%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 12:39:10 EDT 2022
% Result : Theorem 2.78s 2.98s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 41
% Syntax : Number of formulae : 193 ( 81 unt; 0 def)
% Number of atoms : 355 ( 238 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 304 ( 142 ~; 127 |; 23 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 38 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ) ).
fof(dt_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation(relation_inverse(A)) ) ).
fof(fc1_xboole_0,axiom,
empty(empty_set) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ) ).
fof(fc5_relat_1,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ) ).
fof(involutiveness_k4_relat_1,axiom,
! [A] :
( relation(A)
=> relation_inverse(relation_inverse(A)) = A ) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A ).
fof(t37_relat_1,lemma,
! [A] :
( relation(A)
=> ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ) ).
fof(t60_relat_1,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ) ).
fof(t65_relat_1,conjecture,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ) ).
fof(subgoal_0,plain,
! [A] :
( ( relation(A)
& relation_dom(A) = empty_set )
=> relation_rng(A) = empty_set ),
inference(strip,[],[t65_relat_1]) ).
fof(subgoal_1,plain,
! [A] :
( ( relation(A)
& relation_rng(A) = empty_set )
=> relation_dom(A) = empty_set ),
inference(strip,[],[t65_relat_1]) ).
fof(negate_0_0,plain,
~ ! [A] :
( ( relation(A)
& relation_dom(A) = empty_set )
=> relation_rng(A) = empty_set ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] :
( relation_rng(A) != empty_set
& relation_dom(A) = empty_set
& relation(A) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( relation_rng(skolemFOFtoCNF_A_4) != empty_set
& relation_dom(skolemFOFtoCNF_A_4) = empty_set
& relation(skolemFOFtoCNF_A_4) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
relation_rng(skolemFOFtoCNF_A_4) != empty_set,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
relation(skolemFOFtoCNF_A_4),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[d6_relat_1]) ).
fof(normalize_0_5,plain,
! [A] :
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : set_union2(A,empty_set) = A,
inference(canonicalize,[],[t1_boole]) ).
fof(normalize_0_7,plain,
! [A] : set_union2(A,empty_set) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[commutativity_k2_xboole_0]) ).
fof(normalize_0_9,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
relation_dom(skolemFOFtoCNF_A_4) = empty_set,
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_11,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(canonicalize,[],[fc4_relat_1]) ).
fof(normalize_0_12,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_0_13,plain,
relation(empty_set),
inference(simplify,[],[normalize_0_11,normalize_0_12]) ).
fof(normalize_0_14,plain,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(canonicalize,[],[t60_relat_1]) ).
fof(normalize_0_15,plain,
relation_rng(empty_set) = empty_set,
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
relation_dom(empty_set) = empty_set,
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_0_18,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc5_relat_1]) ).
fof(normalize_0_20,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
relation_rng(skolemFOFtoCNF_A_4) != empty_set,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
relation(skolemFOFtoCNF_A_4),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ relation(A)
| relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| relation_field(skolemFOFtoCNF_A_4) = set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_4,plain,
relation_field(skolemFOFtoCNF_A_4) = set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
set_union2(A,empty_set) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
set_union2(A,B) = set_union2(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
set_union2(A,empty_set) = set_union2(empty_set,A),
inference(subst,[],[refute_0_6:[bind(B,$fot(empty_set))]]) ).
cnf(refute_0_8,plain,
( set_union2(A,empty_set) != A
| set_union2(A,empty_set) != set_union2(empty_set,A)
| set_union2(empty_set,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(A,empty_set),A) ),[0],$fot(set_union2(empty_set,A))]]) ).
cnf(refute_0_9,plain,
( set_union2(A,empty_set) != A
| set_union2(empty_set,A) = A ),
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),set_union2(empty_set,A)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
set_union2(empty_set,A) = A,
inference(resolve,[$cnf( $equal(set_union2(A,empty_set),A) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)) = relation_rng(skolemFOFtoCNF_A_4),
inference(subst,[],[refute_0_10:[bind(A,$fot(relation_rng(skolemFOFtoCNF_A_4)))]]) ).
cnf(refute_0_12,plain,
relation_dom(skolemFOFtoCNF_A_4) = empty_set,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),
introduced(tautology,[refl,[$fot(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)))]]) ).
cnf(refute_0_14,plain,
( relation_dom(skolemFOFtoCNF_A_4) != empty_set
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) != set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_15,plain,
( relation_dom(skolemFOFtoCNF_A_4) != empty_set
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_12,refute_0_15]) ).
cnf(refute_0_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_18,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_19,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)) != relation_rng(skolemFOFtoCNF_A_4)
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) != set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4))
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = relation_rng(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)))),bind(Y,$fot(set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)))),bind(Z,$fot(relation_rng(skolemFOFtoCNF_A_4)))]]) ).
cnf(refute_0_23,plain,
( set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)) != relation_rng(skolemFOFtoCNF_A_4)
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = relation_rng(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4))) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) = relation_rng(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( $equal(set_union2(empty_set,relation_rng(skolemFOFtoCNF_A_4)),relation_rng(skolemFOFtoCNF_A_4)) )],[refute_0_11,refute_0_23]) ).
cnf(refute_0_25,plain,
( relation_field(skolemFOFtoCNF_A_4) != set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))
| set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) != relation_rng(skolemFOFtoCNF_A_4)
| relation_field(skolemFOFtoCNF_A_4) = relation_rng(skolemFOFtoCNF_A_4) ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_field(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) ),[0],$fot(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)))]]) ).
cnf(refute_0_26,plain,
( relation_field(skolemFOFtoCNF_A_4) != set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))
| relation_field(skolemFOFtoCNF_A_4) = relation_rng(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)),relation_rng(skolemFOFtoCNF_A_4)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
relation_field(skolemFOFtoCNF_A_4) = relation_rng(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),set_union2(relation_dom(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4))) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
( relation_field(skolemFOFtoCNF_A_4) != relation_rng(skolemFOFtoCNF_A_4)
| relation_rng(skolemFOFtoCNF_A_4) = relation_field(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(relation_field(skolemFOFtoCNF_A_4))),bind(Y,$fot(relation_rng(skolemFOFtoCNF_A_4)))]]) ).
cnf(refute_0_29,plain,
relation_rng(skolemFOFtoCNF_A_4) = relation_field(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),relation_rng(skolemFOFtoCNF_A_4)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( relation_field(skolemFOFtoCNF_A_4) != empty_set
| relation_rng(skolemFOFtoCNF_A_4) != relation_field(skolemFOFtoCNF_A_4)
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),relation_field(skolemFOFtoCNF_A_4)) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_31,plain,
( relation_field(skolemFOFtoCNF_A_4) != empty_set
| relation_rng(skolemFOFtoCNF_A_4) = empty_set ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),relation_field(skolemFOFtoCNF_A_4)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
relation_field(skolemFOFtoCNF_A_4) != empty_set,
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_31,refute_0_0]) ).
cnf(refute_0_33,plain,
relation(empty_set),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_34,plain,
( ~ relation(empty_set)
| relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_35,plain,
relation_field(empty_set) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
inference(resolve,[$cnf( relation(empty_set) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
set_union2(empty_set,empty_set) = empty_set,
inference(subst,[],[refute_0_10:[bind(A,$fot(empty_set))]]) ).
cnf(refute_0_37,plain,
relation_rng(empty_set) = empty_set,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_38,plain,
set_union2(empty_set,relation_rng(empty_set)) = set_union2(empty_set,relation_rng(empty_set)),
introduced(tautology,[refl,[$fot(set_union2(empty_set,relation_rng(empty_set)))]]) ).
cnf(refute_0_39,plain,
( relation_rng(empty_set) != empty_set
| set_union2(empty_set,relation_rng(empty_set)) != set_union2(empty_set,relation_rng(empty_set))
| set_union2(empty_set,relation_rng(empty_set)) = set_union2(empty_set,empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(empty_set,relation_rng(empty_set)),set_union2(empty_set,relation_rng(empty_set))) ),[1,1],$fot(empty_set)]]) ).
cnf(refute_0_40,plain,
( relation_rng(empty_set) != empty_set
| set_union2(empty_set,relation_rng(empty_set)) = set_union2(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(empty_set,relation_rng(empty_set)),set_union2(empty_set,relation_rng(empty_set))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
set_union2(empty_set,relation_rng(empty_set)) = set_union2(empty_set,empty_set),
inference(resolve,[$cnf( $equal(relation_rng(empty_set),empty_set) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
relation_dom(empty_set) = empty_set,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_43,plain,
set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(relation_dom(empty_set),relation_rng(empty_set)),
introduced(tautology,[refl,[$fot(set_union2(relation_dom(empty_set),relation_rng(empty_set)))]]) ).
cnf(refute_0_44,plain,
( relation_dom(empty_set) != empty_set
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) != set_union2(relation_dom(empty_set),relation_rng(empty_set))
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,relation_rng(empty_set)) ),
introduced(tautology,[equality,[$cnf( $equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),set_union2(relation_dom(empty_set),relation_rng(empty_set))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_45,plain,
( relation_dom(empty_set) != empty_set
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,relation_rng(empty_set)) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),set_union2(relation_dom(empty_set),relation_rng(empty_set))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,relation_rng(empty_set)),
inference(resolve,[$cnf( $equal(relation_dom(empty_set),empty_set) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( set_union2(empty_set,relation_rng(empty_set)) != set_union2(empty_set,empty_set)
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) != set_union2(empty_set,relation_rng(empty_set))
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,empty_set) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(set_union2(relation_dom(empty_set),relation_rng(empty_set)))),bind(Y,$fot(set_union2(empty_set,relation_rng(empty_set)))),bind(Z,$fot(set_union2(empty_set,empty_set)))]]) ).
cnf(refute_0_48,plain,
( set_union2(empty_set,relation_rng(empty_set)) != set_union2(empty_set,empty_set)
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,empty_set) ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),set_union2(empty_set,relation_rng(empty_set))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
set_union2(relation_dom(empty_set),relation_rng(empty_set)) = set_union2(empty_set,empty_set),
inference(resolve,[$cnf( $equal(set_union2(empty_set,relation_rng(empty_set)),set_union2(empty_set,empty_set)) )],[refute_0_41,refute_0_48]) ).
cnf(refute_0_50,plain,
( set_union2(empty_set,empty_set) != empty_set
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) != set_union2(empty_set,empty_set)
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = empty_set ),
inference(subst,[],[refute_0_21:[bind(X,$fot(set_union2(relation_dom(empty_set),relation_rng(empty_set)))),bind(Y,$fot(set_union2(empty_set,empty_set))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_0_51,plain,
( set_union2(empty_set,empty_set) != empty_set
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) = empty_set ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),set_union2(empty_set,empty_set)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
set_union2(relation_dom(empty_set),relation_rng(empty_set)) = empty_set,
inference(resolve,[$cnf( $equal(set_union2(empty_set,empty_set),empty_set) )],[refute_0_36,refute_0_51]) ).
cnf(refute_0_53,plain,
( relation_field(empty_set) != set_union2(relation_dom(empty_set),relation_rng(empty_set))
| set_union2(relation_dom(empty_set),relation_rng(empty_set)) != empty_set
| relation_field(empty_set) = empty_set ),
introduced(tautology,[equality,[$cnf( ~ $equal(relation_field(empty_set),empty_set) ),[0],$fot(set_union2(relation_dom(empty_set),relation_rng(empty_set)))]]) ).
cnf(refute_0_54,plain,
( relation_field(empty_set) != set_union2(relation_dom(empty_set),relation_rng(empty_set))
| relation_field(empty_set) = empty_set ),
inference(resolve,[$cnf( $equal(set_union2(relation_dom(empty_set),relation_rng(empty_set)),empty_set) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
relation_field(empty_set) = empty_set,
inference(resolve,[$cnf( $equal(relation_field(empty_set),set_union2(relation_dom(empty_set),relation_rng(empty_set))) )],[refute_0_35,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_57,plain,
( ~ empty(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 = empty_set ),
inference(subst,[],[refute_0_56:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_58,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_59,plain,
( ~ empty(relation_dom(skolemFOFtoCNF_A_4))
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_60,plain,
( relation_dom(skolemFOFtoCNF_A_4) != empty_set
| ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4)) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_dom(skolemFOFtoCNF_A_4)) ),[0],$fot(empty_set)]]) ).
cnf(refute_0_61,plain,
( ~ empty(empty_set)
| empty(relation_dom(skolemFOFtoCNF_A_4)) ),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_12,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ empty(empty_set)
| ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(relation_dom(skolemFOFtoCNF_A_4)) )],[refute_0_61,refute_0_59]) ).
cnf(refute_0_63,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_64,plain,
( ~ relation(skolemFOFtoCNF_A_4)
| empty(skolemFOFtoCNF_A_4) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_0_63,refute_0_62]) ).
cnf(refute_0_65,plain,
empty(skolemFOFtoCNF_A_4),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_4) )],[refute_0_1,refute_0_64]) ).
cnf(refute_0_66,plain,
skolemFOFtoCNF_A_4 = empty_set,
inference(resolve,[$cnf( empty(skolemFOFtoCNF_A_4) )],[refute_0_65,refute_0_57]) ).
cnf(refute_0_67,plain,
relation_field(skolemFOFtoCNF_A_4) = relation_field(skolemFOFtoCNF_A_4),
introduced(tautology,[refl,[$fot(relation_field(skolemFOFtoCNF_A_4))]]) ).
cnf(refute_0_68,plain,
( relation_field(skolemFOFtoCNF_A_4) != relation_field(skolemFOFtoCNF_A_4)
| skolemFOFtoCNF_A_4 != empty_set
| relation_field(skolemFOFtoCNF_A_4) = relation_field(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),relation_field(skolemFOFtoCNF_A_4)) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_0_69,plain,
( skolemFOFtoCNF_A_4 != empty_set
| relation_field(skolemFOFtoCNF_A_4) = relation_field(empty_set) ),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),relation_field(skolemFOFtoCNF_A_4)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
relation_field(skolemFOFtoCNF_A_4) = relation_field(empty_set),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_A_4,empty_set) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( relation_field(empty_set) != empty_set
| relation_field(skolemFOFtoCNF_A_4) != relation_field(empty_set)
| relation_field(skolemFOFtoCNF_A_4) = empty_set ),
inference(subst,[],[refute_0_21:[bind(X,$fot(relation_field(skolemFOFtoCNF_A_4))),bind(Y,$fot(relation_field(empty_set))),bind(Z,$fot(empty_set))]]) ).
cnf(refute_0_72,plain,
( relation_field(empty_set) != empty_set
| relation_field(skolemFOFtoCNF_A_4) = empty_set ),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),relation_field(empty_set)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
relation_field(skolemFOFtoCNF_A_4) = empty_set,
inference(resolve,[$cnf( $equal(relation_field(empty_set),empty_set) )],[refute_0_55,refute_0_72]) ).
cnf(refute_0_74,plain,
( empty_set != empty_set
| relation_field(skolemFOFtoCNF_A_4) != empty_set
| relation_field(skolemFOFtoCNF_A_4) = empty_set ),
introduced(tautology,[equality,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),empty_set) ),[1],$fot(empty_set)]]) ).
cnf(refute_0_75,plain,
( empty_set != empty_set
| relation_field(skolemFOFtoCNF_A_4) = empty_set ),
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
empty_set != empty_set,
inference(resolve,[$cnf( $equal(relation_field(skolemFOFtoCNF_A_4),empty_set) )],[refute_0_75,refute_0_32]) ).
cnf(refute_0_77,plain,
empty_set = empty_set,
introduced(tautology,[refl,[$fot(empty_set)]]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,empty_set) )],[refute_0_77,refute_0_76]) ).
fof(negate_1_0,plain,
~ ! [A] :
( ( relation(A)
& relation_rng(A) = empty_set )
=> relation_dom(A) = empty_set ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
( empty(empty_set)
& relation(empty_set) ),
inference(canonicalize,[],[fc4_relat_1]) ).
fof(normalize_1_1,plain,
empty(empty_set),
inference(canonicalize,[],[fc1_xboole_0]) ).
fof(normalize_1_2,plain,
relation(empty_set),
inference(simplify,[],[normalize_1_0,normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(canonicalize,[],[t37_relat_1]) ).
fof(normalize_1_4,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) = relation_rng(relation_inverse(A))
& relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] :
( ( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) )
& ( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] :
( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
inference(canonicalize,[],[t60_relat_1]) ).
fof(normalize_1_8,plain,
relation_rng(empty_set) = empty_set,
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
? [A] :
( relation_dom(A) != empty_set
& relation_rng(A) = empty_set
& relation(A) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_10,plain,
( relation_dom(skolemFOFtoCNF_A_5) != empty_set
& relation_rng(skolemFOFtoCNF_A_5) = empty_set
& relation(skolemFOFtoCNF_A_5) ),
inference(skolemize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
relation(skolemFOFtoCNF_A_5),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [A] :
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(canonicalize,[],[involutiveness_k4_relat_1]) ).
fof(normalize_1_13,plain,
! [A] :
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[t6_boole]) ).
fof(normalize_1_15,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[fc5_relat_1]) ).
fof(normalize_1_17,plain,
! [A] :
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
relation_rng(skolemFOFtoCNF_A_5) = empty_set,
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_19,plain,
! [A] :
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(canonicalize,[],[dt_k4_relat_1]) ).
fof(normalize_1_20,plain,
! [A] :
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
relation_dom(skolemFOFtoCNF_A_5) != empty_set,
inference(conjunct,[],[normalize_1_10]) ).
cnf(refute_1_0,plain,
relation(empty_set),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ relation(empty_set)
| relation_rng(empty_set) = relation_dom(relation_inverse(empty_set)) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(empty_set))]]) ).
cnf(refute_1_3,plain,
relation_rng(empty_set) = relation_dom(relation_inverse(empty_set)),
inference(resolve,[$cnf( relation(empty_set) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
relation_rng(empty_set) = empty_set,
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_5,plain,
( relation_rng(empty_set) != empty_set
| relation_rng(empty_set) != relation_dom(relation_inverse(empty_set))
| empty_set = relation_dom(relation_inverse(empty_set)) ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(empty_set),relation_dom(relation_inverse(empty_set))) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_6,plain,
( relation_rng(empty_set) != relation_dom(relation_inverse(empty_set))
| empty_set = relation_dom(relation_inverse(empty_set)) ),
inference(resolve,[$cnf( $equal(relation_rng(empty_set),empty_set) )],[refute_1_4,refute_1_5]) ).
cnf(refute_1_7,plain,
empty_set = relation_dom(relation_inverse(empty_set)),
inference(resolve,[$cnf( $equal(relation_rng(empty_set),relation_dom(relation_inverse(empty_set))) )],[refute_1_3,refute_1_6]) ).
cnf(refute_1_8,plain,
relation(skolemFOFtoCNF_A_5),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_9,plain,
( ~ relation(A)
| relation_inverse(relation_inverse(A)) = A ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_10,plain,
( ~ relation(skolemFOFtoCNF_A_5)
| relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = skolemFOFtoCNF_A_5 ),
inference(subst,[],[refute_1_9:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_11,plain,
relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = skolemFOFtoCNF_A_5,
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_1_8,refute_1_10]) ).
cnf(refute_1_12,plain,
( ~ empty(A)
| A = empty_set ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_13,plain,
( ~ empty(relation_inverse(skolemFOFtoCNF_A_5))
| relation_inverse(skolemFOFtoCNF_A_5) = empty_set ),
inference(subst,[],[refute_1_12:[bind(A,$fot(relation_inverse(skolemFOFtoCNF_A_5)))]]) ).
cnf(refute_1_14,plain,
( ~ empty(relation_dom(A))
| ~ relation(A)
| empty(A) ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_15,plain,
( ~ empty(relation_dom(relation_inverse(skolemFOFtoCNF_A_5)))
| ~ relation(relation_inverse(skolemFOFtoCNF_A_5))
| empty(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(subst,[],[refute_1_14:[bind(A,$fot(relation_inverse(skolemFOFtoCNF_A_5)))]]) ).
cnf(refute_1_16,plain,
( ~ relation(skolemFOFtoCNF_A_5)
| relation_rng(skolemFOFtoCNF_A_5) = relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(subst,[],[refute_1_1:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_17,plain,
relation_rng(skolemFOFtoCNF_A_5) = relation_dom(relation_inverse(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_1_8,refute_1_16]) ).
cnf(refute_1_18,plain,
relation_rng(skolemFOFtoCNF_A_5) = empty_set,
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_19,plain,
( relation_rng(skolemFOFtoCNF_A_5) != empty_set
| relation_rng(skolemFOFtoCNF_A_5) != relation_dom(relation_inverse(skolemFOFtoCNF_A_5))
| empty_set = relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) ),
introduced(tautology,[equality,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_5),relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_20,plain,
( relation_rng(skolemFOFtoCNF_A_5) != relation_dom(relation_inverse(skolemFOFtoCNF_A_5))
| empty_set = relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
empty_set = relation_dom(relation_inverse(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( $equal(relation_rng(skolemFOFtoCNF_A_5),relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) )],[refute_1_17,refute_1_20]) ).
cnf(refute_1_22,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_23,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_24,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
( empty_set != relation_dom(relation_inverse(skolemFOFtoCNF_A_5))
| relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) = empty_set ),
inference(subst,[],[refute_1_24:[bind(X,$fot(empty_set)),bind(Y,$fot(relation_dom(relation_inverse(skolemFOFtoCNF_A_5))))]]) ).
cnf(refute_1_26,plain,
relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) = empty_set,
inference(resolve,[$cnf( $equal(empty_set,relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) )],[refute_1_21,refute_1_25]) ).
cnf(refute_1_27,plain,
( relation_dom(relation_inverse(skolemFOFtoCNF_A_5)) != empty_set
| ~ empty(empty_set)
| empty(relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) ),
introduced(tautology,[equality,[$cnf( ~ empty(relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) ),[0],$fot(empty_set)]]) ).
cnf(refute_1_28,plain,
( ~ empty(empty_set)
| empty(relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) ),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(skolemFOFtoCNF_A_5)),empty_set) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
( ~ empty(empty_set)
| ~ relation(relation_inverse(skolemFOFtoCNF_A_5))
| empty(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(resolve,[$cnf( empty(relation_dom(relation_inverse(skolemFOFtoCNF_A_5))) )],[refute_1_28,refute_1_15]) ).
cnf(refute_1_30,plain,
empty(empty_set),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_31,plain,
( ~ relation(relation_inverse(skolemFOFtoCNF_A_5))
| empty(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(resolve,[$cnf( empty(empty_set) )],[refute_1_30,refute_1_29]) ).
cnf(refute_1_32,plain,
( ~ relation(A)
| relation(relation_inverse(A)) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_33,plain,
( ~ relation(skolemFOFtoCNF_A_5)
| relation(relation_inverse(skolemFOFtoCNF_A_5)) ),
inference(subst,[],[refute_1_32:[bind(A,$fot(skolemFOFtoCNF_A_5))]]) ).
cnf(refute_1_34,plain,
relation(relation_inverse(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( relation(skolemFOFtoCNF_A_5) )],[refute_1_8,refute_1_33]) ).
cnf(refute_1_35,plain,
empty(relation_inverse(skolemFOFtoCNF_A_5)),
inference(resolve,[$cnf( relation(relation_inverse(skolemFOFtoCNF_A_5)) )],[refute_1_34,refute_1_31]) ).
cnf(refute_1_36,plain,
relation_inverse(skolemFOFtoCNF_A_5) = empty_set,
inference(resolve,[$cnf( empty(relation_inverse(skolemFOFtoCNF_A_5)) )],[refute_1_35,refute_1_13]) ).
cnf(refute_1_37,plain,
relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),
introduced(tautology,[refl,[$fot(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)))]]) ).
cnf(refute_1_38,plain,
( relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) != relation_inverse(relation_inverse(skolemFOFtoCNF_A_5))
| relation_inverse(skolemFOFtoCNF_A_5) != empty_set
| relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = relation_inverse(empty_set) ),
introduced(tautology,[equality,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),relation_inverse(relation_inverse(skolemFOFtoCNF_A_5))) ),[1,0],$fot(empty_set)]]) ).
cnf(refute_1_39,plain,
( relation_inverse(skolemFOFtoCNF_A_5) != empty_set
| relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = relation_inverse(empty_set) ),
inference(resolve,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),relation_inverse(relation_inverse(skolemFOFtoCNF_A_5))) )],[refute_1_37,refute_1_38]) ).
cnf(refute_1_40,plain,
relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) = relation_inverse(empty_set),
inference(resolve,[$cnf( $equal(relation_inverse(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_36,refute_1_39]) ).
cnf(refute_1_41,plain,
( relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) != relation_inverse(empty_set)
| relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) != skolemFOFtoCNF_A_5
| relation_inverse(empty_set) = skolemFOFtoCNF_A_5 ),
introduced(tautology,[equality,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),skolemFOFtoCNF_A_5) ),[0],$fot(relation_inverse(empty_set))]]) ).
cnf(refute_1_42,plain,
( relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)) != skolemFOFtoCNF_A_5
| relation_inverse(empty_set) = skolemFOFtoCNF_A_5 ),
inference(resolve,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),relation_inverse(empty_set)) )],[refute_1_40,refute_1_41]) ).
cnf(refute_1_43,plain,
relation_inverse(empty_set) = skolemFOFtoCNF_A_5,
inference(resolve,[$cnf( $equal(relation_inverse(relation_inverse(skolemFOFtoCNF_A_5)),skolemFOFtoCNF_A_5) )],[refute_1_11,refute_1_42]) ).
cnf(refute_1_44,plain,
relation_dom(relation_inverse(empty_set)) = relation_dom(relation_inverse(empty_set)),
introduced(tautology,[refl,[$fot(relation_dom(relation_inverse(empty_set)))]]) ).
cnf(refute_1_45,plain,
( relation_dom(relation_inverse(empty_set)) != relation_dom(relation_inverse(empty_set))
| relation_inverse(empty_set) != skolemFOFtoCNF_A_5
| relation_dom(relation_inverse(empty_set)) = relation_dom(skolemFOFtoCNF_A_5) ),
introduced(tautology,[equality,[$cnf( $equal(relation_dom(relation_inverse(empty_set)),relation_dom(relation_inverse(empty_set))) ),[1,0],$fot(skolemFOFtoCNF_A_5)]]) ).
cnf(refute_1_46,plain,
( relation_inverse(empty_set) != skolemFOFtoCNF_A_5
| relation_dom(relation_inverse(empty_set)) = relation_dom(skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(empty_set)),relation_dom(relation_inverse(empty_set))) )],[refute_1_44,refute_1_45]) ).
cnf(refute_1_47,plain,
relation_dom(relation_inverse(empty_set)) = relation_dom(skolemFOFtoCNF_A_5),
inference(resolve,[$cnf( $equal(relation_inverse(empty_set),skolemFOFtoCNF_A_5) )],[refute_1_43,refute_1_46]) ).
cnf(refute_1_48,plain,
( empty_set != relation_dom(relation_inverse(empty_set))
| relation_dom(relation_inverse(empty_set)) != relation_dom(skolemFOFtoCNF_A_5)
| empty_set = relation_dom(skolemFOFtoCNF_A_5) ),
introduced(tautology,[equality,[$cnf( ~ $equal(empty_set,relation_dom(skolemFOFtoCNF_A_5)) ),[0],$fot(relation_dom(relation_inverse(empty_set)))]]) ).
cnf(refute_1_49,plain,
( empty_set != relation_dom(relation_inverse(empty_set))
| empty_set = relation_dom(skolemFOFtoCNF_A_5) ),
inference(resolve,[$cnf( $equal(relation_dom(relation_inverse(empty_set)),relation_dom(skolemFOFtoCNF_A_5)) )],[refute_1_47,refute_1_48]) ).
cnf(refute_1_50,plain,
empty_set = relation_dom(skolemFOFtoCNF_A_5),
inference(resolve,[$cnf( $equal(empty_set,relation_dom(relation_inverse(empty_set))) )],[refute_1_7,refute_1_49]) ).
cnf(refute_1_51,plain,
relation_dom(skolemFOFtoCNF_A_5) != empty_set,
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_52,plain,
( empty_set != relation_dom(skolemFOFtoCNF_A_5)
| relation_dom(skolemFOFtoCNF_A_5) = empty_set ),
inference(subst,[],[refute_1_24:[bind(X,$fot(empty_set)),bind(Y,$fot(relation_dom(skolemFOFtoCNF_A_5)))]]) ).
cnf(refute_1_53,plain,
empty_set != relation_dom(skolemFOFtoCNF_A_5),
inference(resolve,[$cnf( $equal(relation_dom(skolemFOFtoCNF_A_5),empty_set) )],[refute_1_52,refute_1_51]) ).
cnf(refute_1_54,plain,
$false,
inference(resolve,[$cnf( $equal(empty_set,relation_dom(skolemFOFtoCNF_A_5)) )],[refute_1_50,refute_1_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU189+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 12:26:45 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.78/2.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.78/2.98
% 2.78/2.98 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.78/2.99
%------------------------------------------------------------------------------