TSTP Solution File: SWB090+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWB090+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 : 300s
% DateTime : Tue Sep 20 08:32:16 EDT 2022
% Result : Theorem 0.79s 0.80s
% Output : Proof 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 105
% Syntax : Number of formulae : 227 ( 51 unt; 22 typ; 0 def)
% Number of atoms : 2742 ( 248 equ)
% Maximal formula atoms : 60 ( 13 avg)
% Number of connectives : 4822 (2371 ~;1994 |; 284 &)
% ( 138 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 86 ( 86 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 8 >; 9 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-3 aty)
% Number of variables : 807 ( 761 !; 0 ?; 807 :)
% Comments :
%------------------------------------------------------------------------------
tff(iext_type,type,
iext: ( $i * $i * $i ) > $o ).
tff(tptp_fun_Y1_44_type,type,
tptp_fun_Y1_44: ( $i * $i * $i ) > $i ).
tff(uri_ex_p2_type,type,
uri_ex_p2: $i ).
tff(uri_ex_c_type,type,
uri_ex_c: $i ).
tff(tptp_fun_X_61_type,type,
tptp_fun_X_61: ( $i * $i ) > $i ).
tff(uri_ex_x1_type,type,
uri_ex_x1: $i ).
tff(uri_ex_x2_type,type,
uri_ex_x2: $i ).
tff(uri_ex_p1_type,type,
uri_ex_p1: $i ).
tff(icext_type,type,
icext: ( $i * $i ) > $o ).
tff(tptp_fun_Y2_43_type,type,
tptp_fun_Y2_43: ( $i * $i * $i ) > $i ).
tff(uri_owl_onClass_type,type,
uri_owl_onClass: $i ).
tff(uri_owl_onProperty_type,type,
uri_owl_onProperty: $i ).
tff(literal_typed_type,type,
literal_typed: ( $i * $i ) > $i ).
tff(uri_xsd_nonNegativeInteger_type,type,
uri_xsd_nonNegativeInteger: $i ).
tff(dat_str_1_type,type,
dat_str_1: $i ).
tff(uri_owl_maxQualifiedCardinality_type,type,
uri_owl_maxQualifiedCardinality: $i ).
tff(uri_rdfs_subPropertyOf_type,type,
uri_rdfs_subPropertyOf: $i ).
tff(ic_type,type,
ic: $i > $o ).
tff(uri_rdfs_subClassOf_type,type,
uri_rdfs_subClassOf: $i ).
tff(uri_owl_Restriction_type,type,
uri_owl_Restriction: $i ).
tff(uri_xml_nonNegativeInteger_type,type,
uri_xml_nonNegativeInteger: $i ).
tff(ip_type,type,
ip: $i > $o ).
tff(1,plain,
( iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
<=> iext(uri_owl_onClass,uri_ex_x2,uri_ex_c) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
& iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
& iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
& iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',premise_rdfbased_sem_restrict_maxqcr_cmp_prop) ).
tff(3,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
& iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
& iext(uri_owl_onClass,uri_ex_x1,uri_ex_c) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
& iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
& iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
& iext(uri_owl_onClass,uri_ex_x2,uri_ex_c) ),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
iext(uri_owl_onClass,uri_ex_x2,uri_ex_c),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
iext(uri_owl_onClass,uri_ex_x2,uri_ex_c),
inference(modus_ponens,[status(thm)],[7,1]) ).
tff(9,plain,
( iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
<=> iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2) ),
inference(and_elim,[status(thm)],[6]) ).
tff(11,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2),
inference(modus_ponens,[status(thm)],[11,9]) ).
tff(13,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[10]) ).
tff(15,plain,
iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
^ [Z: $i,P: $i,C: $i] :
refl(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [Z: $i,P: $i,C: $i] :
rewrite(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [Z: $i,P: $i,C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
rewrite(
( ~ ~ ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )),
quant_intro(
proof_bind(
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
<=> ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) ) )),
trans(
monotonicity(
rewrite(
( ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) )
<=> ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) )),
( ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) )
<=> ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) )),
rewrite(
( ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) )
<=> ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) )),
( ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) )
<=> ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) )),
( ( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) )
<=> ( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
& ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )),
rewrite(
( ( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
& ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )),
( ( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) )
<=> ~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ))),
( ! [X: $i] :
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )),
( ( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) )),
rewrite(
( ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) )),
( ( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
^ [Z: $i,P: $i,C: $i] :
trans(
monotonicity(
rewrite(
( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
<=> ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) ) )),
quant_intro(
proof_bind(
^ [X: $i] :
rewrite(
( ( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) )
<=> ( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ))),
( ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) )
<=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) )),
( ( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) ) )
<=> ( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ) )),
rewrite(
( ( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) )
<=> ( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ) )),
( ( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) ) )
<=> ( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) ) )
<=> ! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [Z: $i,P: $i,C: $i] :
( ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
=> ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
=> ( Y2 = Y1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_restrict_maxqcr_object_001) ).
tff(27,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( icext(Z,X)
<=> ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [Z: $i,P: $i,C: $i] :
( ~ ( iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
& iext(uri_owl_onProperty,Z,P)
& iext(uri_owl_onClass,Z,C) )
| ! [X: $i] :
( ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ~ ( iext(P,X,Y1)
& icext(C,Y1)
& iext(P,X,Y2)
& icext(C,Y2) )
| ( Y2 = Y1 ) ) )
& ( icext(Z,X)
| ~ ( ~ ( iext(P,X,tptp_fun_Y1_44(X,C,P))
& icext(C,tptp_fun_Y1_44(X,C,P))
& iext(P,X,tptp_fun_Y2_43(X,C,P))
& icext(C,tptp_fun_Y2_43(X,C,P)) )
| ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) ) ) ) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,33]) ).
tff(38,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ) ),
inference(transitivity,[status(thm)],[38,32]) ).
tff(40,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x2,uri_ex_p2)
| ~ iext(uri_owl_onClass,uri_ex_x2,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) ),
inference(unit_resolution,[status(thm)],[41,31,15,12,8]) ).
tff(43,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x2,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,X,Y1)
| ~ iext(uri_ex_p2,X,Y2) ) )
| ~ ( icext(uri_ex_x2,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p2)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
~ ( ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( ~ ( ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(48,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
^ [C1: $i,C2: $i] :
refl(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(50,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
( ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(transitivity,[status(thm)],[52,50]) ).
tff(54,plain,
^ [C1: $i,C2: $i] :
trans(
monotonicity(
rewrite(
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
rewrite(
( ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
rewrite(
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) )
<=> ! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [C1: $i,C2: $i] :
rewrite(
( ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) )
<=> ! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( icext(C1,X)
=> icext(C2,X) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_rdfsext_subclassof) ).
tff(62,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [C1: $i,C2: $i] :
( iext(uri_rdfs_subClassOf,C1,C2)
<=> ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C1)
| ~ ic(C2)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [C1: $i,C2: $i] :
( ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ( ic(C1)
& ic(C2)
& ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
& ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[65,55]) ).
tff(67,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) )
| ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) ) ),
inference(modus_ponens,[status(thm)],[66,53]) ).
tff(68,plain,
! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,48]) ).
tff(69,plain,
( ~ ! [C1: $i,C2: $i] :
~ ( ~ ( iext(uri_rdfs_subClassOf,C1,C2)
| ~ ic(C2)
| ~ ic(C1)
| ~ ( ~ icext(C1,tptp_fun_X_61(C2,C1))
| icext(C2,tptp_fun_X_61(C2,C1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,C1,C2)
| ~ ( ~ ic(C2)
| ~ ic(C1)
| ~ ! [X: $i] :
( ~ icext(C1,X)
| icext(C2,X) ) ) ) )
| ~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(70,plain,
~ ( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ( ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ! [X: $i] :
( ~ icext(uri_ex_x1,X)
| icext(uri_ex_x2,X) ) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],]) ).
tff(72,plain,
( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( iext(uri_owl_maxQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i,Y: $i] :
( iext(uri_owl_maxQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) )
<=> ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i,Y: $i] :
( iext(uri_owl_maxQualifiedCardinality,X,Y)
=> ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_prop_maxqualifiedcardinality_ext) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ( icext(uri_owl_Restriction,X)
& icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x2,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
~ ( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(unit_resolution,[status(thm)],[88,85,15]) ).
tff(90,plain,
( ~ icext(uri_owl_Restriction,uri_ex_x2)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| icext(uri_owl_Restriction,uri_ex_x2) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
icext(uri_owl_Restriction,uri_ex_x2),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
^ [X: $i] :
refl(
( ( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
( ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
^ [X: $i] :
rewrite(
( ( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ( ic(X)
| ~ icext(uri_owl_Restriction,X) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) )
<=> ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,axiom,
! [X: $i] :
( icext(uri_owl_Restriction,X)
=> ic(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',owl_class_restriction_ext) ).
tff(98,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[98,94]) ).
tff(100,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(skolemize,[status(sab)],[99]) ).
tff(101,plain,
! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) ),
inference(modus_ponens,[status(thm)],[100,93]) ).
tff(102,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x2)
| ~ icext(uri_owl_Restriction,uri_ex_x2) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
ic(uri_ex_x2),
inference(unit_resolution,[status(thm)],[104,101,91]) ).
tff(106,plain,
( iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
<=> iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(and_elim,[status(thm)],[5]) ).
tff(108,plain,
iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_owl_maxQualifiedCardinality,X,Y)
| ~ ( ~ icext(uri_owl_Restriction,X)
| ~ icext(uri_xml_nonNegativeInteger,Y) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
~ ( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger)) ),
inference(unit_resolution,[status(thm)],[111,85,108]) ).
tff(113,plain,
( ~ icext(uri_owl_Restriction,uri_ex_x1)
| ~ icext(uri_xml_nonNegativeInteger,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| icext(uri_owl_Restriction,uri_ex_x1) ),
inference(tautology,[status(thm)],]) ).
tff(114,plain,
icext(uri_owl_Restriction,uri_ex_x1),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
( ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) )
<=> ( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
( ~ ! [X: $i] :
( ic(X)
| ~ icext(uri_owl_Restriction,X) )
| ic(uri_ex_x1)
| ~ icext(uri_owl_Restriction,uri_ex_x1) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
ic(uri_ex_x1),
inference(unit_resolution,[status(thm)],[117,101,114]) ).
tff(119,plain,
( ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
<=> ~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2) ),
inference(rewrite,[status(thm)],]) ).
tff(120,axiom,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion_rdfbased_sem_restrict_maxqcr_cmp_prop) ).
tff(121,plain,
~ iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(tautology,[status(thm)],]) ).
tff(123,plain,
( ~ ( iext(uri_rdfs_subClassOf,uri_ex_x1,uri_ex_x2)
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) )
| ~ ic(uri_ex_x2)
| ~ ic(uri_ex_x1)
| ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ) ),
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(unit_resolution,[status(thm)],[123,118,105,72]) ).
tff(125,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],]) ).
tff(126,plain,
~ icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) )
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(tautology,[status(thm)],]) ).
tff(128,plain,
( ~ ( icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) )
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(unit_resolution,[status(thm)],[127,126]) ).
tff(129,plain,
~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(unit_resolution,[status(thm)],[128,46]) ).
tff(130,plain,
( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(tautology,[status(thm)],]) ).
tff(131,plain,
iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
( iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1)
<=> iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1),
inference(and_elim,[status(thm)],[2]) ).
tff(134,plain,
iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
^ [P: $i,Q: $i] :
refl(
( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(136,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[135]) ).
tff(137,plain,
^ [P: $i,Q: $i] :
rewrite(
( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(138,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[137]) ).
tff(139,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[138,136]) ).
tff(140,plain,
^ [P: $i,Q: $i] :
rewrite(
( ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(143,plain,
^ [P: $i,Q: $i] :
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [X: $i,Y: $i] :
rewrite(
( ( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ))),
( ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
rewrite(
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) )
<=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
rewrite(
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
( ( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) )
<=> ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,axiom,
! [P: $i,Q: $i] :
( iext(uri_rdfs_subPropertyOf,P,Q)
=> ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( iext(P,X,Y)
=> iext(Q,X,Y) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWB001+0.ax',rdfs_subpropertyof_main) ).
tff(146,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[146,142]) ).
tff(148,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ( ip(P)
& ip(Q)
& ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[148,141]) ).
tff(150,plain,
! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[149,139]) ).
tff(151,plain,
( ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ) )
<=> ( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [P: $i,Q: $i] :
( ~ iext(uri_rdfs_subPropertyOf,P,Q)
| ~ ( ~ ip(Q)
| ~ ip(P)
| ~ ! [X: $i,Y: $i] :
( ~ iext(P,X,Y)
| iext(Q,X,Y) ) ) )
| ~ iext(uri_rdfs_subPropertyOf,uri_ex_p2,uri_ex_p1)
| ~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
~ ( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ),
inference(unit_resolution,[status(thm)],[153,150,134]) ).
tff(155,plain,
( ~ ip(uri_ex_p1)
| ~ ip(uri_ex_p2)
| ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ) ),
inference(tautology,[status(thm)],]) ).
tff(156,plain,
! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) ),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(158,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[159,156,131]) ).
tff(161,plain,
( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(tautology,[status(thm)],]) ).
tff(162,plain,
iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[161,129]) ).
tff(163,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(164,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
( ~ ! [X: $i,Y: $i] :
( ~ iext(uri_ex_p2,X,Y)
| iext(uri_ex_p1,X,Y) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[165,156,162]) ).
tff(167,plain,
( iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
<=> iext(uri_owl_onClass,uri_ex_x1,uri_ex_c) ),
inference(rewrite,[status(thm)],]) ).
tff(168,plain,
iext(uri_owl_onClass,uri_ex_x1,uri_ex_c),
inference(and_elim,[status(thm)],[3]) ).
tff(169,plain,
iext(uri_owl_onClass,uri_ex_x1,uri_ex_c),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
( iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
<=> iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(and_elim,[status(thm)],[4]) ).
tff(172,plain,
iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(174,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) )
<=> ~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(176,plain,
( ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[176]) ).
tff(178,plain,
( ( ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(transitivity,[status(thm)],[177,174]) ).
tff(179,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
( ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) )
<=> ( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ) ),
inference(transitivity,[status(thm)],[179,173]) ).
tff(181,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ icext(uri_ex_c,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(182,plain,
( ~ ! [Z: $i,P: $i,C: $i] :
( ~ iext(uri_owl_onProperty,Z,P)
| ~ iext(uri_owl_onClass,Z,C)
| ~ iext(uri_owl_maxQualifiedCardinality,Z,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ! [X: $i] :
~ ( ~ ( ~ icext(Z,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(C,Y2)
| ~ iext(P,X,Y1)
| ~ icext(C,Y1)
| ~ iext(P,X,Y2) ) )
| ~ ( icext(Z,X)
| ~ ( ( tptp_fun_Y2_43(X,C,P) = tptp_fun_Y1_44(X,C,P) )
| ~ iext(P,X,tptp_fun_Y1_44(X,C,P))
| ~ icext(C,tptp_fun_Y1_44(X,C,P))
| ~ iext(P,X,tptp_fun_Y2_43(X,C,P))
| ~ icext(C,tptp_fun_Y2_43(X,C,P)) ) ) ) )
| ~ iext(uri_owl_maxQualifiedCardinality,uri_ex_x1,literal_typed(dat_str_1,uri_xsd_nonNegativeInteger))
| ~ iext(uri_owl_onProperty,uri_ex_x1,uri_ex_p1)
| ~ iext(uri_owl_onClass,uri_ex_x1,uri_ex_c)
| ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) ),
inference(unit_resolution,[status(thm)],[182,31,108,172,169]) ).
tff(184,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ icext(uri_ex_x1,X)
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,X,Y1)
| ~ iext(uri_ex_p1,X,Y2) ) )
| ~ ( icext(uri_ex_x1,X)
| ~ ( ( tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,X,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(X,uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,X,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(X,uri_ex_c,uri_ex_p1)) ) ) )
| ~ ( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(185,plain,
~ ( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) ) ),
inference(unit_resolution,[status(thm)],[184,183]) ).
tff(186,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ ( icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ~ ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1) )
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p1)) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) ),
inference(tautology,[status(thm)],]) ).
tff(187,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) ),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)) ),
inference(tautology,[status(thm)],]) ).
tff(189,plain,
icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1)),
inference(unit_resolution,[status(thm)],[188,124]) ).
tff(190,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) ),
inference(tautology,[status(thm)],]) ).
tff(191,plain,
( ~ ( ~ icext(uri_ex_x1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1))
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) )
| ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ) ),
inference(unit_resolution,[status(thm)],[190,189]) ).
tff(192,plain,
! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) ),
inference(unit_resolution,[status(thm)],[191,187]) ).
tff(193,plain,
( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(tautology,[status(thm)],]) ).
tff(194,plain,
icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[193,129]) ).
tff(195,plain,
( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(tautology,[status(thm)],]) ).
tff(196,plain,
icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)),
inference(unit_resolution,[status(thm)],[195,129]) ).
tff(197,plain,
( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p2,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) != tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) ) ),
inference(tautology,[status(thm)],]) ).
tff(198,plain,
tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) != tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2),
inference(unit_resolution,[status(thm)],[197,129]) ).
tff(199,plain,
( ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) )
<=> ( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
( ~ ! [Y1: $i,Y2: $i] :
( ( Y2 = Y1 )
| ~ icext(uri_ex_c,Y1)
| ~ icext(uri_ex_c,Y2)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y1)
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),Y2) )
| ( tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) = tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2) )
| ~ icext(uri_ex_c,tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ icext(uri_ex_c,tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y2_43(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2))
| ~ iext(uri_ex_p1,tptp_fun_X_61(uri_ex_x2,uri_ex_x1),tptp_fun_Y1_44(tptp_fun_X_61(uri_ex_x2,uri_ex_x1),uri_ex_c,uri_ex_p2)) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
$false,
inference(unit_resolution,[status(thm)],[204,198,196,194,192,166,160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWB090+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 20:24:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.79/0.80 % SZS status Theorem
% 0.79/0.80 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------