof(p2,axiom,
! [B] :
( ilf_type(B,binary_relation_type)
=> inverse2(B,range_of(B)) = domain_of(B) ) ).
fof(p3,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ( image4(B,C,D,B) = range(B,C,D)
& inverse4(B,C,D,C) = domain(B,C,D) ) ) ) ) ).
fof(p4,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(p12,axiom,
! [B] :
( ilf_type(B,set_type)
=> ( ilf_type(B,binary_relation_type)
<=> ( relation_like(B)
& ilf_type(B,set_type) ) ) ) ).
fof(p23,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,subset_type(cross_product(B,C)))
=> relation_like(D) ) ) ) ).
fof(p27,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> domain(B,C,D) = domain_of(D) ) ) ) ).
fof(p29,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> range(B,C,D) = range_of(D) ) ) ) ).
fof(p31,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> image4(B,C,D,E) = image(D,E) ) ) ) ) ).
fof(p33,axiom,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(B,C))
=> ! [E] :
( ilf_type(E,set_type)
=> inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ) ).
fof(p35,axiom,
! [B] : ilf_type(B,set_type) ).
fof(prove_relset_1_39,conjecture,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> ( image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D)
& inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D) ) ) ) ) ).
fof(subgoal_0,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ilf_type(D,relation_type(C,B))
=> image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) ) ) ),
inference(strip,[],[prove_relset_1_39]) ).
fof(subgoal_1,plain,
! [B] :
( ilf_type(B,set_type)
=> ! [C] :
( ilf_type(C,set_type)
=> ! [D] :
( ( ilf_type(D,relation_type(C,B))
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) )
=> inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D) ) ) ),
inference(strip,[],[prove_relset_1_39]) ).
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))
=> image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( image4(C,B,D,inverse4(C,B,D,B)) != range(C,B,D)
& ilf_type(D,relation_type(C,B)) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p35]) ).
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] :
( image4(C,B,D,inverse4(C,B,D,B)) != range(C,B,D)
& ilf_type(D,relation_type(C,B)) ) ),
inference(simplify,[],[normalize_0_0,normalize_0_2]) ).
fof(normalize_0_4,plain,
( ilf_type(skolemFOFtoCNF_C_4,set_type)
& ? [D] :
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D,skolemFOFtoCNF_B_1)) != range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
? [D] :
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D,skolemFOFtoCNF_B_1)) != range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)
& ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) ),
inference(skolemize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p29]) ).
fof(normalize_0_10,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( image4(B,C,D,B) = range(B,C,D)
& inverse4(B,C,D,C) = domain(B,C,D) ) ) ) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_0_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( image4(B,C,D,B) = range(B,C,D)
& inverse4(B,C,D,C) = domain(B,C,D) ) ) ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_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(canonicalize,[],[p27]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,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_17]) ).
fof(normalize_0_19,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| image(B,domain_of(B)) = range_of(B) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_20,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| image(B,domain_of(B)) = range_of(B) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p12]) ).
fof(normalize_0_22,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p23]) ).
fof(normalize_0_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,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,[],[p4]) ).
fof(normalize_0_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,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_30]) ).
fof(normalize_0_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ) ) ) ),
inference(canonicalize,[],[p31]) ).
fof(normalize_0_33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ) ) ) ),
inference(specialize,[],[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,relation_type(B,C))
| ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ),
inference(clausify,[],[normalize_0_33]) ).
cnf(refute_0_0,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_1,plain,
ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_2,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(C))]]) ).
cnf(refute_0_6,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) = range_of(skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_6:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_8,plain,
range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) = range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_7]) ).
cnf(refute_0_9,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range_of(skolemFOFtoCNF_D_4)
| range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) ),[1],$fot(range_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_10,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),range(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_10,refute_0_0]) ).
cnf(refute_0_12,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) = domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_14:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_16,plain,
inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) = domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_18,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) = domain_of(skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_19:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_21,plain,
domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) = domain_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_20]) ).
cnf(refute_0_22,plain,
( domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4) != domain_of(skolemFOFtoCNF_D_4)
| inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)
| inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) = domain_of(skolemFOFtoCNF_D_4) ),
introduced(tautology,[equality,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1),domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_23,plain,
( inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) != domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)
| inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) = domain_of(skolemFOFtoCNF_D_4) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4),domain_of(skolemFOFtoCNF_D_4)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) = domain_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1),domain(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4)) )],[refute_0_16,refute_0_23]) ).
cnf(refute_0_25,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),
introduced(tautology,[refl,[$fot(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)))]]) ).
cnf(refute_0_26,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1))
| inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) != domain_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) ),
introduced(tautology,[equality,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1))) ),[1,3],$fot(domain_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_27,plain,
( inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1) != domain_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) ),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1),domain_of(skolemFOFtoCNF_D_4)) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) != image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4))
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = range_of(skolemFOFtoCNF_D_4) ),
introduced(tautology,[equality,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4))) ),[1],$fot(range_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_30,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)) = range_of(skolemFOFtoCNF_D_4) ),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,inverse4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,skolemFOFtoCNF_B_1)),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_30,refute_0_11]) ).
cnf(refute_0_32,plain,
( ~ ilf_type(B,binary_relation_type)
| image(B,domain_of(B)) = range_of(B) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_33,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,binary_relation_type)
| image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_32:[bind(B,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_34,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_35,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ relation_like(skolemFOFtoCNF_D_4)
| ilf_type(skolemFOFtoCNF_D_4,binary_relation_type) ),
inference(subst,[],[refute_0_35:[bind(B,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_37,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_27]) ).
cnf(refute_0_38,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)))
| relation_like(skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_39:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_41,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_42,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| ilf_type(skolemFOFtoCNF_D_4,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) ),
inference(subst,[],[refute_0_43:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(E,$fot(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_45,plain,
ilf_type(skolemFOFtoCNF_D_4,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_44]) ).
cnf(refute_0_46,plain,
relation_like(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,subset_type(cross_product(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))) )],[refute_0_45,refute_0_40]) ).
cnf(refute_0_47,plain,
ilf_type(skolemFOFtoCNF_D_4,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_4) )],[refute_0_46,refute_0_36]) ).
cnf(refute_0_48,plain,
image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,binary_relation_type) )],[refute_0_47,refute_0_33]) ).
cnf(refute_0_49,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_50,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_0_3,refute_0_49]) ).
cnf(refute_0_51,plain,
( ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| image4(B,C,D,E) = image(D,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_0_5,refute_0_50]) ).
cnf(refute_0_52,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_0_3:[bind(B,$fot(E))]]) ).
cnf(refute_0_53,plain,
( ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,E) = image(D,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_0_52,refute_0_51]) ).
cnf(refute_0_54,plain,
( ~ ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1))
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,X_1535) = image(skolemFOFtoCNF_D_4,X_1535) ),
inference(subst,[],[refute_0_53:[bind(B,$fot(skolemFOFtoCNF_C_4)),bind(C,$fot(skolemFOFtoCNF_B_1)),bind(D,$fot(skolemFOFtoCNF_D_4)),bind(E,$fot(X_1535))]]) ).
cnf(refute_0_55,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,X_1535) = image(skolemFOFtoCNF_D_4,X_1535),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_4,relation_type(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1)) )],[refute_0_1,refute_0_54]) ).
cnf(refute_0_56,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),
inference(subst,[],[refute_0_55:[bind(X_1535,$fot(domain_of(skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_0_57,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_58,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_59,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_61,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4))
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4) ),
inference(subst,[],[refute_0_61:[bind(X,$fot(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)))),bind(Y,$fot(image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)))),bind(Z,$fot(range_of(skolemFOFtoCNF_D_4)))]]) ).
cnf(refute_0_63,plain,
( image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4) ),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4))) )],[refute_0_56,refute_0_62]) ).
cnf(refute_0_64,plain,
image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( $equal(image(skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_48,refute_0_63]) ).
cnf(refute_0_65,plain,
( image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) != range_of(skolemFOFtoCNF_D_4)
| range_of(skolemFOFtoCNF_D_4) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),range_of(skolemFOFtoCNF_D_4)) ),[0],$fot(range_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_66,plain,
( range_of(skolemFOFtoCNF_D_4) != range_of(skolemFOFtoCNF_D_4)
| image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)) = range_of(skolemFOFtoCNF_D_4) ),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
range_of(skolemFOFtoCNF_D_4) != range_of(skolemFOFtoCNF_D_4),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_4,skolemFOFtoCNF_B_1,skolemFOFtoCNF_D_4,domain_of(skolemFOFtoCNF_D_4)),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_66,refute_0_31]) ).
cnf(refute_0_68,plain,
range_of(skolemFOFtoCNF_D_4) = range_of(skolemFOFtoCNF_D_4),
introduced(tautology,[refl,[$fot(range_of(skolemFOFtoCNF_D_4))]]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( $equal(range_of(skolemFOFtoCNF_D_4),range_of(skolemFOFtoCNF_D_4)) )],[refute_0_68,refute_0_67]) ).
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))
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D) )
=> inverse4(C,B,D,image4(C,B,D,C)) = domain(C,B,D) ) ) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [B] :
( ilf_type(B,set_type)
& ? [C] :
( ilf_type(C,set_type)
& ? [D] :
( inverse4(C,B,D,image4(C,B,D,C)) != domain(C,B,D)
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D)
& ilf_type(D,relation_type(C,B)) ) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
! [B] : ilf_type(B,set_type),
inference(canonicalize,[],[p35]) ).
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] :
( inverse4(C,B,D,image4(C,B,D,C)) != domain(C,B,D)
& image4(C,B,D,inverse4(C,B,D,B)) = range(C,B,D)
& ilf_type(D,relation_type(C,B)) ) ),
inference(simplify,[],[normalize_1_0,normalize_1_2]) ).
fof(normalize_1_4,plain,
( ilf_type(skolemFOFtoCNF_C_5,set_type)
& ? [D] :
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,skolemFOFtoCNF_C_5)) != domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,skolemFOFtoCNF_B_2)) = range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) ) ),
inference(skolemize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
? [D] :
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,skolemFOFtoCNF_C_5)) != domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D,skolemFOFtoCNF_B_2)) = range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,D)
& ilf_type(D,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) ),
inference(conjunct,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)
& image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_B_2)) = range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)
& ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) ),
inference(skolemize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(conjunct,[],[normalize_1_6]) ).
fof(normalize_1_9,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ) ) ),
inference(canonicalize,[],[p27]) ).
fof(normalize_1_10,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_9]) ).
fof(normalize_1_11,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_10]) ).
fof(normalize_1_12,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( image4(B,C,D,B) = range(B,C,D)
& inverse4(B,C,D,C) = domain(B,C,D) ) ) ) ),
inference(canonicalize,[],[p3]) ).
fof(normalize_1_13,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ( image4(B,C,D,B) = range(B,C,D)
& inverse4(B,C,D,C) = domain(B,C,D) ) ) ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [B,C,D] :
( ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) )
& ( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,C) = domain(B,C,D) ) ),
inference(clausify,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) ),
inference(conjunct,[],[normalize_1_14]) ).
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))
| range(B,C,D) = range_of(D) ) ) ),
inference(canonicalize,[],[p29]) ).
fof(normalize_1_17,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ) ) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(clausify,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| inverse2(B,range_of(B)) = domain_of(B) ),
inference(canonicalize,[],[p2]) ).
fof(normalize_1_20,plain,
! [B] :
( ~ ilf_type(B,binary_relation_type)
| inverse2(B,range_of(B)) = domain_of(B) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(canonicalize,[],[p12]) ).
fof(normalize_1_22,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ( ~ ilf_type(B,binary_relation_type)
<=> ( ~ ilf_type(B,set_type)
| ~ relation_like(B) ) ) ),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [B] :
( ( ~ ilf_type(B,binary_relation_type)
| ~ ilf_type(B,set_type)
| relation_like(B) )
& ( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ) ),
inference(clausify,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(canonicalize,[],[p23]) ).
fof(normalize_1_26,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ) ) ),
inference(specialize,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
! [B,C,D] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(clausify,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [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,[],[p4]) ).
fof(normalize_1_29,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ( ! [D] :
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| ilf_type(D,relation_type(B,C)) )
& ! [E] :
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
inference(specialize,[],[normalize_1_28]) ).
fof(normalize_1_30,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_29]) ).
fof(normalize_1_31,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_30]) ).
fof(normalize_1_32,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(canonicalize,[],[p33]) ).
fof(normalize_1_33,plain,
! [B] :
( ~ ilf_type(B,set_type)
| ! [C] :
( ~ ilf_type(C,set_type)
| ! [D] :
( ~ ilf_type(D,relation_type(B,C))
| ! [E] :
( ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ) ) ) ),
inference(specialize,[],[normalize_1_32]) ).
fof(normalize_1_34,plain,
! [B,C,D,E] :
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(clausify,[],[normalize_1_33]) ).
cnf(refute_1_0,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_1,plain,
ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_2,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_11]) ).
cnf(refute_1_3,plain,
ilf_type(B,set_type),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_4,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_2]) ).
cnf(refute_1_5,plain,
ilf_type(C,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(C))]]) ).
cnf(refute_1_6,plain,
( ~ ilf_type(D,relation_type(B,C))
| domain(B,C,D) = domain_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_4]) ).
cnf(refute_1_7,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_6:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_8,plain,
domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_7]) ).
cnf(refute_1_9,plain,
( domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_10,plain,
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),domain(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)) )],[refute_1_10,refute_1_0]) ).
cnf(refute_1_12,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_13,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_12]) ).
cnf(refute_1_14,plain,
( ~ ilf_type(D,relation_type(B,C))
| image4(B,C,D,B) = range(B,C,D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_13]) ).
cnf(refute_1_15,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) = range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_14:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_16,plain,
image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) = range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_15]) ).
cnf(refute_1_17,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_18,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_17]) ).
cnf(refute_1_19,plain,
( ~ ilf_type(D,relation_type(B,C))
| range(B,C,D) = range_of(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) = range_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_19:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_21,plain,
range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) = range_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_20]) ).
cnf(refute_1_22,plain,
( image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) != range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)
| range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5) != range_of(skolemFOFtoCNF_D_5)
| image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) = range_of(skolemFOFtoCNF_D_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5),range_of(skolemFOFtoCNF_D_5)) ),[0],$fot(range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_23,plain,
( image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) != range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)
| image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) = range_of(skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5),range_of(skolemFOFtoCNF_D_5)) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) = range_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5),range(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5)) )],[refute_1_16,refute_1_23]) ).
cnf(refute_1_25,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),
introduced(tautology,[refl,[$fot(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)))]]) ).
cnf(refute_1_26,plain,
( image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) != range_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5))
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) ),
introduced(tautology,[equality,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5))) ),[1,3],$fot(range_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_27,plain,
( image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5) != range_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5))) )],[refute_1_25,refute_1_26]) ).
cnf(refute_1_28,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),
inference(resolve,[$cnf( $equal(image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5),range_of(skolemFOFtoCNF_D_5)) )],[refute_1_24,refute_1_27]) ).
cnf(refute_1_29,plain,
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) != inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5))
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = domain_of(skolemFOFtoCNF_D_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),domain_of(skolemFOFtoCNF_D_5)) ),[0],$fot(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_1_30,plain,
( inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)) = domain_of(skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5))) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,image4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,skolemFOFtoCNF_C_5)),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_30,refute_1_11]) ).
cnf(refute_1_32,plain,
( ~ ilf_type(B,binary_relation_type)
| inverse2(B,range_of(B)) = domain_of(B) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_33,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,binary_relation_type)
| inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_32:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_34,plain,
( ~ ilf_type(B,set_type)
| ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_35,plain,
( ~ relation_like(B)
| ilf_type(B,binary_relation_type) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_34]) ).
cnf(refute_1_36,plain,
( ~ relation_like(skolemFOFtoCNF_D_5)
| ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) ),
inference(subst,[],[refute_1_35:[bind(B,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_37,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_38,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_37]) ).
cnf(refute_1_39,plain,
( ~ ilf_type(D,subset_type(cross_product(B,C)))
| relation_like(D) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_38]) ).
cnf(refute_1_40,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)))
| relation_like(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_39:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_41,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_42,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ ilf_type(E,relation_type(B,C))
| ilf_type(E,subset_type(cross_product(B,C))) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_42]) ).
cnf(refute_1_44,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) ),
inference(subst,[],[refute_1_43:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(E,$fot(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_45,plain,
ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_44]) ).
cnf(refute_1_46,plain,
relation_like(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,subset_type(cross_product(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))) )],[refute_1_45,refute_1_40]) ).
cnf(refute_1_47,plain,
ilf_type(skolemFOFtoCNF_D_5,binary_relation_type),
inference(resolve,[$cnf( relation_like(skolemFOFtoCNF_D_5) )],[refute_1_46,refute_1_36]) ).
cnf(refute_1_48,plain,
inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,binary_relation_type) )],[refute_1_47,refute_1_33]) ).
cnf(refute_1_49,plain,
( ~ ilf_type(B,set_type)
| ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(canonicalize,[],[normalize_1_34]) ).
cnf(refute_1_50,plain,
( ~ ilf_type(C,set_type)
| ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(B,set_type) )],[refute_1_3,refute_1_49]) ).
cnf(refute_1_51,plain,
( ~ ilf_type(D,relation_type(B,C))
| ~ ilf_type(E,set_type)
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(C,set_type) )],[refute_1_5,refute_1_50]) ).
cnf(refute_1_52,plain,
ilf_type(E,set_type),
inference(subst,[],[refute_1_3:[bind(B,$fot(E))]]) ).
cnf(refute_1_53,plain,
( ~ ilf_type(D,relation_type(B,C))
| inverse4(B,C,D,E) = inverse2(D,E) ),
inference(resolve,[$cnf( ilf_type(E,set_type) )],[refute_1_52,refute_1_51]) ).
cnf(refute_1_54,plain,
( ~ ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2))
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,X_3246) = inverse2(skolemFOFtoCNF_D_5,X_3246) ),
inference(subst,[],[refute_1_53:[bind(B,$fot(skolemFOFtoCNF_C_5)),bind(C,$fot(skolemFOFtoCNF_B_2)),bind(D,$fot(skolemFOFtoCNF_D_5)),bind(E,$fot(X_3246))]]) ).
cnf(refute_1_55,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,X_3246) = inverse2(skolemFOFtoCNF_D_5,X_3246),
inference(resolve,[$cnf( ilf_type(skolemFOFtoCNF_D_5,relation_type(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2)) )],[refute_1_1,refute_1_54]) ).
cnf(refute_1_56,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),
inference(subst,[],[refute_1_55:[bind(X_3246,$fot(range_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_1_57,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_58,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_59,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_57,refute_1_58]) ).
cnf(refute_1_60,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_61,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_59,refute_1_60]) ).
cnf(refute_1_62,plain,
( inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5))
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5) ),
inference(subst,[],[refute_1_61:[bind(X,$fot(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)))),bind(Y,$fot(inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)))),bind(Z,$fot(domain_of(skolemFOFtoCNF_D_5)))]]) ).
cnf(refute_1_63,plain,
( inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5))) )],[refute_1_56,refute_1_62]) ).
cnf(refute_1_64,plain,
inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(inverse2(skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_48,refute_1_63]) ).
cnf(refute_1_65,plain,
( domain_of(skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5) ),
introduced(tautology,[equality,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),domain_of(skolemFOFtoCNF_D_5)) ),[1],$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_66,plain,
( domain_of(skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5)
| inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)) = domain_of(skolemFOFtoCNF_D_5) ),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_64,refute_1_65]) ).
cnf(refute_1_67,plain,
domain_of(skolemFOFtoCNF_D_5) != domain_of(skolemFOFtoCNF_D_5),
inference(resolve,[$cnf( $equal(inverse4(skolemFOFtoCNF_C_5,skolemFOFtoCNF_B_2,skolemFOFtoCNF_D_5,range_of(skolemFOFtoCNF_D_5)),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_66,refute_1_31]) ).
cnf(refute_1_68,plain,
domain_of(skolemFOFtoCNF_D_5) = domain_of(skolemFOFtoCNF_D_5),
introduced(tautology,[refl,[$fot(domain_of(skolemFOFtoCNF_D_5))]]) ).
cnf(refute_1_69,plain,
$false,
inference(resolve,[$cnf( $equal(domain_of(skolemFOFtoCNF_D_5),domain_of(skolemFOFtoCNF_D_5)) )],[refute_1_68,refute_1_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET675+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 : n027.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 08:17:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.10/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/1.31
% 1.10/1.31 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.10/1.33
%------------------------------------------------------------------------------